tag:www.math.bgu.ac.il,2005:/en/research/seminars/bgu-probability-and-ergodic-theory-pet-seminar/meetingsBGU BGU Probability and Ergodic Theory (PET) seminarDr. Shrey Sanadhyasanadhya@post.bgu.ac.ilhttps://sites.google.com/view/shrey-sanadhya/home2018-03-12T23:38:13+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/3832018-03-12T23:38:13+02:002018-03-12T23:38:17+02:00<span class="mathjax">Tom Meyerovitch: On pointwise periodicity and expansiveness</span>March 20, 11:00—12:00, 2018, 201<div class="mathjax"><p>Following Kaul, a discrete (topological) group G of transformations of set
X is pointwise periodic if the stabilizer of every point is of finite index (co-compact) in G.
Equivalently, all G-orbits are finite (compact).
Generalizing a result of Montgomery, Kaul showed in the early 70’s that a
pointwise periodic transformation group is always compact when the group acts (faithfully) on a connected
manifold without boundary.
I will discuss implications of expansiveness and pointwise periodicity
of certain groups and semigroups of transformations.
In particular I’ll state implications for cellular automata and for planner tilings.
Based on joint work with Ville Salo.</p></div>Tom MeyerovitchBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/3762018-02-28T08:56:31+02:002018-03-20T13:32:27+02:00<span class="mathjax">Jeremias Epperlein: Derivative Algebras and Topological Conjugacies Between Cellular Automata</span>March 27, 11:10—12:00, 2018, 201<div class="mathjax"><p>Topologial conjugacy is most probably the most natural notion of
isomorphism for topological dynamical systems. Classifying subshifts
of finite type up to topological conjugacy is a notoriously hard
problem with a long history of results. Much less is known about the
corresponding problem for
endomorphisms of subshifts of finite type (aka cellular automata).
I will discuss necessary and sufficient criteria under which periodic
cellular automata are topologically conjugate.
The main tool will be derivative algebras in the sense of Tarski and
McKinsey, an algebraic
structure based on the Cantor-Bendixson derivative.</p></div>Jeremias EpperleinBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/3782018-03-01T10:09:41+02:002018-04-08T18:53:06+03:00<span class="mathjax">Matan Harel: Discontinuity of the phase transition for the planar random-cluster and Potts models with q > 4</span>April 10, 11:00—12:00, 2018, 201<div class="mathjax"><p>The random-cluster model is a dependent percolation model where the weight of a configuration is proportional to q to the power of the number of connected components. It is highly related to the ferromagnetic q-Potts model, where every vertex is assigned one of q colors, and monochromatic neighbors are encouraged. Through non-rigorous means, Baxter showed that the phase transition is first-order whenever q > 4 - i.e. there are multiple Gibbs measures at criticality. We provide a rigorous proof of this claim. Like Baxter, our proof uses the correspondence between the above models and the six-vertex model, which we analyze using the Bethe ansatz and transfer matrix techniques. We also prove Baxter’s formula for the correlation length of the models at criticality. This is joint work with Hugo Duminil-Copin, Maxime Gangebin, Ioan Manolescu, and Vincent Tassion.</p></div>Matan HarelTel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/3792018-03-01T10:11:42+02:002018-04-10T09:23:52+03:00<span class="mathjax">Gady Kozma : Irreducibility of random polynomials</span>April 17, 11:00—12:00, 2018, 201<div class="mathjax"><p>Examine a polynomial with random, independent coefficients, uniform between 1 and 210. We show that it is irreducible over the integers with probability going to one as the degree goes to infinity. Joint work with Lior Bary-Soroker.</p></div>Gady Kozma Weizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/3812018-03-04T21:53:06+02:002018-04-18T14:52:55+03:00<span class="mathjax">Ron Peled: A power-law upper bound on the decay of correlations in the two-dimensional random-field Ising model</span>April 24, 11:00—12:00, 2018, 201<div class="mathjax"><p>The random-field Ising model (RFIM) is a standard model for a disordered magnetic system, obtained by placing the standard ferromagnetic Ising model in a random external magnetic field. Imry-Ma (1975) predicted, and Aizenman-Wehr (1989) proved, that the two-dimensional RFIM has a unique Gibbs state at any positive intensity of the random �field and at all temperatures. Thus, the addition of an arbitrarily weak random field suffices to destroy the famed phase transition of the two-dimensional Ising model. We study quantitative features of this phenomenon, bounding the decay rate of the effect of boundary conditions on the magnetization in fi�nite systems. This is known to decay exponentially fast for a strong random fi�eld. The main new result is a power-law upper bound which is valid at all �field strengths and at all temperatures, including zero. Our analysis proceeds through a streamlined and quantified version of the Aizenman-Wehr proof. Several open problems will be mentioned.
Joint work with Michael Aizenman.</p></div>Ron PeledTel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4012018-04-24T14:24:08+03:002018-04-24T15:50:28+03:00<span class="mathjax">Sebastián Donoso: Good lower bounds for multiple recurrence</span>April 30, 11:00—12:00, 2018, -101<div class="mathjax"><p>In 2005, Bergelson, Host and Kra showed that if $(X,\mu,T)$ is an ergodic measure preserving system and $A\subset X$, then for every $\epsilon>0$ there exists a syndetic set of $n\in\mathbb{N}$ such that
$\mu(A\cap T^{-n}A\cap\dots\cap T^{-kn}A)>\mu^{k+1}(A)-\epsilon$ for
$k\leq3$, extending Khintchine’s theorem. This phenomenon is called multiple recurrence with good lower bounds.
Good lower bounds for certain polynomial expressions was studied by
Frantzikinakis but several questions remain open.
In this talk I will survey this topic, and present some progress regarding
polynomial expressions, commuting transformations,
and configurations involving the prime numbers.
This is work in progress with Joel Moreira, Ahn Le and Wenbo Sun.</p></div> Sebastián DonosoUniversidad de O’Higginstag:www.math.bgu.ac.il,2005:MeetingDecorator/3872018-03-18T17:11:38+02:002018-04-09T13:31:02+03:00<span class="mathjax">Chen Dubi: Limit theorems for a counting process with extendable dead time (Type II counter)</span>May 1, 11:00—12:00, 2018, 201<div class="mathjax"><p>Measuring occurrence times of random events, aimed to determine the statistical properties of the governing stochastic process, is a basic topic in science and engineering, and has been the topic of numerous mathematical modeling techniques. Often, the true statistical properties of the random process deviate from the measured properties due to the so called “dead time” phenomenon, defined as a time period after a reaction in which the detection system is not operational. From a mathematical point of view, the dead time can be interpreted as a rarefied series of the original time series, obtained by removing all events which are within the dead time period inflicted by previous events.</p>
<p>When the waiting times between consecutive events form a series of
independent identically distributed random variables, a natural setting for analyzing the distribution of the number of event- or the event counter- is a renewal process. In particular, for high rate measurements (or, equivalently, large measurement time), the limit distribution of the counter is well understood, and can be described directly through the first two moments of the waiting time between consecutive events.</p>
<p>In the talk we will discuss limit theorems for counters with paralyzing dead time (type II counter), expressed directly through the probability density function of the waiting time between consecutive events. This is done by writing explicit formulas for the for the first and second moments of a waiting time distribution between consecutive events in the rarefied process, in terms of the probability density function of the waiting of the original process.</p></div>Chen DubiBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/3972018-04-15T10:33:41+03:002018-04-22T10:36:06+03:00<span class="mathjax">Erez Nesharim: The t-adic Littlewood conjecture is false</span>May 8, 11:00—12:00, 2018, 201<div class="mathjax"><p>The Littlewood and the p-adic Littlewood conjectures are famous open problems on the border between number theory and dynamics. In a joint work with Faustin Adiceam and Fred Lunnon we show that the analogue of the p-adic Littlewood conjecture over $F_3((1/t))$ is false. The counterexample is given by the Laurent series whose coefficients are the regular paper folding sequence, and the method of proof is by reduction to the non vanishing of certain Hankel determinants. The proof is computer assisted and it uses substitution tilings of $Z^2$ and a generalisation of Dodson’s condensation algorithm for computing the determinant of any Hankel matrix.</p></div>Erez NesharimUniversity of Yorktag:www.math.bgu.ac.il,2005:MeetingDecorator/4082018-05-09T21:16:36+03:002018-05-14T20:42:30+03:00<span class="mathjax">Idan Perl: Harmonic functions on locally compact groups</span>May 22, 11:00—12:00, 2018, 201<div class="mathjax"><p>Spaces of harmonic functions on a given group have a strong relationship with its large-scale geometry. Classically, mostly bounded harmonic functions have been studied. We review some results about bounded harmonic functions and present the recent research on spaces of unbounded harmonic functions.</p></div>Idan PerlBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/4002018-04-22T10:37:45+03:002018-04-29T17:48:53+03:00<span class="mathjax">Tal Horesh: Equidistribution of Iwasawa components of lattices and asymptotic properties of primitive points</span>June 5, 11:00—12:00, 2018, 201<div class="mathjax"><p>I will discuss the equidistribution of certain parameters of primitive integral points in Euclidean space, as their norms tend to infinity.
These parameters include directions of integral points on the unit sphere, the integral grids in their orthogonal hyperplanes, and the shortest solutions to their associated gcd equations.
These equidistribution statements follow from counting lattice points in the real Special Linear group.</p></div>Tal HoreshIHEStag:www.math.bgu.ac.il,2005:MeetingDecorator/3982018-04-15T10:38:11+03:002018-05-29T09:33:46+03:00<span class="mathjax">Yotam Smilansky: Kakutani’s splitting procedure for multiscale substitution schemes</span>June 12, 11:00—12:00, 2018, 201<div class="mathjax"><p>In 1975, S. Kakutani introduced a splitting procedure which generates a sequence of partitions of the unit interval [0,1], and showed that this sequence is uniformly distributed in [0,1]. We present generalizations of this procedure in higher dimensions, which correspond to constructions used when defining substitution and multiscale substitution tilings of Euclidean space. We prove uniform distribution of these sequences of partitions using new path counting results on graphs and establish Kakutani’s result as a special case.</p></div>Yotam Smilanskytag:www.math.bgu.ac.il,2005:MeetingDecorator/4182018-05-27T13:04:49+03:002018-05-28T16:11:43+03:00<span class="mathjax">Ofer Busani: The Multi-Lane Totally Asymmetric Simple Exclusion Process</span>June 19, 11:00—12:00, 2018, 201<div class="mathjax"><p>The Totally Asymmetric Simple Exclusion Process (TASEP) is a well-studied model where one assumes every site on Z to be either occupied by a particle or vacant. Each site has a Poisson clock attached to it, if the clock rings for site x, where there happens to be a particle, the particle makes a jump to site x+1 if it is vacant. The TASEP is often used to model traffic on a one lane road.
In this work we generalize this model to a finite number of lanes where cars can move from one lane to another at different rates, and having different speed on each lane. We consider the problem of finding the stationary measures for this model as well as its hydrodynamics (what would the traffic look like from the point of view of a helicopter).
The talk will be as self-contained as possible. Joint work with Gidi Amir, Christoph Bahadoran and Ellen Saada.</p></div>Ofer BusaniBar Ilantag:www.math.bgu.ac.il,2005:MeetingDecorator/4362018-10-09T09:42:12+03:002018-10-10T12:39:25+03:00<span class="mathjax">Rachel Skipper: Quasi-isometry classes of simple groups</span>October 18, 11:00—12:00, 2018, -101<div class="mathjax"><p>We will consider a class of groups defined by their action on Cantor space and use the invariant of finiteness properties to find among these groups an infinite family of quasi-isometry classes of finitely presented simple groups.</p>
<p>This is a joint work with Stefan Witzel and Matthew C. B. Zaremsky.</p></div>Rachel SkipperGeorg-August-University, Göttingentag:www.math.bgu.ac.il,2005:MeetingDecorator/4312018-10-03T10:21:31+03:002018-10-18T14:34:28+03:00<span class="mathjax">Yair Hartman: Stationary C*-Dynamical Systems</span>October 25, 11:00—12:00, 2018, -101<div class="mathjax"><p>We introduce the notion of stationary actions in the context of C<em>-algebras, and prove a new characterization of C</em>-simplicity in terms of unique stationarity. This ergodic theoretical characterization provides an intrinsic understanding for the relation between C<em>-simplicity and the unique trace property, and provides a framework in which C</em>-simplicity and random walks interact. Joint work with Mehrdad Kalantar.</p></div>Yair HartmanBen-Gurion University tag:www.math.bgu.ac.il,2005:MeetingDecorator/4322018-10-06T21:17:37+03:002018-10-10T09:09:22+03:00<span class="mathjax">J.C. Saunders: Sieve Methods in Random Graph Theory</span>November 1, 11:00—12:00, 2018, -101<div class="mathjax"><p>We apply the Tur\´an sieve and the simple sieve developed by Ram Murty and Yu-Ru Liu to study problems in random graph theory. More speciﬁcally, we obtain bounds on the probability of a graph having diameter 2 (or diameter 3 in the case of bipartite graphs). An interesting feature revealed in these results is that the Tur´an sieve and the simple sieve “almost completely” complement to each other. This is joint work with Yu-Ru Liu.</p></div> J.C. SaundersBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4342018-10-07T11:57:19+03:002018-10-24T11:36:54+03:00<span class="mathjax">הסמינר מבוטל בשל סדנא על stack: TBA</span>November 8, 11:00—12:00, 2018, -101הסמינר מבוטל בשל סדנא על stacktag:www.math.bgu.ac.il,2005:MeetingDecorator/4352018-10-08T15:39:50+03:002018-11-06T15:55:02+02:00<span class="mathjax">Jeremias Epperlein: Sheltered sets, dead ends and horoballs in groups</span>November 15, 11:00—12:00, 2018, -101<div class="mathjax"><p>The talk discusses a convexity structure on metric spaces which
we call sheltered sets. This structure arises in the study
of the dynamics of the maximum cellular automaton over the binary alphabet
on finitely generated groups. I will discuss relations to
horoballs and dead ends in groups and present many open questions.
This is work in progress with Tom Meyerovitch.</p></div>Jeremias EpperleinBen-Gurion University tag:www.math.bgu.ac.il,2005:MeetingDecorator/4402018-10-10T09:10:51+03:002018-11-18T20:45:33+02:00<span class="mathjax">Yiftach Dayan: Diophantine approximations on random fractals</span>November 22, 11:00—12:00, 2018, -101<div class="mathjax"><p>We will present a model for construction of random fractals which is called fractal percolation. The main result that will be presented in this talk states that a typical fractal percolation set E intersects every set which is winning for a certain game that is called the “hyperplane absolute game”, and the intersection has the same Hausdorff dimension as E. An example of such a winning set is the set of badly approximable vectors in dimension d.
In order to prove this theorem one may show that a typical fractal percolation set E contains a sequence of Ahlfors-regular subsets with dimensions approaching the dimension of E, where all the subsets in this sequence are also “hyperplane diffuse”, which means that they are not concentrated around affine hyperplanes when viewed in small enough scales.
If time permits, we will sketch the proof of this theorem and present a generalization to a more general model for random construction of fractals which is given by projecting Galton-Watson trees against any similarity IFS whose attractor is not contained in a single affine hyperplane.</p></div>Yiftach DayanTel-Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4412018-10-10T09:11:42+03:002018-11-26T09:01:01+02:00<span class="mathjax">Daniel Luckhardt: Benjamini-Schramm Continuity of Normalized Characteristic numbers on Riemannian manifolds</span>November 29, 11:00—12:00, 2018, -101<div class="mathjax"><p>The concept of Benjamini-Schramm convergence can be extended to Riemannian manifolds. In this setup a question frequently studied is whether topological invariants that can be expressed as integers are continuous when normalized by the volume. An example of such an invariant is the Euler characteristic, that also exists for graphs. A vast generalization of the Euler characteristic for Riemannian manifolds are characteristic numbers. I will speak on my results showing continuity of normalized characteristic numbers on a suitable class of random Riemannian manifolds defined by a lower Ricci curvature and injectivity radius bound.</p></div>Daniel LuckhardtBen-Gurion University tag:www.math.bgu.ac.il,2005:MeetingDecorator/4432018-10-10T09:27:47+03:002018-10-11T20:36:42+03:00<span class="mathjax">חנוכה: TBA</span>December 6, 11:00—12:00, 2018, -101חנוכהtag:www.math.bgu.ac.il,2005:MeetingDecorator/4422018-10-10T09:27:07+03:002018-12-10T08:37:28+02:00<span class="mathjax">Ron Peled: On the site percolation threshold of circle packings and planar graphs, with application to the loop O(n) model</span>December 13, 11:00—12:00, 2018, -101<div class="mathjax"><p>A circle packing is a collection of circles in the plane with disjoint interiors. An accumulation point of the circle packing is a point with infinitely many circles in any neighborhood of it. A site percolation with parameter p on the circle packing means retaining each circle with probability p and deleting it with probability 1-p, independently between circles. We will explain the proof of the following result: There exists p>0 satisfying that for any circle packing with finitely many accumulation points, after a site percolation with parameter p there is no infinite connected component of retained circles, almost surely. This implies, in particular, that the site percolation threshold of any planar recurrent graph is at least p. It is conjectured that the same should hold with p=1/2.
The result gives a partial answer to a question of Benjamini, who conjectured that square packings of the unit square admit long crossings after site percolation with parameter p=1/2 and asked also about other values of p.
Time permitting, we will discuss an application of the result to the existence of macroscopic loops in the loop O(n) model on the hexagonal lattice.
Portions joint with Nick Crawford, Alexandar Glazman and Matan Harel.</p></div>Ron PeledTel-Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4442018-10-10T09:27:58+03:002018-12-13T09:17:52+02:00<span class="mathjax">Ross Pinsky: A Natural probabilistic model on the integers and its relation to Dickman-type distributions and Buchstab’s function</span>December 20, 11:00—12:00, 2018, -101<div class="mathjax"><p>Let <span class="kdmath">$\{p_j\}_{j=1}^\infty$</span> denote the set of prime numbers in increasing order, let <span class="kdmath">$\Omega_N\subset \mathbb{N}$</span> denote the set of positive integers with no prime factor larger than <span class="kdmath">$p_N$</span> and
let <span class="kdmath">$P_N$</span> denote the probability measure on <span class="kdmath">$\Omega_N$</span> which gives to each <span class="kdmath">$n\in\Omega_N$</span> a probability proportional to <span class="kdmath">$\frac{1}{n}$</span>.
This measure is in fact the distribution of the random integer <span class="kdmath">$I_N\in\Omega_N$</span> defined by <span class="kdmath">$I_N=\prod_{j=1}^Np_j^{X_{p_j}}$</span>, where
<span class="kdmath">$\{X_{p_j}\}_{j=1}^\infty$</span> are independent random variables and <span class="kdmath">$X_{p_j}$</span> is distributed as Geom<span class="kdmath">$(1-\frac{1}{p_j})$</span>.
We show that <span class="kdmath">$\frac{\log n}{\log N}$</span> under <span class="kdmath">$P_N$</span> converges weakly to the <em>Dickman distribution</em>. As a corollary, we recover a classical result from classical multiplicative number theory—<em>Mertens’
formula</em>, which states that <span class="kdmath">$\sum_{n\in\Omega_N}\frac{1}{n}\sim e^\gamma\log N$</span> as <span class="kdmath">$N\to\infty$</span>.</p>
<p>Let $D_{\text{nat}}(A)$ denote the natural density of $A\subset\mathbb{N}$, if it exists, and let <span class="kdmath">$D_{\text{log-indep}}(A)=\lim_{N\to\infty}P_N(A\cap\Omega_N)$</span> denote the
density of $A$ arising from <span class="kdmath">$\{P_N\}_{N=1}^\infty$</span>, if it exists. We show that the two densities coincide on a natural algebra of subsets of $\mathbb{N}$.
We also show that they do not agree on the sets of <span class="kdmath">$n^\frac{1}{s}$</span>- <em>smooth numbers</em> <span class="kdmath">$\{n\in\mathbb{N}: p^+(n)\le n^\frac{1}{s}\}$</span>, $s>1$, where <span class="kdmath">$p^+(n)$</span> is the largest prime divisor of $n$.
This last consideration concerns distributions involving the <em>Dickman function</em>.
We also consider the
sets of $n^\frac{1}{s}$- <em>rough numbers</em> ${n\in\mathbb{N}:p^-(n)\ge n^{\frac{1}{s}}}$, $s>1$, where $p^-(n)$ is the smallest prime divisor of $n$.
We show that the probabilities of these sets, under
the uniform distribution on $[N]={1,\ldots, N}$ and under the $P_N$-distribution on $\Omega_N$, have the same
asymptotic decay profile as functions of $s$, although their rates are necessarily different. This profile involves the <em>Buchstab function</em>. We also prove a new representation for the Buchstab function.</p></div>Ross Pinskyhttp://www2.math.technion.ac.il/~pinsky/index.htmlTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/4452018-10-10T09:28:08+03:002018-12-12T15:22:23+02:00<span class="mathjax">The talk has been cancelled: TBA</span>December 27, 11:00—12:00, 2018, -101The talk has been cancelledtag:www.math.bgu.ac.il,2005:MeetingDecorator/4462018-10-10T09:28:15+03:002018-10-22T14:12:41+03:00<span class="mathjax">Chandrika Sadanand: You can hear the shape of a polygonal billiard table</span>January 3, 11:00—12:00, 2019, -101<div class="mathjax"><p>Consider a polygon-shaped billiard table on which a ball can roll along straight lines and reflect off of edges infinitely. In work joint with Moon Duchin, Viveka Erlandsson and Chris Leininger, we have characterized the relationship between the shape of a polygonal billiard table and the set of possible infinite edge itineraries of balls travelling on it. In this talk, we will explore this relationship and the tools used in our characterization (notably a new rigidity result for flat cone metrics).</p></div>Chandrika SadanandThe Hebrew University of Jerusalemtag:www.math.bgu.ac.il,2005:MeetingDecorator/4472018-10-10T09:28:21+03:002019-01-06T23:40:33+02:00<span class="mathjax">Nishant Chandgotia: Universal models for Z^d actions</span>January 10, 11:00—12:00, 2019, -101<div class="mathjax"><p>Krieger’s generator theorem shows that any free invertible ergodic measure preserving action <span class="kdmath">$(Y,\mu, S)$</span> can be modelled by <span class="kdmath">$A^Z$</span> (equipped with the shift action) provided the natural entropy constraint is satisfied; we call such systems (here it is <span class="kdmath">$A^Z$</span>) universal. Along with Tom Meyerovitch, we establish general specification like conditions under which <span class="kdmath">$Z^d$</span>-dynamical systems are universal. These conditions are general enough to prove that</p>
<p>1) A self-homeomorphism with almost weak specification on a compact metric space (answering a question by Quas and Soo and recovering recent results by David Burguet)
2) Proper colourings of the <span class="kdmath">$Z^d$</span> lattice with more than two colours and the domino tilings of the <span class="kdmath">$Z^2$</span> lattice (answering a question by Şahin and Robinson) are universal. Our results also extend to the almost Borel category giving partial answers to some questions by Gao and Jackson.</p></div>Nishant Chandgotiahttp://math.huji.ac.il/~nishant/The Hebrew University of Jerusalemtag:www.math.bgu.ac.il,2005:MeetingDecorator/4622018-11-01T15:33:10+02:002019-02-24T12:03:19+02:00<span class="mathjax">Dirk Frettlöh: Bounded distance equivalence of aperiodic Delone sets and bounded remainder sets</span>February 28, 11:10—12:00, 2019, -101<div class="mathjax"><p>Delone sets are generalizations of point lattices: unformly discrete
point sets with no large holes. In 1997 Gromov asked whether any
Delone set in the Euclidean plane is bilipschitz equivalent to the
integer lattice <span class="kdmath">$Z^2$</span>. A simpler but stronger condition than bilipschitz
equivalence is bounded distance equivalence. So it is natural to ask
which Delone sets in <span class="kdmath">$R^d$</span> are bounded distance equivalent to (some scaled
copy of) <span class="kdmath">$Z^d$</span>. This talk gives a gentle introduction to the problem
and presents recent results in this context, mostly for cut-and-project
sets on the line. In particular we show a connection between bouded
remainder sets and cut-and-project sets that are bounded distance
equivalent to some lattice.</p></div>Dirk Frettlöhhttps://www.math.uni-bielefeld.de/~frettloe/Bielefeld universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4742018-12-01T21:03:57+02:002019-02-11T14:18:37+02:00<span class="mathjax">Omri Sarig: Local limit theorem for inhomogeneous Markov chains (joint with Dolgopyat)</span>March 7, 11:10—12:00, 2019, -101<div class="mathjax"><p>An inhomogeneous Markov chain <span class="kdmath">$X_n$</span> is a Markov chain whose state spaces and transition kernels change in time. A “local limit theorem” is an asymptotic formula for probabilities of the form</p>
<p><span class="kdmath">$Prob[S_N-z_N\in (a,b)]$</span>, <span class="kdmath">$S_N=f_1(X_1,X_2)+....+f_N(X_N,X_{N+1})$</span></p>
<p>in the limit <span class="kdmath">$N\to\infty$</span>. Here <span class="kdmath">$z_N$</span> is a “suitable” sequence of numbers.
I will describe general sufficient conditions for such results.</p>
<p>If time allows, I will explain why such results are needed for the study of certain problems related to irrational rotations.</p>
<p>This is joint work with Dmitry Dolgopyat.</p></div>Omri Sarighttp://www.weizmann.ac.il/math/sarigo/Weizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/4752018-12-01T21:04:04+02:002019-03-05T08:56:56+02:00<span class="mathjax">David Lipshutz: Pathwise derivatives of reflected diffusions</span>March 14, 11:10—12:00, 2019, -101<div class="mathjax"><p>Reflected diffusions (RDs) constrained to remain in convex polyhedral domains arise in a variety of contexts, including as heavy traffic limits of queueing networks and in the study of rank-based interacting particle models. Pathwise derivatives of an RD with respect to its defining parameters is of interest from both theoretical and applied perspectives. In this talk I will characterize pathwise derivatives of an RD in terms of solutions to a linear constrained stochastic differential equation that can be viewed as a linearization of the constrained stochastic differential equation the RD satisfies. The proofs of these results involve a careful analysis of sample path properties of RDs, as well as geometric properties of the convex polyhedral domain and the associated directions of reflection along its boundary.</p>
<p>This is joint work with Kavita Ramanan.</p></div>David Lipshutzhttps://sites.google.com/view/lipshutz/homeTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/4762018-12-01T21:04:11+02:002018-12-01T21:13:03+02:00<span class="mathjax">Holiday: Purim</span>March 21, 11:10—12:00, 2019, -101Holidaytag:www.math.bgu.ac.il,2005:MeetingDecorator/4772018-12-01T21:04:18+02:002019-01-09T14:43:45+02:00<span class="mathjax">Wojciech Samotij: The lower tail for triangles in sparse random graphs</span>March 28, 11:10—12:00, 2019, -101<div class="mathjax"><p>Let <span class="kdmath">$X$</span> denote the number of triangles in the random graph <span class="kdmath">$G(n,p)$</span>. The problem of determining the asymptotic of the rate of the lower tail of <span class="kdmath">$X$</span>, that is, the function <span class="kdmath">$f_c(n,p) = log Pr(X ≤ c E[X])$</span> for a given <span class="kdmath">$c ∈ [0,1)$</span>, has attracted considerable attention of both the combinatorics and the probability communities. We shall present a proof of the fact that whenever <span class="kdmath">$p >> n^{-1/2}$</span>, then <span class="kdmath">$f_c(n,p)$</span> can be expressed as a solution to a natural combinatorial optimisation problem that generalises Mantel’s / Turan’s theorem. This is joint work with Gady Kozma.</p></div>Wojciech Samotijhttp://www.math.tau.ac.il/~samotij/Tel-Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4782018-12-01T21:04:28+02:002019-03-26T23:25:04+02:00<span class="mathjax">Felix Pogorzelski: New developments on non-commutative quasicrystals</span>April 4, 11:10—12:00, 2019, -101<div class="mathjax"><p>The theory of mathematical quasicrystals essentially goes back to work
of Meyer in the 70’s, who investigated aperiodic point sets in
Euclidean space. Shechtman’s discovery of physical quasicrystals (1982,
Nobel prize for Chemistry 2011) via diffraction experiments triggered
a boom of the mathematical analysis of the arising scatter patterns.
Recent years have seen some progress in understanding the geometry,
Fourier theory and dynamics of well-scattered, aperiodic point sets
in non-commutative groups. We explain some of those developments from the viewpoint of approximation of certain key quantities arising from the underlying group actions via a notion of convergence of dynamical systems. One particular focus in this context will be on sufficient criteria to ensure unique ergodicity of the dynamical system associated with a point set.</p>
<p>Based on joint projects with Siegfried Beckus and
Michael Björklund/Tobias Hartnick.</p></div> Felix Pogorzelskihttp://www.math.uni-leipzig.de/~pogorzelski/Universität Leipzigtag:www.math.bgu.ac.il,2005:MeetingDecorator/4792018-12-01T21:04:35+02:002019-04-08T09:05:18+03:00<span class="mathjax">Federico Vigolo: An introduction to warped cones</span>April 11, 11:10—12:00, 2019, -101<div class="mathjax"><p>Warped cones are families of metric spaces that can be associated with actions of discrete groups on compact metric spaces. They were first introduced by John Roe as means of producing interesting examples of metric spaces (in the context of the coarse Baum-Connes conjecture), and have since evolved as it turned out that they could be used to construct families of expander graphs and that they were good candidates for a definition of a `coarse geometric’ invariant of actions. In this talk I will introduce the warped cone construction and explain how to use it to obtain expanders. I will then indicate some rigidity results that hold in this settings.</p></div>Federico Vigolohttp://www.wisdom.weizmann.ac.il/~vigolo/Weizmann Istitutetag:www.math.bgu.ac.il,2005:MeetingDecorator/4802018-12-01T21:04:43+02:002018-12-01T21:13:15+02:00<span class="mathjax">Holiday: Passover</span>April 18, 11:10—12:00, 2019, -101Holidaytag:www.math.bgu.ac.il,2005:MeetingDecorator/4812018-12-01T21:06:57+02:002018-12-01T21:13:23+02:00<span class="mathjax">Holiday: Passover</span>April 25, 11:10—12:00, 2019, -101Holidaytag:www.math.bgu.ac.il,2005:MeetingDecorator/4822018-12-01T21:07:38+02:002019-05-02T17:03:13+03:00<span class="mathjax">Michael Lin : Joint and double coboundaries of transformations � an application of maximal spectral type of spectral measures</span>May 2, 11:10—12:00, 2019, -101<div class="mathjax"><p>Let T be a bounded linear operator on a Banach space X; the elements
of (I − T)X are called coboundaries. For two commuting operators T and
S, elements of (I − T)X ∩ (I − S)X are called joint coboundaries, and those
of (I − T)(I − S)X are double coboundaries. By commutativity, double
coboundaries are joint ones. Are there any other?
Let θ and τ be commuting invertible measure preserving transformations
of (Ω, Σ, m), with corresponding unitary operators induced on L2(m). We
prove the existence of a joint coboundary g ∈ (I − U)L2 ∩ (I − V )L2 which
is not in (I − U)(I − V )L2.
For the proof, let E be the spectral measure on T
2 obtained by Stone’s
spectral theorem. Joint and double coboundaries are characterized using E,
and properties of the maximal spectral type of E, together with a result of
Foia³ on multiplicative spectral measures acting on L2, are used to show the
existence of the required function.</p></div>Michael Lin Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4832018-12-01T21:09:51+02:002018-12-01T21:13:34+02:00<span class="mathjax">Holiday: Independence Day</span>May 9, 11:10—12:00, 2019, -101Holidaytag:www.math.bgu.ac.il,2005:MeetingDecorator/4842018-12-01T21:10:27+02:002019-02-28T21:36:54+02:00<span class="mathjax">@ weizmann institute: students’ probability day - in memory of Oded Schramm</span>May 16, 11:10—12:00, 2019, -101 @ weizmann institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/4852018-12-01T21:10:48+02:002019-03-05T09:28:51+02:00<span class="mathjax">J.C. Saunders: On (a,b) Pairs in Random Fibonacci Sequences</span>May 23, 11:10—12:00, 2019, -101<div class="mathjax"><table>
<tbody>
<tr>
<td>We deal with the random Fibonacci tree, which is an inﬁnite binary tree with nonnegative integers at each node. The root consists of the number 1 with a single child, also the number 1. We deﬁne the tree recursively in the following way: if x is the parent of y, then y has two children, namely</td>
<td>x−y</td>
<td>and x+y. This tree was studied by Benoit Rittaud who proved that any pair of integers a,b that are coprime occur as a parent-child pair inﬁnitely often. We extend his results by determining the probability that a random inﬁnite walk in this tree contains exactly one pair (1,1), that being at the root of the tree. Also, we give tight upper and lower bounds on the number of occurrences of any speciﬁc coprime pair (a,b) at any given ﬁxed depth in the tree.</td>
</tr>
</tbody>
</table></div> J.C. SaundersBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4862018-12-01T21:10:54+02:002019-03-05T09:56:28+02:00<span class="mathjax">(seminar is cancelled): Open day at the Math department</span>May 30, 11:10—12:00, 2019, -101(seminar is cancelled)tag:www.math.bgu.ac.il,2005:MeetingDecorator/4872018-12-01T21:10:59+02:002019-06-04T09:31:53+03:00<span class="mathjax">Eitan Bachmat: On the index of refraction of a distribution, lenses and probability.</span>June 6, 11:10—12:00, 2019, -101<div class="mathjax"><p>We will consider some basic optimization problems and how they relate to optics. We then define an index of refraction to any given distribution. We conjecture an estimate for the index and explain how its related to some natural operations research questions. We also consider lenses and ask questions about the probabilistic behavior of discrete geodesics in a lens setting.</p></div>Eitan Bachmathttps://www.cs.bgu.ac.il/~ebachmat/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4892018-12-01T21:11:08+02:002019-06-10T23:14:10+03:00<span class="mathjax">Dina Barak: Maximum of exponential random variables and Hurwitz’s zeta function</span>June 20, 11:10—12:00, 2019, -101<div class="mathjax"><p>A problem, arising naturally in the context of the coupon collector’s problem, is the behavior of the maximum of independent geometrically distributed random variables (with distinct parameters). This question has been addressed by Brennan et al. (British J. of Math. & CS.:8 (2015), 330-336). Here we provide explicit asymptotic expressions for the moments of that maximum, as well as of the maximum of exponential random variables with the same parameters. We also deal with the probability of each of the variables being the maximal one.</p>
<p>The calculations lead to expressions involving Hurwitz’s zeta function at certain special points. We find here explicitly the values of the function at these points.</p></div>Dina BarakBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5252019-04-10T11:21:11+03:002019-04-11T09:00:42+03:00<span class="mathjax">Stanislav Molchanov: Random exponentials and Dickmann’s laws: survey and applications</span>June 27, 11:10—12:00, 2019, -101<div class="mathjax"><p>The Dickmann’s law was discovered in the number theory (statistics of the natural
numbers with a small prime factors). The Derrida’s model of the random energies
demonstrated the physical phase transitions of the second type. These models
are from the completely different areas, however they have the same background
and many similarities.
The talk will contain the discussion of such similarities and the numerous
applications, in particular, to the cell growth model.</p></div>Stanislav Molchanovhttp://math2.uncc.edu/~molchanov/University of North Carolina (UNC) at Charlotte; Higher School of Economics (HSE), Moscowtag:www.math.bgu.ac.il,2005:MeetingDecorator/4882018-12-01T21:11:03+02:002019-06-18T10:18:47+03:00<span class="mathjax">Itay Londner: Optimal arithmetic structure in interpolation sets</span>June 27, 14:10—15:10, 2019, -101<div class="mathjax"><p>Given a set S of positive measure on the unit circle, a set of integers K is an interpolation set (IS) for S if for any data <span class="kdmath">${c(k)}$</span> in <span class="kdmath">$l^2(K)$</span> there exists a function <span class="kdmath">$f$</span> in <span class="kdmath">$L^2(S)$</span> such that its Fourier coefficients satisfy <span class="kdmath">$\hat{f}(k)=c(k)$</span> for all k in K.
In the talk I will discuss the relationship between the concept of IS and the existence arithmetic structure in the set K, I will focus primarily on the case where K contains arbitrarily long arithmetic progressions with specified lengths and step sizes.
Multidimensional analogue and recent developments on this subject will also be considered.
This talk is based in part on joint work with Alexander Olevskii.</p></div>Itay Londnerhttp://www.math.ubc.ca/~itayl/University of British Columbiatag:www.math.bgu.ac.il,2005:MeetingDecorator/5402019-06-26T12:25:55+03:002019-06-26T20:49:59+03:00<span class="mathjax">Adam Dor-On: Problems on Markov chains arising from operator algebras</span>July 1, 13:10—14:00, 2019, -101Adam Dor-Onhttps://adoronmath.wordpress.com/University of Illinois at Urbana-Champaigntag:www.math.bgu.ac.il,2005:MeetingDecorator/5562019-09-08T12:07:16+03:002019-09-08T12:22:46+03:00<span class="mathjax">Davide Giraudo: Bounded law of the iterated logarithms for stationary random fields</span>September 18, 14:10—15:00, 2019, 201<div class="mathjax"><p>We will give sufficient conditions for the bounded law of the iterated logarithms for strictly stationary random fields with summation on rectangles. The case of martingales differences with respect to the lexicographic order and the orthormartingales will be investigated, as well as martingale approximation.</p></div>Davide Giraudohttps://sites.google.com/site/davidegiraudomathematics/Ruhr-Universität Bochumtag:www.math.bgu.ac.il,2005:MeetingDecorator/5412019-07-30T13:18:08+03:002019-10-22T14:16:48+03:00<span class="mathjax">Barak Weiss: Geometric invariants of lattices and points close to a line, and their asymptotics</span>October 31, 11:10—12:00, 2019, -101<div class="mathjax"><p>Given a lattice <span class="kdmath">$\Lambda$</span> and a (perhaps long) vector <span class="kdmath">$v \in \Lambda$</span>, we consider two geometric quantities:
- the projection <span class="kdmath">$\Delta$</span> of <span class="kdmath">$\Lambda$</span> along the line through <span class="kdmath">$v$</span>
- the “lift functional” which encodes how one can recover <span class="kdmath">$\Lambda$</span> from the projection <span class="kdmath">$\Delta$</span>
Fixing <span class="kdmath">$\Lambda$</span> and taking some infinite sequences of vectors <span class="kdmath">$v_n$</span>, we identify the asymptotic distribution of these two quantities. For example, for a.e. line <span class="kdmath">$L$</span>, if <span class="kdmath">$v_n$</span> is the sequence of <span class="kdmath">$\epsilon$</span>-approximants to <span class="kdmath">$L$</span> then the sequence <span class="kdmath">$\Delta(v_n)$</span> equidistributes according to Haar measure, and if <span class="kdmath">$v'_n$</span> is the sequence of best approximants to <span class="kdmath">$L$</span> then there is another measure which <span class="kdmath">$\Delta(v'_n)$</span> equidistributes according to. The basic tool is a cross section for a diagonal flow on the space of lattices, and after some analysis of this cross section, the results follow from the Birkhoff pointwise ergodic theorem.</p>
<p>Joint work with Uri Shapira.</p></div>Barak Weisshttp://www.math.tau.ac.il/~barakw/Tel-Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5422019-07-30T13:19:12+03:002019-10-27T13:20:38+02:00<span class="mathjax">Tom Meyerovitch: Efficient finitary codings by Bernoulli processes</span>November 7, 11:10—12:00, 2019, -101<div class="mathjax"><p>Recently Uri Gabor refuted an old conjecture stating that any finitary factor of an i.i.d process is finitarly isomorphic to an i.i.d process. Complementing Gabor’s result, in this talk, which is based on work in progress with Yinon Spinka, we will prove that any countable-valued process which is admits a finitary a coding by some i.i.d process furthermore admits an <span class="kdmath">$\epsilon$</span>-efficient finitary coding, for any positive <span class="kdmath">$\epsilon$</span>. Here an ‘’<span class="kdmath">$\epsilon$</span>-efficient coding’’ means that the entropy increase of the coding i.i.d process compared to the (mean) entropy of the coded process is at most <span class="kdmath">$\epsilon$</span>.
For processes having finite entropy this in particular implies a finitary i.i.d coding by finite valued processes. As an application we give an affirmative answer to an old question about the existence of finite valued finitary coding of the critical Ising model, posed by van den Berg and Steif in their 1999 paper ‘‘On the Existence and Nonexistence of Finitary Codings for a Class of Random Fields’’.</p></div>Tom Meyerovitchhttps://sites.google.com/site/tommeyerovitch/homeBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5432019-07-30T13:19:28+03:002019-11-13T22:03:33+02:00<span class="mathjax">Talk has been cancelled : TBA</span>November 14, 11:10—12:00, 2019, -101Talk has been cancelled tag:www.math.bgu.ac.il,2005:MeetingDecorator/5442019-07-30T13:19:45+03:002019-11-12T20:58:33+02:00<span class="mathjax">Uriel Gabor: On the failure of Ornstein’s theory in the finitary category.</span>November 21, 11:10—12:00, 2019, -101<div class="mathjax"><p>I’ll show the invalidity of finitary counterparts for three theorems in classification theory: The preservation of being a Bernoulli shift through factors, Sinai’s factor theorem, and the weak Pinsker property. This gives a negative answer to an old conjecture and to a recent open problem.</p></div>Uriel GaborThe Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5452019-07-30T13:19:53+03:002019-11-24T08:43:55+02:00<span class="mathjax">Manuel Luethi: Effective equidistribution of primitive rational points along long horocycle orbits and disjointness to Kloosterman sums</span>November 28, 11:10—12:00, 2019, -101<div class="mathjax"><p>An observation by Jens Marklof shows that the primitive
rational points of a fixed denominator along the periodic unipotent
orbit of volume equal to the square of the denominator equidistribute
inside a proper submanifold of the modular surface. This concentration
as well as the equidistribution are intimately related to classical
questions of number theoretic origin. We discuss the distribution of the
primitive rational points along periodic orbits of intermediate size. In
this case, we can show joint equidistribution with polynomial rate in
the modular surface and in the torus. We also deduce simultaneous
equidistribution of primitive rational points in the modular surface and
of modular hyperbolas in the two-torus under certain congruence
conditions. This is joint work with M. Einsiedler and N. Shah.</p></div>Manuel Luethihttps://people.math.ethz.ch/~luethman/Tel-Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5462019-07-30T13:20:03+03:002019-11-17T14:18:54+02:00<span class="mathjax">Amnon Yekutieti: An averaging process for unipotent group actions – in differential geometry</span>December 5, 11:10—12:00, 2019, -101<div class="mathjax"><p>The usual weighted average of points <span class="kdmath">$(z_0, ..., z_q)$</span> in the real vector space <span class="kdmath">$R^n$</span>, with weights <span class="kdmath">$(w_0, ..., w_q)$</span>, is translation invariant. Hence it can be seen as an average of points in a torsor Z over the Lie group <span class="kdmath">$G = R^n$</span> (A <span class="kdmath">$G$</span>-torsor is a <span class="kdmath">$G$</span>-manifold with a simply transitive action.)</p>
<p>In this talk I will explain how this averaging process can be generalized to a torsor Z over a unipotent Lie group <span class="kdmath">$G$</span>. (In differential geometry, a unipotent group is a simply connected nilpotent Lie group. <span class="kdmath">$R^n$</span> is an abelian unipotent group.)</p>
<p>I will explain how to construct the unipotent weighted average, and discuss its properties (functoriality, symmetry and simpliciality). If time permits, I will talk about torsors over a base manifold, and families of
sections parametrized by simplices. I will indicate how I came about this idea, while working on a problem in deformation quantization.</p>
<p>Such an averaging process exists only for unipotent groups. For instance, it does not exist for a torus <span class="kdmath">$G$</span> (an abelian Lie group that’s not simply connected). In algebraic geometry the unipotent averaging has arithmetic significance, but this is not visible in differential geometry.</p>
<p>Notes for the talk can be founds here:
https://www.math.bgu.ac.il/~amyekut/lectures/average-diff-geom/abstract.html</p></div>Amnon Yekutietihttps://www.math.bgu.ac.il/~amyekut/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5472019-07-30T13:20:13+03:002019-11-28T13:48:15+02:00<span class="mathjax">Jeremias Epperlein: Automorphisms of topological Markov shifts and Wagoner’s complexes</span>December 12, 11:10—12:00, 2019, -101<div class="mathjax"><p>A topological Markov shift is the set of two sided inifinite paths in a finite directed graph endowed with the product topology and with the left shift acting on this space. The automorphisms of the space are the shift commuting self-homeomorphisms. Wagoner realized the automorphism group of a topological Markov shift as the fundamental group of a certain CW complex. This construction has been crucial in many results regarding automorphisms and
isomorphism in symbolic dynamics. We give a simplified construction of this complex, which also works in more general contexts, and sketch some applications.</p></div>Jeremias Epperleinhttps://www.math.bgu.ac.il/~jeremias/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5482019-07-30T13:20:24+03:002019-12-03T13:51:58+02:00<span class="mathjax">Rene Rühr: Cut-And-Project quasicrystals and their moduli spaces</span>December 19, 11:10—12:00, 2019, -101<div class="mathjax"><p>A cut-and-project set is constructed by restricting a lattice <span class="kdmath">$L$</span> in <span class="kdmath">$(d+m)$</span>-space to a domain bounded in the last m coordinates, and projecting these points to the the space spanned by its d-dimensional orthogonal complement. These point sets constitute an important example of so-called quasicrystals.</p>
<p>During the talk, we shall present and give some classification results of the moduli spaces of cut-and-project sets, which were introduced by Marklof-Strömbergsson. These are obtained by considering the orbit closure of the special linear group in <span class="kdmath">$d$</span>-space acting on the lattice <span class="kdmath">$L$</span> inside the space of unimodular lattices of rank <span class="kdmath">$d+m$</span>. Theorems of Ratner imply that these are meaningful objects.</p>
<p>We then describe quantitative counting result for patches in generic cut-and-project sets. Patches are local configuration of point sets whose multitude reflects aperiodicity.</p>
<p>The count follows some old argument of Schmidt using moment bounds. These bounds are obtained by integrability properties of the Siegel transform, which in turn follow from reduction theory and a symmetrisation argument of Rogers. This argument is of independent interest, giving an alternative
account to recent work of Kelmer-Yu (which is based on the theory of Eisenstein series) on counting points in generic symplectic lattices.</p>
<p>This is a joint endeavour with Yotam Smilansky and Barak Weiss.</p></div>Rene Rührhttps://sites.google.com/site/reneruehrTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/5492019-07-30T13:20:37+03:002019-12-10T21:42:49+02:00<span class="mathjax">Asaf Katz: Measure rigidity for Anosov flows via the factorization method</span>December 26, 11:10—12:00, 2019, -101<div class="mathjax"><p>Anosov flows are central objects in dynamics, generalizing the basic example of a geodesic flow over a Riemann surface.</p>
<p>In the talk we will introduce those flows and their dynamical behavior.
Moreover, we show how the factorization method, pioneered by Eskin and Mirzakhani in their groundbreaking work about measure rigidity for the moduli space of translation surfaces, can be adapted to smooth ergodic theory and in particular towards the study of Anosov flows.</p>
<p>Using this adaption, we show that for a quantitatively non-integrable Anosov flow, every generalized u-Gibbs measure is absolutely continuous with respect to the whole unstable manifold.</p></div>Asaf Katzhttps://sites.google.com/view/asafkatzUniversity of Chicagotag:www.math.bgu.ac.il,2005:MeetingDecorator/5502019-07-30T13:20:44+03:002019-12-30T09:43:22+02:00<span class="mathjax">Amitay Kamber: Cutoff on graphs and the Sarnak-Xue density of eigenvalues</span>January 2, 11:10—12:00, 2020, -101<div class="mathjax"><p>The cutoff phenomenon of random walks on graphs is conjectured to be very common. However, it is unknown whether many natural examples of large graphs of fixed degree satisfy this phenomenon.
It was recently shown by Lubetzky and Peres that Ramanujan graphs, i.e., graphs with the optimal spectrum, exhibit cutoff of the simple random walk in optimal time.
We show that the spectral condition can be replaced by a weaker spectral condition, based on the work of Sarnak and Xue in automorphic forms. This property is also equivalent to a geometrical path counting property, which can be verified in some cases. As an example, we show that the theorems hold for some families of Schreier graphs of the <span class="kdmath">$SL_2(F_p)$</span> action on the projective line, for a finite field <span class="kdmath">$F_p$</span>.
Based on joint work with Konstantin Golubev.</p></div>Amitay KamberThe Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5512019-07-30T13:20:54+03:002020-01-06T11:57:15+02:00<span class="mathjax">Aron Wennman: The hole event for Gaussian Entire Functions and a curious emergence of quadrature domains</span>January 9, 11:10—12:00, 2020, -101<div class="mathjax"><p>The Gaussian Entire Function (GEF) is the random Taylor series, whose coefficients are independent centered complex Gaussians such that the n-th coefficient has variance 1/n!. The zero set of the GEF is a random point process in the plane, which is invariant with respect to isometries. The topic of this talk is the zero distribution of the GEF conditioned on the event that no zero lies in a given (large) region.</p>
<p>If the hole is a disk of radius r, Ghosh and Nishry observed a striking feature. As r tends to infinity, the density of particles vanishes not only on the given hole, but also on an annulus beyond the (rescaled) hole — a forbidden region emerges. Here, we study this problem for general simply connected holes, and find a curious connection to quadrature domains and a seemingly novel type of free boundary problem.</p>
<p>This reports on joint work in progress with Alon Nishry.</p></div>Aron Wennmanhttps://people.kth.se/~aronw/Tel-Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5522019-07-30T13:21:12+03:002019-12-19T10:11:40+02:00<span class="mathjax">Geoffrey Wolfer: Estimating the mixing time of non-reversible Markov chains</span>January 16, 11:10—12:00, 2020, -101<div class="mathjax"><p>The mixing time is a fundamental quantity measuring the rate of convergence of a Markov chain towards its stationary distribution. We will discuss the problem of estimating the mixing time from one single long trajectory of observations. The reversible setting was addressed using spectral methods by Hsu et al. (2015), who left the general case as an open problem. In the reversible setting, the analysis is greatly facilitated by the fact that the Markov operator is self-adjoint, and Weyl’s inequality allows for dimension-free perturbation analysis of the empirical eigenvalues. In the absence of reversibility, the existing perturbation analysis has a worst-case exponential dependence on the number of states. Furthermore, even if an eigenvalue perturbation analysis with better dependence on the number of states were available, in the non-reversible case the connection between the spectral gap and the mixing time is not nearly as straightforward as in the reversible case. We design a procedure, using spectral methods, that allows us to overcome the loss of self-adjointness and to recover a sample size with a polynomial dependence in some natural complexity parameters of the chain. Additionally, we will present an alternative estimation procedure that moves away from spectral methods entirely and is instead based on a generalized version of Dobrushin’s contraction. Joint work with Aryeh Kontorovich.</p>
<p>Estimating the Mixing Time of Ergodic Markov Chains
Geoffrey Wolfer, Aryeh Kontorovich - COLT2019
http://proceedings.mlr.press/v99/wolfer19a.html<br />
https://arxiv.org/abs/1902.01224</p>
<p>Mixing Time Estimation in Ergodic Markov Chains from a Single Trajectory with Contraction Methods
Geoffrey Wolfer - ALT2020
https://arxiv.org/abs/1912.06845</p></div>Geoffrey Wolferhttp://web.dagama.org/resumeBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5532019-07-30T14:54:08+03:002020-01-15T10:21:03+02:00<span class="mathjax">Tom Gilat: Decomposition of random walk measures on the one-dimensional torus</span>January 23, 11:10—12:00, 2020, -101<div class="mathjax"><p>The main result in this talk is a decomposition theorem for a measure on the
one-dimensional torus. Given a sufficiently large subset
S of the positive
integers, an arbitrary measure on the torus is decomposed as the sum of two
measures. The first one <span class="kdmath">$\mu_1$</span> has the property that the random walk with
initial distribution <span class="kdmath">$\mu_1$</span> evolved by the action of S equidistributes very
fast. The second measure <span class="kdmath">$\mu_2$</span> in the decomposition is concentrated on very
small neighborhoods of a small number of points.</p></div>Tom GilatBar-Ilan Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/6062019-11-11T22:01:33+02:002020-01-26T09:21:07+02:00<span class="mathjax">Sebastián Barbieri: On the relation between topological entropy and asymptotic pairs</span>January 27, 11:10—12:00, 2020, -101<div class="mathjax"><p>I will present some results that state that under certain topological conditions, any action of a countable amenable group with positive topological entropy admits off-diagonal asymptotic pairs. I shall explain the latest results on this topic and present a new approach, inspired from thermodynamical formalism and developed in collaboration with Felipe García-Ramos and Hanfeng Li, which unifies all previous results and yields new classes of algebraic actions for which positive entropy yields non-triviality of their associated homoclinic group.</p></div>Sebastián Barbierihttps://www.labri.fr/perso/sbarbieri/index.htmlUniversité de Bordeauxtag:www.math.bgu.ac.il,2005:MeetingDecorator/6262020-02-05T08:45:09+02:002020-02-05T08:45:09+02:00<span class="mathjax">Yuqing (Frank) Lin: A subshift of finite type with two different positive sofic entropies</span>February 6, 11:10—12:00, 2020, -101<div class="mathjax"><p>Dynamical entropy is an important tool in classifying measure-preserving or topological dynamical systems up to measure or topological conjugacy. Classical dynamical entropy theory, of an action of a single transformation, has been studied since the 50s and 60s. Recently L. Bowen and Kerr-Li have introduced entropy theory for actions of sofic groups. Although a conjugacy invariant, sofic entropy in general appears to be less well-behaved than classical entropy. In particular, sofic entropy may depend on the choice of sofic approximation, although only degenerate examples have been known until now.</p>
<p>We present an example, inspired by hypergraph 2-colorings from statistical physics literature, of a mixing subshift of finite type with two different positive topological sofic entropies corresponding to different sofic approximations. The measure-theoretic case remains open. This is joint work with Lewis Bowen and Dylan Airey.</p></div>Yuqing (Frank) Linhttps://web.ma.utexas.edu/users/ylin/The University of Texas at Austintag:www.math.bgu.ac.il,2005:MeetingDecorator/6192019-12-20T14:09:56+02:002020-02-06T10:28:20+02:00<span class="mathjax">Houcein Elabdalaoui: Sarnak’s Möbius disjointness conjecture for dendrites and Veech systems</span>February 20, 11:10—12:00, 2020, -101Houcein Elabdalaouihttp://elabdalaoui.perso.math.cnrs.fr/Université de Rouentag:www.math.bgu.ac.il,2005:MeetingDecorator/6482020-03-03T08:21:27+02:002020-03-03T08:22:38+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5832019-10-26T10:27:24+03:002020-03-11T09:42:40+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5842019-10-26T10:28:06+03:002020-03-11T11:16:18+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5852019-10-26T10:28:41+03:002019-11-11T23:44:28+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5862019-10-26T10:28:49+03:002019-11-04T09:42:17+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5882019-10-26T10:29:43+03:002020-02-02T12:52:14+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5892019-10-26T10:29:57+03:002020-02-02T12:52:25+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5872019-10-26T10:29:31+03:002020-03-11T10:42:30+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5902019-10-26T10:30:06+03:002019-11-26T13:17:28+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5912019-10-26T10:30:14+03:002019-12-15T15:49:26+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5922019-10-26T10:30:22+03:002020-02-03T11:43:37+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5932019-10-26T10:30:29+03:002020-01-27T14:56:44+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5942019-10-26T10:30:35+03:002020-02-02T12:52:50+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5952019-10-26T10:31:22+03:002019-10-26T12:05:42+03:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5962019-10-26T10:31:30+03:002019-10-26T10:31:30+03:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5972019-10-26T10:31:37+03:002020-02-18T13:58:11+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/5982019-10-26T10:31:42+03:002019-10-26T10:31:42+03:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/6702020-08-14T11:34:37+03:002020-09-01T07:25:50+03:00<span class="mathjax">Bashir Abu Khalil: Extracting an invariant of conjugacy from independence entropy</span>September 3, 11:10—12:00, 2020, online<div class="mathjax"><p>In this talk Bashir Abu Khalil will present results from his MSc. Thesis about the notion of “independence entropy” for shifts of finite type, sofic shifts and general shift spaces.</p></div>Bashir Abu KhalilBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/6882020-10-12T18:00:55+03:002021-10-28T09:05:22+03:00<span class="mathjax">Dor Bitan: Homomorphic operations over secret shares</span>October 22, 11:10—12:00, 2020, OnlineDor BitanBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/6892020-10-12T21:28:00+03:002021-10-28T09:04:17+03:00<span class="mathjax">Yair Hartman: Random walks on dense subgroups</span>October 29, 11:10—12:00, 2020, Online<div class="mathjax"><p>Imagine you have a group, with a discrete subgroup. Wouldn’t that be nice to relate random walks, and Poisson boundaries of the group and of the subgroup, in a meaningful way?
This was done by Furstenberg for lattices in semisimple Lie groups as an essential tool in an important rigidity result. We are concerned with dense subgroups. We develop a technique for doing it that allows us to exhibit some new interesting phenomena in Poisson boundary theory. I’ll explain the setting in which we work, and will focus mainly on our construction (leaving the applications as “further reading”).
Joint work with Michael Björklund and Hanna Oppelmayer</p></div>Yair Hartmanhttps://www.math.bgu.ac.il/~hartmany/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/6902020-10-12T21:30:34+03:002021-10-28T09:06:57+03:00<span class="mathjax">Arielle Leitner: Deformations of generalized cusps on convex projective manifolds</span>November 5, 11:10—12:00, 2020, Online<div class="mathjax"><p>Convex projective manifolds are a generalization of hyperbolic manifolds. Koszul showed that the set of holonomies of convex projective structures on a compact manifold is open in the representation variety. We will describe an extension of this result to convex projective manifolds whose ends are generalized cusps, due to Cooper-Long-Tillmann. Generalized cusps are certain ends of convex projective manifolds. They may contain both hyperbolic and parabolic elements. We will describe their classification (due to Ballas-Cooper-Leitner), and explain how generalized cusps turn out to be deformations of cusps of hyperbolic manifolds. We will also explore the moduli space of generalized cusps, it is a semi-algebraic set of dimension n^2-n, contractible, and may be studied using several different invariants. For the case of three manifolds, the moduli space is homeomorphic to R^2 times a cone on a solid torus.</p></div>Arielle Leitnerhttp://www.wisdom.weizmann.ac.il/~ariellel/Weizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/6912020-10-12T21:31:54+03:002021-10-28T08:29:15+03:00<span class="mathjax">: TBA</span>November 12, 11:10—12:00, 2020, Onlinetag:www.math.bgu.ac.il,2005:MeetingDecorator/6922020-10-12T21:32:27+03:002021-10-28T09:08:49+03:00<span class="mathjax">Ariel Yadin: Non-trivial phase transition in percolation</span>November 19, 11:10—12:00, 2020, Online<div class="mathjax"><p>In 1920 Ising showed that the infinite line Z does not admit a phase transition for percolation. In fact, no “one-dimensional” graph does. However, it has been asked if this is the only obstruction. Specifically, Benjamini & Schramm conjectured in 1996 that any graph with isoperimetric dimension greater than 1 will have a non-trivial phase transition.<br />
We prove this conjecture for all dimensions greater than 4. When the graph is transitive this solves the question completely, since low-dimensional transitive graphs are quasi-isometric to Cayley graphs, which we can classify thanks to Gromov’s theorem.
This is joint work with H. Duminil-Copin, S. Goswami, A. Raufi, F. Severo.</p></div>Ariel Yadinhttps://www.math.bgu.ac.il/~yadina/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/6932020-10-12T21:32:55+03:002020-11-26T16:07:49+02:00<span class="mathjax">Gil Goffer: Is invariable generation hereditary?</span>November 26, 11:10—12:00, 2020, Online<div class="mathjax"><p>I will discuss the notion of invariably generated groups and present a construction of an invariably generated group that admits an index two subgroup that is not invariably generated. The construction answers questions of Wiegold and of Kantor-Lubotzky-Shalev. This is a joint work with Nir Lazarovich.</p></div>Gil Gofferhttps://www.weizmann.ac.il/pages/search/people?language=english&single=1&person_id=52900Weizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/6942020-10-12T21:33:15+03:002021-10-28T09:09:36+03:00<span class="mathjax">Yaar Solomon: TBA</span>December 3, 16:00—17:00, 2020, OnlineYaar Solomontag:www.math.bgu.ac.il,2005:MeetingDecorator/6952020-10-12T21:33:31+03:002021-10-28T09:08:14+03:00<span class="mathjax">Erez Nesharim: Approximation by algebraic numbers and homogeneous dynamics</span>December 10, 11:10—12:00, 2020, Online<div class="mathjax"><p>Diophantine approximation quantifies the density of the rational numbers in the real line. The extension of this theory to algebraic numbers raises many natural questions. I will focus on a dynamical resolution to Davenport’s problem and show that there are uncountably many badly approximable pairs on the parabola. The proof uses the Kleinbock–Margulis uniform estimate for nondivergence of nondegenerate curves in the space of lattices and a variant of Schmidt’s game. The same ideas applied to Ahlfors-regular measures show the existence of real numbers which are badly approximable by algebraic numbers. This talk is based on joint works with Victor Beresnevich and Lei Yang.</p></div>Erez Nesharimhttp://math.huji.ac.il/~ereznesh/The Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/6962020-10-12T21:33:46+03:002021-10-27T17:22:28+03:00<span class="mathjax">Yotam Smilansky: Multiscale substitution tilings</span>December 17, 15:30—16:30, 2020, Online<div class="mathjax"><p>Multiscale substitution tilings are a new family of tilings of Euclidean space that are generated by multiscale substitution rules. Unlike the standard setup of substitution tilings, which is a basic object of study within the aperiodic order community and includes examples such as the Penrose and the pinwheel tilings, multiple distinct scaling constants are allowed, and the defining process of inflation and subdivision is a continuous one. Under a certain irrationality assumption on the scaling constants, this construction gives rise to a new class of tilings, tiling spaces, and tiling dynamical systems, which are intrinsically different from those that arise in the standard setup. In the talk, I will describe these new objects and discuss various structural, geometrical, statistical, and dynamical results. Based on joint work with Yaar Solomon.</p></div>Yotam Smilanskyhttps://sites.math.rutgers.edu/~smilansky/Rutgers Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/6972020-10-12T21:34:04+03:002021-10-28T08:33:03+03:00<span class="mathjax">Zemer Kosloff: On the local limit theorem in dynamical systems</span>December 24, 11:10—12:00, 2020, Online<div class="mathjax"><p>In 1987, Burton and Denker proved the remarkable result that in every aperiodic dynamical system (including irrational rotations for example) there is a square integrable, zero mean function such that its corresponding time series satisfies a CLT. Subsequently, Volny showed that one can find a function which satisfies the strong (almost sure) invariance principle. All these constructions resulted in a non-lattice distribution.</p>
<p>In a joint work with Dalibor Volny we show that there exists an integer valued cocycle which satisfies the local limit theorem.</p></div>Zemer Kosloffhttp://math.huji.ac.il/~zemkos/The Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/6982020-10-12T21:34:17+03:002021-10-28T08:27:58+03:00<span class="mathjax">Amir Algom: On the decay of the Fourier transform of self-conformal measures</span>December 31, 15:30—16:30, 2020, Online<div class="mathjax"><p>Let P be a self-conformal measure with respect to an IFS consisting of finitely many smooth contractions of [0,1]. Assuming a mild and natural condition on the derivative cocycle, we prove that the Fourier transform of P decays to zero at infinity. This is related to the highly active study of the properties of the Fourier transform of dynamically defined measures, dating back to the important work of Erdos about Bernoulli convolutions in the late 1930’s.
This is joint work with Federico Rodriguez Hertz and Zhiren Wang.</p></div>Amir Algomhttps://sites.psu.edu/amira/Penn State Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/6992020-10-12T21:34:50+03:002021-06-27T08:43:13+03:00<span class="mathjax">Guy Salomon: Amenability, proximality, and higher order syndeticity</span>January 7, 11:10—12:00, 2021, Online<div class="mathjax"><p>An action of a discrete group G on a compact Hausdorff space X is called proximal if for every two points x and y of X there is a net g_i in G such that lim(g_i x)=lim(g_i y), and strongly proximal if the action of G on the space Prob(X) of probability measures on X is proximal. The group G is called strongly amenable if all of its proximal actions have a fixed point and amenable if all of its strongly proximal actions have a fixed point.</p>
<p>In this talk, I will present a correspondence between (strongly) proximal actions of G and Boolean algebras of subsets of G consisting of certain kinds of “large” subsets. I will use these Boolean algebras to establish new characterizations of amenability and strong amenability. Furthermore, I will show how this machinery helps to characterize “dense orbit sets” answering a question of Glasner, Tsankov, Weiss, and Zucker.</p>
<p>This is joint work with Matthew Kennedy and Sven Raum.</p></div>Guy SalomonWeizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/7002020-10-12T21:36:10+03:002021-01-15T09:19:07+02:00<span class="mathjax">Jeremias Epperlein: Conjugacy of free automorphisms of finite order of subshifts of finite type</span>January 14, 11:10—12:00, 2021, Online<div class="mathjax"><p>An old question in symbolic dynamics asks if every two involutions
without fixed points in the automorphism group of the 2-shift are
conjugate.
Based on work of Fiebig, Boyle and Schmieding we show that they are at
least conjugate in the stabilized automorphism group.</p></div>Jeremias Epperleinhttps://www.fim.uni-passau.de/en/dynamical-systems/publications/dr-jeremias-epperlein/University of Passautag:www.math.bgu.ac.il,2005:MeetingDecorator/7192021-01-27T12:20:50+02:002021-02-14T21:35:16+02:00<span class="mathjax">Shrey Sanadhya: Substitution on infinite alphabets and generalized Bratteli-Vershik models.</span>February 11, 16:25—17:30, 2021, Online<div class="mathjax"><p>We consider substitutions on countably infinite alphabets as Borel dynamical system and build their Bratteli-Vershik models. We prove two versions of Rokhlin’s lemma for such substitution dynamical systems. Using the Bratteli-Vershik model we give an explicit formula for a shift-invariant measure (finite and infinite) and provide a criterion for this measure to be ergodic. This is joint work with Sergii Bezuglyi and Palle Jorgensen.</p></div>Shrey Sanadhyahttps://sites.google.com/view/shrey-sanadhya/homeThe University of Iowatag:www.math.bgu.ac.il,2005:MeetingDecorator/7202021-02-11T10:51:24+02:002021-02-11T10:51:49+02:00<span class="mathjax">: TBA</span>March 4, 11:10—12:00, 2021, Onlinetag:www.math.bgu.ac.il,2005:MeetingDecorator/7212021-02-11T10:52:06+02:002021-03-11T17:46:31+02:00<span class="mathjax">Nattalie Tamam: Effective equidistribution of horospherical flows in infinite volume</span>March 11, 16:00—17:00, 2021, Online<div class="mathjax"><p>Horospherical flows in homogeneous spaces have been studied intensively over the last several decades and have many surprising applications in various fields. Many basic results are under the assumption that the volume of the space is finite, which is crucial as many basic ergodic theorems fail in the setting of an infinite measure space. In the talk we will discuss the infinite volume setting, and specifically, when can we expect horospherical orbits to equidistribute. Our goal will be to provide an effective equidistribution result, with polynomial rate, for horospherical orbits in the frame bundle of certain infinite volume hyperbolic manifolds. This is a joint work with Jacqueline Warren.</p></div>Nattalie Tamamhttps://www.math.ucsd.edu/~natamam/University of California, San Diegotag:www.math.bgu.ac.il,2005:MeetingDecorator/7222021-02-11T10:52:18+02:002021-03-18T16:41:24+02:00<span class="mathjax">Yuqing Frank Lin: A multiplicative ergodic theorem for von Neumann algebra valued cocycles</span>March 18, 11:10—12:00, 2021, Online<div class="mathjax"><p>Oseledets’ multiplicative ergodic theorem (MET) is an important tool in smooth ergodic theory. It may be viewed as a generalization of Birkhoff’s pointwise ergodic theorem where numbers are replaced by matrices and arithmetic means are replaced by geometric means. Starting from Ruelle in 1982, many infinite-dimensional generalizations of the MET have been produced; however, these results assume quasi-compactness conditions and so do not deal with continuous spectrum. In a different direction Karlsson-Margulis obtained a geometric generalization of the MET, which we apply in our work to obtain an MET with operators in von Neumann algebras with semi-finite trace. We do not assume any compactness conditions on the operators. Joint work with Lewis Bowen and Ben Hayes.</p></div>Yuqing Frank Linhttps://web.ma.utexas.edu/users/ylin/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7232021-02-11T10:53:19+02:002021-02-11T10:53:34+02:00<span class="mathjax">: Passover break</span>March 25, 11:10—12:00, 2021, -101tag:www.math.bgu.ac.il,2005:MeetingDecorator/7242021-02-11T10:53:55+02:002021-02-11T10:53:55+02:00<span class="mathjax">: Passover break</span>April 1, 11:10—12:00, 2021, -101tag:www.math.bgu.ac.il,2005:MeetingDecorator/7252021-02-11T10:54:47+02:002021-02-11T10:54:47+02:00<span class="mathjax">: Holocaust Memorial Day</span>April 8, 11:10—12:00, 2021, -101tag:www.math.bgu.ac.il,2005:MeetingDecorator/7262021-02-11T10:56:05+02:002021-02-11T10:56:05+02:00<span class="mathjax">: Memorial day for Israel’s fallen</span>April 15, 11:10—12:00, 2021, -101tag:www.math.bgu.ac.il,2005:MeetingDecorator/7272021-02-11T10:56:33+02:002021-04-22T12:06:52+03:00<span class="mathjax">Zohar Reizis: Random walks on finite partite simplicial complexes</span>April 22, 11:10—12:00, 2021, Online<div class="mathjax"><p>Random walks on graphs (and their spectral analysis) is an extensively explored topic with many applications in pure math and computer science. Recently, there has been much interest (by both the math and the CS communities) in the study of random walks on simplicial complexes as a high dimensional generalization on random walks on graphs.
In this talk, we consider the spectrum of random walks on finite partite simplicial complexes and show how with a general decomposition theorem on Hilbert spaces we can improve previous works. All the definitions will be given. This is a joint work with Izhar Oppenheim.</p></div>Zohar ReizisBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7282021-02-11T10:57:04+02:002021-04-29T13:40:56+03:00<span class="mathjax">Nishant Chandgotia: About Borel and almost Borel embeddings for Z^d actions</span>April 29, 11:10—12:00, 2021, Online<div class="mathjax"><p>Krieger’s generator theorem says that all free ergodic measure preserving actions (under natural entropy constraints) can be modelled by a full shift. Recently, in a sequence of two papers Mike Hochman proved that this theorem can be strengthened: He showed that all free homeomorphisms of a Polish space (under entropy constraints) can be Borel embedded into the full shift. In this talk we will discuss some results along this line from a recent paper with Tom Meyerovitch and ongoing work with Spencer Unger.</p>
<p>With Meyerovitch, we established a condition called flexibility under which a large class of systems are almost Borel universal, meaning that such systems can model any free Z^d action on a Polish space up to a universally null set. The condition of flexibility covered a large class of examples including those of domino tilings and the space of proper 3-colourings (among many non-symbolic examples) and answered questions by Robinson and Sahin. However extending the embedding to include the null set is a daunting task and there are many partial results towards this. Using tools developed by Gao, Jackson, Krohne and Seward, along with Spencer Unger we were able to get Borel embeddings of symbolic systems (as opposed to all Borel systems) under assumptions very similar to flexibility. This answers questions by Gao and Jackson and recovered some results announced by Gao, Jackson, Krohne and Seward.</p></div>Nishant Chandgotiahttp://math.huji.ac.il/~nishant/The Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7292021-02-11T10:57:46+02:002021-05-06T14:35:57+03:00<span class="mathjax">Tsachik Gelander: Infinite volume and infinite injectivity radius</span>May 6, 11:10—12:00, 2021, Online<div class="mathjax"><p>We prove the following conjecture of Margulis. Let M=Λ\G/K be a locally symmetric space where G is a simple Lie group of real rank at least 2. If M has infinite volume then it admits injected contractible balls of any radius. This generalizes the celebrated normal subgroup theorem of Margulis to the context of arbitrary discrete subgroups of G and has various other applications. We prove this result by studying random walks on the space of discrete subgroups of G and analysing the possible stationary limits.</p>
<p>This is a joint work with Mikolaj Fraczyk.</p></div> Tsachik Gelanderhttps://www.weizmann.ac.il/pages/search/people?language=english&single=1&person_id=48373Weizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/7302021-02-11T10:57:58+02:002021-05-13T12:38:01+03:00<span class="mathjax">Faustin Adiceam: Around the Danzer problem and the construction of dense forests.</span>May 13, 11:10—12:00, 2021, Online<div class="mathjax"><p>The still open Danzer problem (1965) asks for the existence of a set with finite density intersecting any convex body of volume one. It has so far attracted a considerable number of ideas revolving around many different areas (ergodic theory, probability, dynamical systems, Diophantine approximation, harmonic analysis, the theory of quasicrystals…).</p>
<p>After surveying the state of the art in this problem, we will focus our attention on the construction of so-called dense forests. These are discrete point sets emerging from the weakening of the volume constraint in Danzer’s question. The emphasis will be put on the effectiveness of such construction.</p>
<p>Based on joint work with Yaar Solomon and Barak Weiss.</p></div>Faustin Adiceamhttps://sites.google.com/site/fadiceammaths/The University of Manchestertag:www.math.bgu.ac.il,2005:MeetingDecorator/7322021-02-11T10:58:22+02:002021-05-20T21:35:19+03:00<span class="mathjax">Yiftach Dayan: Random walks on tori and an application to normality of numbers in self-similar sets.</span>May 20, 11:10—12:00, 2021, Online<div class="mathjax"><p>We show that under certain conditions, random walks on a d-dim torus by affine expanding maps have a unique stationary measure. We then use this result to show that given an IFS of contracting similarity maps of the real line with a uniform contraction ratio 1/D, where D is some integer > 1, under some suitable condition, almost every point in the attractor of the given IFS (w.r.t. a natural measure) is normal to base D. (Joint work with Arijit Ganguly and Barak Weiss.)</p></div>Yiftach DayanTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/7312021-02-11T10:58:08+02:002021-05-12T20:42:10+03:00<span class="mathjax">Doron Puder: TBA</span>May 27, 10:00—10:45, 2021, OnlineDoron Puderhttps://sites.google.com/site/doronpuder/Tel-Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7332021-02-11T10:58:47+02:002021-06-10T12:29:07+03:00<span class="mathjax">Daren Wei: Slow entropy of higher rank abelian unipotent actions</span>June 3, 11:10—12:00, 2021, Online<div class="mathjax"><p>We study slow entropy invariants for abelian unipotent actions U on any finite volume homogeneous space <span class="kdmath">$G/\Gamma$</span>. For every such action we show that the topological complexity can be computed directly from the dimension of a special decomposition of Lie(G) induced by Lie(U). Moreover, we are able to show that the metric complexity of the action coincides with its topological complexity, which provides a classification of these actions in isomorphic class. As a corollary, we obtain that the complexity of any abelian horocyclic action is only related to the dimension of G. This generalizes our previous rank one results from to higher rank abelian actions. This is a joint work with Adam Kanigowski, Philipp Kunde and Kurt Vinhage.</p></div>Daren Weihttps://sites.google.com/view/darenweimath/The Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7342021-02-11T10:58:59+02:002021-06-10T14:52:48+03:00<span class="mathjax">Henna Koivusalo: Linear repetitivity in polytopal cut and project sets</span>June 10, 11:10—12:00, 2021, Online<div class="mathjax"><p>Cut and project sets are aperiodic point patterns obtained by projecting an irrational slice of the integer lattice to a subspace. One way of classifying aperiodic sets is to study the number and repetition of finite patterns. Sets with patterns repeating linearly often, called linearly repetitive sets, can be viewed as the most ordered aperiodic sets. Repetitivity of a cut and project set depends on the slope and shape of the irrational slice. In an earlier work, joint with of Haynes and Walton, we showed that when the slice has a cube shape, linear repetitivity holds if and only if the following two conditions are satisfied: (i) the cut and project set has the minimal number of different finite patterns (minimal complexity), and (ii) the irrational slope satisfies a badly approximable condition. In a new joint work with Jamie Walton, we give a generalisation of this result to all convex polytopal shapes satisfying a mild geometric condition. A key step in the proof is a decomposition of the cut and project scheme, which allows us to make sense of condition (ii) for general polytopal windows.</p></div>Henna Koivusalohttps://people.maths.bris.ac.uk/~te20281/University of Bristoltag:www.math.bgu.ac.il,2005:MeetingDecorator/7352021-02-11T10:59:17+02:002021-06-24T14:40:04+03:00<span class="mathjax">Eitan Bachmat: Heaviest increasing subsequences and airplane boarding</span>June 24, 11:40—12:30, 2021, Physically (at building 32, class 111)<div class="mathjax"><p>We consider some conjectures (and a few results on maximal increasing subsequences) which are motivated by airplane boarding.</p></div>Eitan Bachmathttps://www.cs.bgu.ac.il/~ebachmat/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7912021-09-23T19:31:40+03:002021-10-22T21:58:12+03:00<span class="mathjax">Tattwamasi Amrutam: Intermediate subalgebras of commutative crossed products of discrete group actions.</span>October 21, 11:10—12:00, 2021, Building 34, room 14<div class="mathjax"><p>In this talk, we shall focus our attention on intermediate subalgebras of <span class="kdmath">$C(X)\rtimes_r\Gamma$</span> (and <span class="kdmath">$L^{\infty}(X,\nu)\ltimes\Gamma$</span>). We begin by describing the construction of the commutative crossed product <span class="kdmath">$C(X)\rtimes_r\Gamma$</span> and how the group contributes to its structure. We shall talk about various (generalized) averaging properties in this context. As a first application, we will show that every intermediate <span class="kdmath">$C^*$</span>-subalgebra <span class="kdmath">$\mathcal{A}$</span> of the form <span class="kdmath">$C(Y)\rtimes_r\Gamma\subseteq\mathcal{A}\subseteq C(X)\rtimes_r\Gamma$</span> is simple for an inclusion <span class="kdmath">$C(Y)\subset C(X)$</span> of minimal <span class="kdmath">$\Gamma$</span>-spaces whenever <span class="kdmath">$C(Y)\rtimes_r\Gamma$</span> is simple. We shall also show that, for a large class of actions of <span class="kdmath">$C^*$</span>-simple groups <span class="kdmath">$\Gamma\curvearrowright X$</span>, including non-faithful action of any hyperbolic group with trivial amenable radical, every intermediate <span class="kdmath">$C^*$</span>-algebra <span class="kdmath">$\mathcal{A}$</span>, <span class="kdmath">$C_r^*(\Gamma)\subset \mathcal{A}\subset C(X)\rtimes_r\Gamma$</span> is a crossed product of the form <span class="kdmath">$C(Y)\rtimes_r\Gamma$</span>, <span class="kdmath">$C(Y)\subset C(X)$</span> is an inclusion of <span class="kdmath">$\Gamma$</span>-<span class="kdmath">$C^*$</span>-algebras.</p></div>Tattwamasi Amrutamhttps://www.math.uh.edu/~tamrutam/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7932021-09-23T19:32:40+03:002021-11-04T15:56:27+02:00<span class="mathjax">Matan Tal: Bohr Chaos and Invariant Measures</span>November 4, 11:10—12:00, 2021, Building 34, room 14<div class="mathjax"><p>A topological dynamical system is said to be Bohr chaotic if for any bounded sequence it possesses a continuous function that correlates with the sequence when evaluated along some orbit. The theme of the lecture will be the relation of this property to an abundance of invariant measures of the system.</p></div>Matan TalThe Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7942021-09-23T19:34:54+03:002021-11-11T15:12:47+02:00<span class="mathjax">Matthieu Joseph: Allosteric actions of surface groups</span>November 11, 11:10—12:00, 2021, -101<div class="mathjax"><p>In a recent work, I introduced the notion of allosteric actions: a minimal action of a countable group on a compact space, with an ergodic invariant measure, is allosteric if it is topologically free but not essentially free. In the first part of my talk I will explain some properties of allosteric actions, and their links with Invariant Random Subgroups (IRS) and Uniformly Recurrent Subgroups (URS). In the second part, I will explain a recent result of mine: the fundamental group of a closed hyperbolic surface admits allosteric actions.</p></div>Matthieu Josephhttps://perso.ens-lyon.fr/matthieu.joseph/research.htmlÉcole normale supérieure de Lyontag:www.math.bgu.ac.il,2005:MeetingDecorator/7952021-09-23T19:35:04+03:002021-11-18T16:18:36+02:00<span class="mathjax">Anton Hase: Introduction to bounded cohomology</span>November 18, 11:10—12:00, 2021, Building 34, room 14<div class="mathjax"><p>While there are earlier works on bounded cohomology, the topic was popularized by Gromov in 1982. In this introductory talk, we will give definitions of bounded cohomology of discrete groups with trivial coefficients. We will interpret bounded cohomology in low degrees in terms of quasimorphisms and central extensions. Then we will mention a few examples of how bounded cohomology has proved useful in applications, before concentrating on the classification of circle actions</p></div>Anton HaseBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7972021-09-23T19:35:19+03:002021-10-31T08:32:32+02:00<span class="mathjax">Trip to the desert of the PET seminar group!!: TBA</span>November 25, 11:10—12:00, 2021, -101Trip to the desert of the PET seminar group!!tag:www.math.bgu.ac.il,2005:MeetingDecorator/7962021-09-23T19:35:12+03:002021-12-02T15:20:52+02:00<span class="mathjax">Olga Lukina: Stabilizers in group Cantor actions and measures</span>December 2, 11:10—12:00, 2021, -101<div class="mathjax"><p>Given a countable group G acting on a Cantor set X by transformations preserving a probability measure, the action is essentially free if the set of points with trivial stabilizers has a full measure. In this talk, we consider actions where no point has a trivial stabilizer, and investigate the properties of the points with non-trivial holonomy. We introduce the notion of a locally non-degenerate action, and show that if an action is locally non-degenerate, then the set of points with trivial holonomy has full measure in X. We discuss applications of this work to the study of invariant random subgroups, induced by actions of countable groups. This is joint work with Maik Gröger.</p></div>Olga Lukinahttps://sites.google.com/view/olgalukina/homeUniversity of Viennatag:www.math.bgu.ac.il,2005:MeetingDecorator/7982021-09-23T19:35:26+03:002021-12-09T13:05:16+02:00<span class="mathjax">Valérie Berthé: Symbolic discrepancy and Pisot dynamics</span>December 9, 11:10—12:00, 2021, -101<div class="mathjax"><p>Discrepancy is a measure of equidistribution for sequences of points. A bounded remainder set is a set with bounded discrepancy, that is, the number of times it is visited differs by the expected time only by a constant. We discuss dynamical, symbolic, and spectral approaches to the study of bounded remainder sets for Kronecker sequences. We consider in particular discrepancy
in the setting of symbolic dynamics and we discuss the existence of bounded remainder sets for some families of zero entropy subshifts.
Note that bounded discrepancy has also to do with the notion of bounded displacement to a lattice in the context of Delone sets. We focus on the case of Pisot parameters for toral translations and then show how to construct symbolic codings in terms of multidimensional continued fraction
algorithms.<br />
This is joint work with W. Steiner and J. Thuswaldner.</p></div>Valérie Berthéhttps://www.irif.fr/~berthe/Université de Paristag:www.math.bgu.ac.il,2005:MeetingDecorator/7992021-09-23T19:35:51+03:002021-12-18T11:40:57+02:00<span class="mathjax">Andreas Wieser: Linnik’s basic lemma with uniformity over the base field</span>December 16, 11:10—12:00, 2021, -101<div class="mathjax"><p>Long periodic geodesics on the unit tangent bundle of the modular surface are not necessarily equidistributed. However, there is a natural way to group finitely many geodesics together so that the so-obtained unions do equidistribute. This theorem (in this instance going back to Duke ‘88) is very well studied nowadays. In the talk, we discuss a dynamical approach due to Linnik through what is nowadays called Linnik’s basic lemma (providing in particular an entropy lower bound). We present here a new proof of Linnik’s basic lemma based on geometric invariant theory. This is joint work with Pengyu Yang.</p></div>Andreas Wieserhttps://people.math.ethz.ch/~awieser/aboutThe Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8002021-09-23T19:36:00+03:002021-11-28T10:56:11+02:00<span class="mathjax">: TBA</span>December 23, 11:10—12:00, 2021, -101tag:www.math.bgu.ac.il,2005:MeetingDecorator/8012021-09-23T19:36:06+03:002021-12-30T15:13:17+02:00<span class="mathjax">Philipp Kunde: Non-classifiability of ergodic flows up to time change</span>December 30, 11:10—12:00, 2021, -101Philipp Kundehttps://www.math.uni-hamburg.de/home/kunde/Universität Hamburg tag:www.math.bgu.ac.il,2005:MeetingDecorator/8022021-09-23T19:36:13+03:002022-01-06T14:55:54+02:00<span class="mathjax">Nadav Ben-David: The Ramanujan Machine: Polynomial Continued Fraction and Irrationality Measure</span>January 6, 11:10—12:00, 2022, Building 34, room 14<div class="mathjax"><p>Apéry’s proof of the irrationality of ζ(3) used a specific linear recursion that formed a Polynomial Continued Fraction (PCF). Similar PCFs can prove the irrationality of other fundamental constants such as 𝜋 and e. However, in general, it is not known which ones create useful Diophantine approximations and under what conditions they can be used to prove irrationality.
Here, we will present theorems and general conclusions about Diophantine approximations created from polynomial recursions. Specifically, we generalize Apéry’s work from his particular choice of PCF to any general PCF, finding the conditions under which a PCF can be used to prove irrationality or to provide an efficient Diophantine approximation. We further propose new conjectures about Diophantine approximations based on PCFs. Our study may contribute to ongoing efforts to answer open questions such as the proof of the irrationality of the Catalan constant or of values of the Riemann zeta function (e.g., ζ(5)).</p></div>Nadav Ben-Davidhttps://emet.net.technion.ac.il/2019/02/27/nadav-ben-david/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8032021-09-23T19:36:45+03:002022-01-15T18:46:42+02:00<span class="mathjax">Dan Rust: Substitutions on compact alphabets</span>January 13, 11:10—12:00, 2022, -101<div class="mathjax"><p>Substitutions and their subshifts are classical objects in symbolic dynamics representing some of the most well-studied and ‘simple’ aperiodic systems. Classically they are defined on finite alphabets, but it has recently become clear that a systematic study of substitutions on infinite alphabets is needed. I’ll introduce natural generalizations of classical concepts like legal words, repetitivity, primitivity, etc. in the compact Hausdorff setting, and report on new progress towards characterising unique ergodicity of these systems, where surprisingly, primitivity is not sufficient. As Perron-Frobenius theory fails in infinite dimensions, more sophisticated technology from the theory of positive (quasicompact) operators is employed. There are still lots of open questions, and so a ground-level introduction to these systems will hopefully be approachable and stimulating.</p>
<p>This is joint work with Neil Mañibo and Jamie Walton.</p></div>Dan Rusthttps://sites.google.com/view/danrust/The Open University (UK)tag:www.math.bgu.ac.il,2005:MeetingDecorator/8312021-11-08T21:01:04+02:002022-03-24T14:02:04+02:00<span class="mathjax">Elad Sayag: Entropy, ultralimits and Poisson boundaries</span>March 24, 11:10—12:00, 2022, -101<div class="mathjax"><p>In many important actions of groups there are no invariant measures. For example: the action of a free group on its boundary and the action of any discrete infinite group on itself. The problem we will discuss in this talk is ‘On a given action, how invariant measure can be?’. Our measuring of non-invariance will be based on entropy (f-divergence).
In the talk I will describe the solution of this problem for the free group acting on its boundary and on itself. For doing so we will introduce the notion of ultra-limit of G-spaces, and give a new description of the Poisson-Furstenberg boundary of (G,k) as an ultra-limit of G action on itself, with ‘Abel sum’ measures. Another application will be that amenable groups possess KL-almost-invariant measures (KL stands for the Kullback-Leibler divergence).</p>
<p>All relevant notions, including the notion of Poisson-Furstenberg boundary and the notion of ultra-filters will be explained during the talk.</p>
<p>This is a master thesis work under the supervision of Yehuda Shalom.</p></div>Elad SayagTel-Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8322021-11-08T21:01:13+02:002022-03-31T13:54:00+03:00<span class="mathjax">Annette Karrer: The rigidity of lattices in products of trees</span>March 31, 11:10—12:00, 2022, -101<div class="mathjax"><p>Each complete CAT(0) space has an associated topological space, called visual boundary, that coincides with the Gromov boundary in case that the space is hyperbolic. A CAT(0) group G is called boundary rigid if the visual boundaries of all CAT(0) spaces admitting a geometric action by G are homeomorphic. If G is hyperbolic, G is boundary rigid. If G is not hyperbolic, G is not always boundary rigid. The first such example was found by Croke-Kleiner.</p>
<p>In this talk we will see that every group acting freely and cocompactly on a product of two regular trees of finite valence is boundary rigid. That means that every CAT(0) space that admits a geometric action of any such group has the boundary homeomorphic to a join of two copies of the Cantor set. The proof of this result uses a generalization of classical dynamics on boundaries introduced by Guralnik and Swenson. I will explain the idea of this generalization by explaining a higher-dimensional version of classical North-south-dynamics obtained this way.</p>
<p>This is a joint work with Kasia Jankiewicz, Kim Ruane and Bakul Sathaye.</p></div>Annette KarrerTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/8332021-11-08T21:01:22+02:002022-03-31T13:52:45+03:00<span class="mathjax">: TBA</span>April 7, 11:10—12:00, 2022, -101tag:www.math.bgu.ac.il,2005:MeetingDecorator/8342021-11-08T21:05:52+02:002021-11-08T21:06:11+02:00<span class="mathjax">Holiday: Passover break</span>April 14, 11:10—12:00, 2022, -101Holidaytag:www.math.bgu.ac.il,2005:MeetingDecorator/8352021-11-08T21:06:23+02:002021-11-08T21:06:35+02:00<span class="mathjax">Holiday: Passover break</span>April 21, 11:10—12:00, 2022, -101Holidaytag:www.math.bgu.ac.il,2005:MeetingDecorator/8362021-11-08T21:06:43+02:002022-04-25T10:34:26+03:00<span class="mathjax">Chris Phillips: Mean dimension of an action and the radius of comparison of its C*-algebra</span>April 28, 11:10—12:00, 2022, -101<div class="mathjax"><p>For an action of a countable amenable group <span class="kdmath">$G$</span> on a compact metric
space <span class="kdmath">$X$</span>, the mean dimension <span class="kdmath">$mdim (G, X)$</span> was introduced by
Lindenstrauss and Weiss, for reasons unrelated to <span class="kdmath">$C^*$</span>-algebras. The
radius of comparison <span class="kdmath">$rc (A)$</span> of a <span class="kdmath">$C^*$</span>-algebra <span class="kdmath">$A$</span> was introduced by
Toms, for use on <span class="kdmath">$C^*$</span>-algebras having nothing to do with dynamics.</p>
<p>A construction called the crossed product <span class="kdmath">$C^* (G, X)$</span> associates a
<span class="kdmath">$C^*$</span>-algebra to a dynamical system. There is significant evidence for
the conjecture that <span class="kdmath">$rc ( C^* (G, X) ) = (1/2) mdim (G, X)$</span> when the
action is free and minimal. We give the first general partial results
towards the direction <span class="kdmath">$rc ( C^* (G, X) ) \geq (1/2) mdim (G, X)$</span>.
We don’t get the exact conjectured bound, but we get nontrivial
results for many of the known examples of free minimal systems with
<span class="kdmath">$mdim (G, X) > 0$</span>. The proof depends, among other things, on Cech
cohomology, and uses something we call the mean cohomological
independence dimension. Unlike the currently known results in the
other direction, it works for all choices of <span class="kdmath">$G$</span>.</p>
<p>The talk will include something about the crossed product
construction; no previous knowledge of it will be assumed.</p>
<p>This is joint work with Ilan Hirshberg.</p></div>Chris Phillipshttps://pages.uoregon.edu/ncp/University of Oregontag:www.math.bgu.ac.il,2005:MeetingDecorator/8382021-11-08T21:09:10+02:002021-11-08T21:09:37+02:00<span class="mathjax">Holiday: Yom Ha’Atzmaut</span>May 5, 11:10—12:00, 2022, -101Holidaytag:www.math.bgu.ac.il,2005:MeetingDecorator/8372021-11-08T21:06:56+02:002022-05-12T13:29:26+03:00<span class="mathjax">Ioannis Tsokanos: Density of oscillating sequences in the real line</span>May 12, 11:10—12:00, 2022, -101<div class="mathjax"><p>In this talk, we study the density properties in the real line of oscillating sequences of the form
<span class="kdmath">$( g(k) \cdot F(kα) )_{k \in \mathbb{N}}$</span>,
where <span class="kdmath">$g$</span> is a positive increasing function and <span class="kdmath">$F$</span> a real continuous <span class="kdmath">$1$</span>-periodic function.
This extends work by Berend, Boshernitzan and Kolesnik who established differential properties on the function F ensuring that the oscillating sequence is dense modulo 1.</p>
<p>More precisely, when <span class="kdmath">$F$</span> has finitely many roots in <span class="kdmath">$[0,1)$</span>, we provide necessary and sufficient conditions for the oscillating sequence under consideration to be dense in <span class="kdmath">$\mathbb{R}$</span>. All the related results are stated in terms of the Diophantine properties of <span class="kdmath">$α$</span>, with the help of the theory of continued fractions.</p></div>Ioannis Tsokanoshttps://sites.google.com/view/ioannis-tsokanosThe University of Manchestertag:www.math.bgu.ac.il,2005:MeetingDecorator/8392021-11-08T21:10:03+02:002022-05-19T15:19:46+03:00<span class="mathjax">Arie Levit: Characters of groups, stability and sofic dynamical systems</span>May 19, 11:10—12:00, 2022, -101<div class="mathjax"><p>We study the character theory of infinite solvable groups, focusing on the metabelian and polycyclic cases. This theory has applications towards the Hilbert-Schmidt stability of such groups - whether almost-homomorphisms into the unitary groups U(n) are nearby honest homomorphisms? We explore an interesting link between stability and topological dynamics via a notion of “sofic dynamical systems”. I will introduce all relevant notions.</p>
<p>The talk is based on a joint work with Itamar Vigdorovich.</p></div>Arie Levithttps://sites.google.com/site/arielevit/Tel-Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8402021-11-08T21:10:13+02:002022-05-23T09:55:37+03:00<span class="mathjax">Shrey Sanadhya: Universality for R^d-flows</span>May 26, 11:10—12:00, 2022, -101<div class="mathjax"><p>A dynamical system is called universal if any system with lower entropy can be embedded into it. In this talk, we will discuss universality for <span class="kdmath">$R^d$</span> flows <span class="kdmath">$(d>1)$</span> both in ergodic and Borel contexts. We will discuss a specification property that implies universality for <span class="kdmath">$R^d$</span> flows and provide an example of a tiling dynamical system with this specification property. This is ongoing work with Tom Meyerovitch. This talk is a preliminary report.</p></div>Shrey SanadhyaBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8412021-11-08T21:10:20+02:002022-06-02T13:32:47+03:00<span class="mathjax">Adam Śpiewak: Probabilistic Takens time-delay embeddings</span>June 2, 11:10—12:00, 2022, room 106, building 28<div class="mathjax"><p>Consider a dynamical system (X,T) consisting of a compact set X in the Euclidean space and a transformation T on X. Takens-type time-delay embedding theorems state that for a generic real-valued observable h on X, one can reconstruct uniquely the initial state x of the system from a sequence of values of h(x), h(Tx), …, h(T^{k-1} x), provided that k is large enough. In the deterministic setting, the number of measurements k has to be at least twice the dimension of the state space X. This was proved in several categories and can be seen as dynamical versions of the classical (non-dynamical) embedding theorems. We provide a probabilistic counterpart of this theory, in which one is interested in reconstructing almost every state x, subject to a given probability measure. We prove that in this setting it suffices to take k greater than the Hausdorff dimension of the considered measure, hence reducing the number of measurements at least twice. Using this, we prove a related conjecture of Shroer, Sauer, Ott and Yorke in the ergodic case. We also construct an example showing that the conjecture does not hold in its original formulation. This is based on joint works with Krzysztof Barański and Yonatan Gutman.</p></div>Adam Śpiewakhttps://adamspiewak.wordpress.com/Bar-Ilan Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8422021-11-08T21:10:28+02:002022-06-13T21:42:12+03:00<span class="mathjax">Edgar Bering: Topological models of abstract commensurators</span>June 9, 11:10—12:00, 2022, room 106, building 28<div class="mathjax"><p>Given a group G, an Eilenberg-MacLane space X = K(G,1) provides a topological model of both G and Aut(G). The latter is understood via Whitehead’s theorem as the group of pointed homotopy equivalences of X up to homotopy. When X has rich structure, such as the case of a closed surface group, this point of view leads to a rich understanding of Aut(G). Motivated by dynamics and mathematical physics, Biswas, Nag, and Sullivan initiated the study of the universal hyperbolic solenoid, the inverse limit of all finite covers of a closed surface of genus at least two. Following their work, Odden proved that the mapping class group of the universal hyperbolic solenoid is isomorphic to the abstract commensurator of a closed surface group. In this talk I will present a general topological analog of Odden’s theorem, realising Comm(G) as a group of homotopy equivalences of a space for any group of type F. I will then use this realisation to classify the locally finite subgroups of the abstract commensurator of a finite-rank free group. This is joint work with Daniel Studenmund.</p></div>Edgar BeringTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/8432021-11-08T21:11:22+02:002022-06-21T12:28:40+03:00<span class="mathjax">Anton Hase: (Non-)Integrability of quaternion-Kähler symmetric spaces</span>June 16, 11:10—12:00, 2022, room 106, building 28<div class="mathjax"><p>It is a famous result of Harish-Chandra that every non-compact Hermitian symmetric space can be realized as a bounded domain in a complex vector spaces. If we replace the complex numbers by the division algebra of quaternions in the definition of Hermitian symmetric spaces, we obtain the class of quaternion-Kähler symmetric spaces. While these spaces emerge in an analogous way, we show that there is no quaternionic analogue of Harish-Chandra’s embedding theorem: A quaternion-Kähler symmetric space is integrable if and only if it is a quaternionic vector space, quaternionic hyperbolic space or quaternionic projective space. In the talk I will explain some of the background and some of the tools used in the proof.</p></div>Anton HaseBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8442021-11-08T21:11:29+02:002022-06-23T12:45:36+03:00<span class="mathjax">Daniel Ingebretson: Hausdorff and packing measure of some decimal and Luroth expansions</span>June 23, 11:10—12:00, 2022, room 106, building 28<div class="mathjax"><p>A common method for quantifying the size of sets of Lebesgue measure zero is via Hausdorff or packing dimension. A more delicate question is to determine the value of the corresponding Hausdorff or packing measure at dimension. In this talk we will show a way to approach this question for some simple fractal sets arising from numeration systems.</p></div>Daniel Ingebretsonhttps://sites.google.com/view/dingebretson/Ben-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8682022-03-14T09:59:23+02:002022-06-30T13:49:35+03:00<span class="mathjax">Maksim Zhukovskii: Extremal independence in discrete random systems</span>June 30, 11:10—12:00, 2022, room 106, building 28<div class="mathjax"><p>Let G be a graph with several vertices v_1,..,v_r being roots. A G-extension of u_1,..,u_r in a graph H is a subgraph G* of H such that there exists a bijection from V(G) to V(G*) that maps v_i to u_i and preserves edges of G with at least one non-root vertex. It is well known that, in dense binomial random graphs, the maximum number of G-extensions obeys the law of large numbers. The talk is devoted to new results describing the limit distribution of the maximum number of G-extensions. To prove these results, we develop new bounds on the probability that none of a given finite set of events occur. Our inequalities allow us to distinguish between weakly and strongly dependent events in contrast to well-known Janson’s and Suen’s inequalities as well as Lovasz Local Lemma. These bounds imply a general result on the convergence of maxima of dependent random variables.</p></div>Maksim Zhukovskiihttps://combgeo.org/en/members/maksim-zhukovskii/Weizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/8972022-08-07T10:31:36+03:002022-10-25T08:40:17+03:00<span class="mathjax">Nishant Chandgotia: The Dimer Model in 3 dimensions</span>October 27, 11:10—12:00, 2022, -101<div class="mathjax"><p>The dimer model, also referred to as domino tilings or perfect matching, are tilings of the <span class="kdmath">$Z^d$</span> lattice by boxes exactly one of whose sides has length 2 and the rest have length 1. This is a very well-studied statistical physics model in two dimensions with many tools like height functions and Kasteleyn determinant representation coming to its aid. The higher dimensional picture is a little daunting because most of these tools are limited to two dimensions. In this talk I will describe what techniques can be extended to higher dimensions and give a brief account of a large deviations principle for dimer tilings in three dimensions that we prove analogous to the results by Cohn, Kenyon and Propp (2000).</p>
<p>This is joint work with Scott Sheffield and Catherine Wolfram.</p></div>Nishant Chandgotiahttps://nishantchandgotia.github.io/Tata Institute of Fundamental Research - Centre for Applicable Mathematicstag:www.math.bgu.ac.il,2005:MeetingDecorator/8982022-08-07T10:31:52+03:002022-10-30T12:28:33+02:00<span class="mathjax">Tomas Persson: Recurrence</span>November 3, 11:10—12:00, 2022, Room 303 in building 28 (or via zoom)<div class="mathjax"><p>Recurrence is a classical topic in ergodic theory and
dynamical systems, which goes back to Poincaré’s recurrence theorem. I
will talk about old, less old, and new results on recurrence. In
particular, I will talk about how to obtain asymptotic results on the
number of times a typical point returns to a shrinking neighbourhood
around itself.</p></div>Tomas Perssonhttps://www.maths.lth.se/matematiklth/personal/tomasp/Lund Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8992022-08-07T10:32:27+03:002022-10-25T08:40:31+03:00<span class="mathjax">Jean-Pierre Conze: Sampling a random field along a stationary process, related questions in ergodic theory</span>November 10, 11:10—12:00, 2022, -101Jean-Pierre Conzehttps://perso.univ-rennes1.fr/jean-pierre.conze/French National Centre for Scientific Researchtag:www.math.bgu.ac.il,2005:MeetingDecorator/9002022-08-07T10:33:08+03:002022-11-13T09:39:50+02:00<span class="mathjax">Michel Abramoff: Generalizations of Furstenberg’s ×2 × 3 Theorem</span>November 17, 11:10—12:00, 2022, -101Michel AbramoffBen-Gurion Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9012022-08-07T10:33:21+03:002022-11-20T16:14:19+02:00<span class="mathjax">Nachi Avraham: Stable processes indexed by amenable groups: from probability to non-singular ergodic theory</span>November 24, 11:10—12:00, 2022, -101<div class="mathjax"><p>Stable processes is an important class of stochastic processes, including Gaussian processes, Cauchy processes and Levy processes. In an analogy to that the ergodicity of a Gaussian process is determined by the spectral measure, it was shown by Rosinski and Samorodnitsky that the ergodicity of a stationary symmetric stable process is characterized by its spectral representation. While this result was known when the process is indexed by <span class="kdmath">$\mathbb{Z}^d$</span> or <span class="kdmath">$\mathbb{R}^d$</span>, the classical techniques fail when it comes to non-Abelian groups and it was an open question whether the ergodicity of such processes admits a similar characterization.</p>
<p>In this talk I will introduce the fundamentals of stable processes, the ergodic theory behind their spectral representation, and the key ideas of the characterization of the ergodicity for processes indexed by amenable groups. If time permits, I will mention recent results in non-singular ergodic theory that allow the constructions of weakly-mixing but not strongly-mixing stable processes indexed by many groups (Abelian groups, Heisenberg group).</p></div>Nachi Avrahamhttps://www.nachi.co.il/homeThe Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9022022-08-07T10:33:31+03:002022-11-28T14:55:36+02:00<span class="mathjax">Mélodie Andrieu: Remarkable symbolic dynamical systems associated with some multidimensional continued fraction algorithms</span>December 1, 11:10—12:00, 2022, -101Mélodie Andrieuhttp://www.i2m.univ-amu.fr/perso/andrieu-es.m/Bar-Ilan Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9032022-08-07T10:33:54+03:002022-12-04T17:06:32+02:00<span class="mathjax">Noy Soffer Aranov: Minkowski’s Conjecture in Function Fields</span>December 8, 11:10—12:00, 2022, -101<div class="mathjax"><p>A fascinating question in the geometry of numbers and diophantine approximation pertains to the maximal covering radius of a lattice with respect to a fixed function. An important covering radius is the multiplicative covering radius, since it is invariant under the diagonal group and relates to the Littlewood’s conjecture. Minkowski conjectured that the multiplicative covering radius of a unimodular lattice in <span class="kdmath">$R^d$</span> is bounded by above by <span class="kdmath">$1/2^d$</span> and that this upper bound is unique to the diagonal orbit of the standard lattice. Minkowski’s conjecture is known to be true for <span class="kdmath">$d\leq 10$</span>, yet there isn’t a general proof for higher dimensions.</p>
<p>In this talk, I will discuss the function field (positive characteristic) analogue of Minkowski’s conjecture, which we stated and proved for every dimension. The proofs and the results are surprisingly different from the real case and have implications in geometry of numbers and dynamics. This talk is based on joint work with Uri Shapira.</p></div>Noy Soffer AranovTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/9042022-08-07T10:34:07+03:002022-12-11T08:52:57+02:00<span class="mathjax">Or Shalom: Structure theorem for the Gowers-Host-Kra seminorms</span>December 15, 11:10—12:00, 2022, -101<div class="mathjax"><p>Szemeredi’s theorem asserts that in every subset of the natural numbers of positive density one can find an arithmetic progression of arbitrary length. In 2001, Gowers gave a quantitative proof for this theorem. A key definition in his work are the Gowers norms which measure the randomness of subsets of the natural numbers. Inspired by Furstenberg’s ergodic theoretical proof of Szemeredi’s theorem, Gowers proved the following dichotomy: Either the given set is close to a random set with respect to these norms, or it admits some algebraic structure. Gowers then proved that in each of these cases Szemeredi’s theorem holds. Later, Host and Kra studied the structure of certain ergodic systems associated with an infinitary version of the Gowers norms. Inspired by their work, Green, Tao and Ziegler improved Gowers’ structure theorem showing that a function (or a set) with large Gowers norm must correlate with a nilsequence. This result is known as the inverse theorem for the Gowers norms. Recently, Jamneshan and Tao proved (roughly speaking) that a generalization of the Host-Kra theorem for ergodic systems associated with actions of the largest countable abelian group <span class="kdmath">$\mathbb{Z}^\omega$</span> will imply the most general version of the inverse theorem for the Gowers norms. In this talk I will survey the above in more detail and mention some recent developments about these structure theorems.</p></div>Or Shalomhttp://www.math.huji.ac.il/~orshalom/Institute of advanced studiestag:www.math.bgu.ac.il,2005:MeetingDecorator/9052022-08-07T10:34:14+03:002022-12-19T14:53:04+02:00<span class="mathjax">Guy Blachar: Probabilistic Laws on Groups</span>December 22, 11:10—12:00, 2022, -101<div class="mathjax"><p>Suppose a finite group satisfies the following property: If you take two random elements, then with probability bigger than 5/8 they commute. Then this group is commutative.
Starting from this well-known result, it is natural to ask: Do similar results hold for other laws (p-groups, nilpotent groups…)? Are there analogous results for infinite groups? Are there phenomena specific to the infinite setup?
We will survey known and new results in this area. New results are joint with Gideon Amir, Maria Gerasimova and Gady Kozma.</p></div>Guy Blacharhttps://math.biu.ac.il/node/1936Bar-Ilan Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9062022-08-07T10:34:23+03:002022-12-13T09:37:07+02:00<span class="mathjax">Action Now day in Tel-Aviv: The seminar is cancelled</span>December 29, 11:10—12:00, 2022, -101Action Now day in Tel-Avivtag:www.math.bgu.ac.il,2005:MeetingDecorator/9072022-08-07T10:34:36+03:002023-01-02T22:40:40+02:00<span class="mathjax">Yotam Smilansky: Classification and statistics of cut-and-project sets</span>January 5, 11:10—12:00, 2023, -101<div class="mathjax"><p>Cut-and-project point sets are constructed by identifying a strip of a fixed n-dimensional lattice (the “cut”), and projecting the lattice points in that strip to a d-dimensional subspace (the “project”). Such sets have a rich history in the study of mathematical models of quasicrystals, and include well-known examples such as the Fibonacci chain and vertex sets of Penrose tilings. Dynamical results concerning the translation action on the hull of a cut-and-project set are known to shed light on certain properties of the point set itself, but what happens when instead of restricting to translations we consider all volume preserving linear actions?</p>
<p>A homogenous space of cut-and-project sets is defined by fixing a cut-and-project construction and varying the n-dimensional lattice according to an SL(d,R) action. In the talk, which is based on joint work with René Rühr and Barak Weiss, I will discuss this construction and introduce the class of Ratner-Marklof-Strömbergsson measures, which are probability measures supported on cut-and-project spaces that are invariant and ergodic for the group action. A classification of these measures is described in terms of data of algebraic groups, and is used to prove analogues of results about a Siegel summation formula and identities and bounds involving higher moments. These in turn imply results about asymptotics, with error estimates, of point-counting and patch-counting statistics for typical cut-and-project sets.</p></div>Yotam Smilanskyhttps://sites.math.rutgers.edu/~smilansky/Rutgers Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9082022-08-07T10:34:42+03:002023-01-05T15:45:29+02:00<span class="mathjax">Arielle Leitner: An Advertisement for Coarse Groups and Coarse Geometry</span>January 12, 11:10—12:00, 2023, -101<div class="mathjax"><p>Coarse structures are used to study the large scale geometry of a space. For example, although the integers and the real line are different topologically, they look the same from “far away”, in the sense that any geometric configuration in the real line can be approximated by one in the integers, up to some uniformly bounded error. A coarse group is a group object in the category of coarse spaces, for example, this means the group operation is only “coarsely associative,” etc. In joint work with Federico Vigolo we study coarse groups. This talk will be an advertisement for our work, as we walk through examples that illustrate some of our main results, and connections to other subjects.</p></div>Arielle Leitnerhttps://www.wisdom.weizmann.ac.il/~ariellel/Weizmann Institute and Afeka College of Engineeringtag:www.math.bgu.ac.il,2005:MeetingDecorator/9092022-08-07T10:34:49+03:002023-01-14T21:54:01+02:00<span class="mathjax">Anurag Rao: Dynamical questions arising from Dirichlet’s theorem on Diophantine approximation</span>January 19, 11:10—12:00, 2023, -101<div class="mathjax"><p>We study the notion of Dirichlet improvability in a variety of settings and make a comparison study between Dirichlet-improvable numbers and badly-approximable numbers as initiated by Davenport-Schmidt. The question we try to answer, in each of the settings, is – whether the set of badly-approximable numbers is contained in the set of Dirichlet-improvable numbers. We show how this translates into a question about the possible limit points of bounded orbits in the space of two-dimensional lattices under the diagonal flow. Our main result gives a construction of a full Hausdorff dimension set of lattices with bounded orbit and with a prescribed limit point. Joint work with Dmitry Kleinbock.</p></div>Anurag RaoTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/9712023-02-02T14:44:07+02:002023-02-20T10:00:16+02:00<span class="mathjax">El Houcein El Abdalaoui: SEMINAR POSTPONED TO APRIL 20th: Mixing sequences for non-mixing locally compact Abelian groups actions</span>February 23, 11:10—12:00, 2023, -101<div class="mathjax"><p>Mixing is an important spectral property of dynamical systems and it can be described concretely. But, “In general a measure preserving transformation is” only “mixing” along a sequence of density one, by the Rhoklin-Halmos theorem. On the other hand, mixing on some sequences implies mixing. Formally, the mixing can be defined by demanding that the ergodic averages along any increasing sequence converge in mean, thanks to the Blum-Hanson theorem. In my talk, I will present my recent joint contribution with Terry Adams to Bergelson’s question asked online during the Lille conference 2021: Does mixing on the squares imply mixing?
We first obtain a characterization of a sequence for which mixing on it implies mixing. We further establish that there are non-mixing maps that are mixing on appropriate sequences. We extend also our results to the group action with the help of the Host-Parreau characterization of the set of continuity from Harmonic Analysis. We further extended our result to the Real line action. As a open question, we ask pour extension our our result to the case of non-commutative case and specially Heisenberg group action.</p></div>El Houcein El Abdalaouihttp://elabdalaoui.perso.math.cnrs.fr/CNRS-Université de Rouentag:www.math.bgu.ac.il,2005:MeetingDecorator/9542023-01-02T23:00:59+02:002023-03-07T09:19:29+02:00<span class="mathjax">Noam Kolodner: A representation of Out(Fn) by counting subwords of cyclic words</span>March 16, 11:10—12:00, 2023, -101<div class="mathjax"><p>We generalize the combinatorial approaches of Rapaport and
Higgins–Lyndon to the Whitehead algorithm. We show that for every
automorphism φ of a free group F and every word u∈F there exists a
finite multiset of words Su,φ satisfying the following property: For
every cyclic word w, the number of times u appears as a subword of
φ(w) depends only on the appearances of words in Su,φ as subwords of
w. We use this fact to construct a faithful representation of Out(Fn)
on an inverse limit of Z-modules, so that each automorphism is
represented by sequence of finite rectangular matrices, which can be
seen as successively better approximations of the automorphism.</p></div> Noam KolodnerTel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9532023-01-02T23:00:21+02:002023-03-06T15:03:19+02:00<span class="mathjax">Andrei Alpeev: Amenability is equivalent to the invariant random order extension property on groups</span>March 16, 14:00—15:00, 2023, -101<div class="mathjax"><p>Classical Szpilrajn theorem states that any partial order could be extended to a linear order.
An invariant random order (IRO) on a countable group is an invariant under the shift-action probability measure on the space of all partial orders on the group.
It is natural to ask whether the invariant analog of Szpilrajn theorem, the invariant random order extension property, holds for IRO’s. This property is easy to demonstrate for amenable groups. Recently, Glasner, Lin a Meyerovitch gave a first example where this property fails. Based on their construction, I will show that the IRO extension property fails for all non-amenable groups.</p></div>Andrei AlpeevThe Weizmann Institute of Sciencetag:www.math.bgu.ac.il,2005:MeetingDecorator/9552023-01-02T23:01:11+02:002023-03-23T08:41:37+02:00<span class="mathjax">Yuval Yifrach: Postponed for later in the semester: Approximation of Diagonally Invariant measure by Tori Measures.</span>March 23, 11:10—12:00, 2023, -101<div class="mathjax"><p>We consider the family of periodic measures for the full diagonal action on the space of unimodular lattices. This family is important and natural due to its tight relation to class groups in number fields. We show that many natural families of measures on the space of lattices can be approximated using this family (in the weak sense). E.g., we show that for any 0<c\leq 1, the measure cm_{X_n} can be approximated this way, where m_{X_n} denotes the Haar probability measure on X_n. Moreover, we show that non ergodic measures can be approximated. Our proof is based on the equidistribution of Hecke neighbors and on constructions of special number fields. We will discuss the results, alternative ways to attack the problem, and our method of proof.
This talk is based on a joint work with Omri Solan.</p></div>Yuval YifrachTechnion - Israel Institute of Technologytag:www.math.bgu.ac.il,2005:MeetingDecorator/9562023-01-02T23:01:17+02:002023-03-25T10:31:52+03:00<span class="mathjax">Thomas Ng: Actions of random quotients on hyperbolic CAT(0) cube complexes</span>March 30, 11:10—12:00, 2023, -101<div class="mathjax"><p>Combinatorial nonpositive curvature of CAT(0) cube complexes plays a surprising role both in topological characterization of hyperbolic 3-manifolds and also in studying algebraic properties of random groups.<br />
With Einstein, Krishna MS, Montee, and Steenbock, we introduce a new model for random quotients of free products that generalizes Gromov’s destiny model. I will discuss challenges that arise in this new setting, connections to work of Futer-Wise and Martin-Steenbock on cubulating quotients, as well as applications to residual finiteness using recent work of Einstein and Groves on relative cubulation.</p></div>Thomas Nghttps://sites.google.com/site/thomasng192/Technion - Israel Institute of Technologytag:www.math.bgu.ac.il,2005:MeetingDecorator/9572023-01-02T23:01:54+02:002023-01-02T23:02:58+02:00<span class="mathjax">Passover break: Passover break</span>April 6, 11:10—12:00, 2023, -101Passover breaktag:www.math.bgu.ac.il,2005:MeetingDecorator/9582023-01-02T23:02:24+02:002023-04-08T17:55:45+03:00<span class="mathjax">Nir Lazarovich: Finite index rigidity</span>April 13, 11:10—12:00, 2023, -101<div class="mathjax"><p>We show that isomorphic finite index subgroups of non-elementary hyperbolic groups must have the same index. In this talk I will present the tools and ideas of the proof.</p></div> Nir Lazarovichhttps://lazarovich.net.technion.ac.il/Technion - Israel Institute of Technologytag:www.math.bgu.ac.il,2005:MeetingDecorator/9592023-01-02T23:02:47+02:002023-02-20T09:58:28+02:00<span class="mathjax">El Houcein El Abdalaoui: Mixing sequences for non-mixing locally compact Abelian groups actions</span>April 20, 11:10—12:00, 2023, -101<div class="mathjax"><p>Mixing is an important spectral property of dynamical systems and it can be described concretely. But, “In general a measure preserving transformation is” only “mixing” along a sequence of density one, by the Rhoklin-Halmos theorem. On the other hand, mixing on some sequences implies mixing. Formally, the mixing can be defined by demanding that the ergodic averages along any increasing sequence converge in mean, thanks to the Blum-Hanson theorem. In my talk, I will present my recent joint contribution with Terry Adams to Bergelson’s question asked online during the Lille conference 2021: Does mixing on the squares imply mixing? We first obtain a characterization of a sequence for which mixing on it implies mixing. We further establish that there are non-mixing maps that are mixing on appropriate sequences. We extend also our results to the group action with the help of the Host-Parreau characterization of the set of continuity from Harmonic Analysis. We further extended our result to the Real line action. As a open question, we ask pour extension our our result to the case of non-commutative case and specially Heisenberg group action.</p></div>El Houcein El Abdalaouihttps://lmrs.univ-rouen.fr/fr/persopage/el-houcein-el-abdalaouiCNRS-Université de Rouen Normandietag:www.math.bgu.ac.il,2005:MeetingDecorator/9602023-01-02T23:03:19+02:002023-04-20T14:22:14+03:00<span class="mathjax">Zemer Kosloff: (alpha Stable) CLT in deterministic dynamical systems</span>April 27, 11:10—12:00, 2023, -101<div class="mathjax"><p>We will discuss a joint work with Dalibor Volny where we show that for every ergodic and aperiodic probability preserving transformation and α∈(0,2) there exists a function whose associated time series is in the standard domain of attraction of a non-degenerate symmetric α-stable distribution.</p></div>Zemer Kosloffhttps://math.huji.ac.il/~zemkos/The Hebrew University of Jerusalemtag:www.math.bgu.ac.il,2005:MeetingDecorator/9612023-01-02T23:03:45+02:002023-04-29T13:57:13+03:00<span class="mathjax">Daren Wei: Time change for unipotent flows and rigidity</span>May 4, 11:10—12:00, 2023, -101<div class="mathjax"><p>Two flows are said to be Kakutani equivalent if one is isomorphic to the other after time change, or equivalently if there are Poincare sections for the flows so that the respective induced maps are isomorphic to each other. Ratner showed that if $G=\operatorname{SL}(2,\mathbb{R})$ and $\Gamma$ is a lattice in $G$, and if $u_t$ is a one parameter unipotent subgroup in $G$ then the $u_t$ action on $G/\Gamma$ equipped with Haar measure is loosely Bernoulli, i.e.\ Kakutani equivalent to a circle rotation. Thus any two such systems $(\operatorname{SL}(2,\mathbb{R})/\Gamma_i, u_t, m_i)$ are Kakutani equivalent to each other. On the other hand, Ratner showed that if $G=\operatorname{SL}(2,\mathbb{R})\times \operatorname{SL}(2,\mathbb{R})$ and $\Gamma$ is a reducible lattice, and $u_t$ is the diagonally embedded one parameter unipotent subgroup in $G$, then $(G/\Gamma, u_t, m)$ is not loosely Bernoulli.</p>
<p>We show that in fact in this case and many other situations one cannot have Kakutani equivalence between such systems unless they are actually isomorphic.</p>
<p>This is a joint work with Elon Lindenstrauss.</p></div>Daren Weihttps://sites.google.com/view/darenweimath/The Hebrew University of Jerusalemtag:www.math.bgu.ac.il,2005:MeetingDecorator/9912023-04-20T14:25:58+03:002023-04-30T05:53:52+03:00<span class="mathjax">Vsevolod L. Chernyshev: Random walks on metric graphs and related problems from analytic number theory</span>May 4, 14:00—15:00, 2023, -101<div class="mathjax"><p>I will discuss a random walk on a metric graph, that is, on a one-dimensional cell complex. The main difference from the often considered case is that the endpoint of a walk can be any point on an edge of a metric graph and not just one of the vertices. Let a point start its motion along the path graph from a hanging vertex at the initial moment of time. The passage time for each individual edge is fixed. At each vertex, the point selects one of the edges for further movement with some nonzero probability. Backward turns on the edges are prohibited in this model. One could find asymptotics for the number N(T) of possible endpoints of such a random walk as the time T increases, i.e. number of all possible lengths of paths on metric graph that not exceed T. Solutions to this problem, depending on the type of graph, are associated with different problems of number theory. An overview of the results, which depend on the arithmetic properties of lengths, will be given as well as review of open problems.</p></div>Vsevolod L. Chernyshevhttps://www.hse.ru/en/org/persons/35919212National Research University Higher School of Economicstag:www.math.bgu.ac.il,2005:MeetingDecorator/9622023-01-02T23:03:55+02:002023-05-05T14:04:57+03:00<span class="mathjax">Petr Naryshkin: Borel asymptotic dimension for boundary actions of hyperbolic groups</span>May 11, 11:10—12:00, 2023, -101<div class="mathjax"><p>We show that the orbit equivalence relation of an action of a hyperbolic group on its Gromov boundary has finite Borel asymptotic dimension. As a corollary, that recovers the theorem of Marquis and Sabok which states that this orbit equivalence relation is hyperfinite.</p></div>Petr Naryshkinhttps://petrnaryshkin.com/WWU Münstertag:www.math.bgu.ac.il,2005:MeetingDecorator/9922023-04-20T14:28:10+03:002023-05-05T14:01:57+03:00<span class="mathjax">Sergey Komech: Geometric approach to the Kolmogorov entropy</span>May 11, 14:00—15:00, 2023, -101<div class="mathjax"><p>A connection between the deformation rate of a small set boundary in the phase space of a dynamical system and the metric entropy of the system was claimed (not too rigorously) in physics literature.</p>
<p>Rigorous results were obtained by B. Gurevich for discrete time Markov shifts and later generalized for synchronized systems by me. Further, such a connection was established in joint work by B.
Gurevich and S. Komech for Anosov diffeomorphisms, and for suspension flows in joint work by B. Gurevich, S. Komech and A. Tempelman. For symbolic dynamical systems, we estimate deformation rate in terms of an ergodic invariant measure, while for Anosov systems we use the volume. We will present specific details of our approach.</p></div>Sergey Komechhttp://iitp.ru/en/users/195.htmThe Institute for Information Transmission Problemstag:www.math.bgu.ac.il,2005:MeetingDecorator/9632023-01-02T23:04:01+02:002023-05-14T12:47:33+03:00<span class="mathjax">Jon Aaronson: Inner functions revisited</span>May 18, 11:10—12:00, 2023, -101<div class="mathjax"><p>An analytic endomorphism of the unit disk is called an inner function if it’s boundary limit defines a transformation of the circle - which is necessarily Lebesgue nonsingular. I’ll review the ergodic theory of inner functions & then present results on:</p>
<p>– their structure;</p>
<p>– spectral gaps for their transfer operators; and</p>
<p>– a conditional central limit theorem;</p>
<p>all recently obtained with Mahendra Nadkarni.</p></div>Jon Aaronsonhttp://www.math.tau.ac.il/~aaro/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9642023-01-02T23:04:07+02:002023-01-02T23:04:30+02:00<span class="mathjax">Shavuot - holiday: Shavuot - holiday</span>May 25, 11:10—12:00, 2023, -101Shavuot - holidaytag:www.math.bgu.ac.il,2005:MeetingDecorator/9652023-01-02T23:04:39+02:002023-05-29T08:18:15+03:00<span class="mathjax">Yuval Yifrach: Approximation of Diagonally Invariant measure by Tori Measures</span>June 1, 11:10—12:00, 2023, -101<div class="mathjax"><p>We consider the family of periodic measures for the full diagonal action on the space of unimodular lattices. This family is important and natural due to its tight relation to class groups in number fields. We show that many natural families of measures on the space of lattices can be approximated using this family (in the weak sense). E.g., we show that for any 0<c\leq 1, the measure cm_{X_n} can be approximated this way, where m_{X_n} denotes the Haar probability measure on X_n. Moreover, we show that non ergodic measures can be approximated. Our proof is based on the equidistribution of Hecke neighbors and on constructions of special number fields. We will discuss the results, alternative ways to attack the problem, and our method of proof.
This talk is based on a joint work with Omri Solan.</p></div>Yuval YifrachTechnion - Israel Institute of Technologytag:www.math.bgu.ac.il,2005:MeetingDecorator/9662023-01-02T23:04:46+02:002023-06-05T13:19:21+03:00<span class="mathjax">Itamar Vigdorovich: The simplex of Traces of a Group (or of a C*-Algebra)</span>June 8, 11:10—12:00, 2023, -101<div class="mathjax"><p>To any group, and more generally a C*-algebra, is associated its simplex of traces. The extreme points are called characters, which are a central notion in harmonic analysis. For a Kazhdan group, the simplex of traces is Bauer - the extreme points are closed. For the free group Fn the simplex of traces is Poulsen - the extreme points are dense. What about the simplex of Out(Fn)-invariant traces on Fn (n>3)? Is it Bauer, Poulsen or something in between? What about free products of finite groups, and free product of matrix algebras? Some answers and proofs will be provided, after an introduction on traces and characters.
The talk is based on works with Levit, Orovitz and Slutsky.</p></div>Itamar VigdorovichWeizmann Institute of Sciencetag:www.math.bgu.ac.il,2005:MeetingDecorator/9672023-01-02T23:04:53+02:002023-06-11T08:48:10+03:00<span class="mathjax">Tomer Zimhoni: Random Permutations from Free Products</span>June 15, 11:10—12:00, 2023, -101<div class="mathjax"><p>Let <span class="kdmath">$\Gamma=G_1*G_2*\dots *G_r$</span> be a free product of a finite number of finite groups and a finite number of copies of the infinite cyclic group. We sample uniformly at random an action of $\Gamma$ on $N$ elements. In this talk, we will discuss a few tools we developed to help answer some natural questions involving the configuration described above, such as: For $\gamma\in \Gamma$, what is the expected number of fixed points of $\gamma$ in the action we sampled? What is the the typical behavior of the cycle structure of the permutation corresponding to $\gamma$ etc.</p>
<p>This is a joint with Doron Puder.</p></div>Tomer ZimhoniBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/9682023-01-02T23:05:01+02:002023-06-15T15:44:18+03:00<span class="mathjax">Amir Algom: Fourier decay for smooth images of self-similar measures</span>June 22, 11:10—12:00, 2023, -101<div class="mathjax"><p>Kaufman (1984) and later Mosquera-Shmerkin (2018) showed that Bernoulli convolutions exhibit fast Fourier decay when perturbed by a smooth non-linear map. This is remarkable, since by a classical Theorem of Erdos (1939) many Bernoulli convolutions don’t have Fourier decay at all. We will present an extension of this result to all self-similar measures: Any smooth non-linear perturbation of a self-similar measure enjoys fast (polynomial) Fourier decay.
Joint with Yuanyang Chang, Meng Wu, and Yu-Liang Wu.</p></div>Amir Algomhttps://mathphys.haifa.ac.il/amir-algom/#pll_switcherUniversity of Haifatag:www.math.bgu.ac.il,2005:MeetingDecorator/9972023-06-29T08:53:05+03:002023-06-29T08:53:05+03:00<span class="mathjax">Tomer Sher: On a conjecture Regarding the uniform distribution in the generalized coupon collector problem</span>July 6, 11:10—12:00, 2023, -101<div class="mathjax"><p>The Coupon Collector’s Problem (CCP) reads as follows: how many drawings are needed on average in order to complete a collection of $n$ types of coupons, if at each step a single coupon is drawn uniformly randomly with replacement, independently of all the other drawings? This problem was introduced by De-Moivre over 300 years ago.
We will discuss about a generalization of the problem, where instead of drawing a single coupon each time we draw a ``package” of coupons of size $s$ and ask the following question: how does the distribution over the collection of possible .packages affect the expected number of drawings needed to complete a collection?</p></div> Tomer SherBen Gurion University of the Negev, Israeltag:www.math.bgu.ac.il,2005:MeetingDecorator/9982023-07-03T12:58:14+03:002023-07-03T12:58:14+03:00<span class="mathjax">Naftali Smith: Large deviations in chaotic systems.</span>July 6, 14:00—15:00, 2023, -101<div class="mathjax"><p>Despite their potentially significant and dramatic consequences, large deviations in chaotic dynamics have been studied very little, with few existing theoretical results. We study large deviations of series of finite lengths N generated by chaotic maps. The distributions generally display an exponential decay with N, associated with large-deviation (rate) functions. We calculate the exact rate functions analytically for the doubling, tent, and logistic maps, and numerically for the cat map. In the latter case, we uncover a remarkable singularity of the rate function that we interpret as a second order dynamical phase transition. Furthermore, we develop a numerical tool for efficiently simulating atypical realizations of sequences if the chaotic map is not invertible, and we apply it to the tent and logistic maps. Our research lays the groundwork for the study of unusual trends of long duration in chaotic systems, such as heatwaves or droughts in climate models, or unusual mean growth rate of a pandemic over a long period of time. The talk is based on the recent work [N. R. Smith, Phys. Rev. E 106, L042202 (2022)].</p></div>Naftali Smithhttps://physics.bgu.ac.il/people/949/Ben Gurion University of the Negev, Israeltag:www.math.bgu.ac.il,2005:MeetingDecorator/10212023-12-11T10:46:45+02:002023-12-11T10:46:45+02:00<span class="mathjax">Ido Grayevsky: Sublinear Rigidity of Lattices in Semisimple Lie Groups</span>December 14, 11:10—12:00, 2023, -101<div class="mathjax"><p>I will talk about the coarse geometry of lattices in real semisimple Lie groups. One great result from the 1990’s is the quasi-isometric rigidity of these lattices: any group that is quasi-isometric to such a lattice must be, up to some minor adjustments, isomorphic to lattice in the same Lie group. In this talk I present a partial generalization of this result to the setting of Sublinear Bilipschitz Equivalences (SBE): these are maps that generalize quasi-isometries in some `sublinear’ fashion.</p></div>Ido GrayevskyBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10222023-12-17T09:00:16+02:002023-12-26T12:23:15+02:00<span class="mathjax">Tom Meyerovitch: Absolute Retracts and the Map Extension Property for Multidimensional Subshifts</span>December 21, 11:10—12:00, 2023, -101<div class="mathjax"><p>Subshifts of finite type are the central objects studied in symbolic dynamics.</p>
<p>In the one dimensional case, (e.g. subshifts of finite type when the acting group is Z, the group of integers), although there are difficult standing unsolved problems (in particular, the isomorphism problem), there is a reasonable and fairly developed structure theory:</p>
<ul>
<li>
<p>Any Z-subshift of finite type “decomposes” into irreducible components and wandering points, where any irreducible SFT becomes topologically mixinig after passing to some power of the shift.</p>
</li>
<li>
<p>Krieger’s embedding theorem provides “essentially checkable” necessary and sufficient conditions for an arbitrary subshift to embed in a given topologically mixing SFT.</p>
</li>
<li>
<p>Boyle’s factor theorems give “essentially checkable” conditions for factoring between mixing SFTs.</p>
</li>
</ul>
<p>The situation for multidimensional subshifts is far less structured and far more mysterious.</p>
<p>By now it is well-known that multidimensional subshifts of finite type can exhibit a wild variety of ``pathological behavior’’.</p>
<p>One is soon faced with undecidability issues, and there seems to be little hope to obtain a tractable structure theory in complete generality.</p>
<p>Over the years various properties of multidimensional subshifts have been introduced and studied, in an attempt to recover and generalize some structural aspects of the one-dimensional theory for a natural class.</p>
<p>Among these properties: “square mixing”, “block gluing”, “strong irreducibility”, “topological strong spatial mixing”, “the finite extension property” and more…</p>
<p>In this talk I will introduce a natural class of multidimensional subshifts of finite type for which I have obtained extensions of the fundamental theorems from the one dimensional case.</p>
<p>This new class of subshifts has various equivalent characterizations. The first characterization is the map extension property of subshifts.</p>
<p>The map extension property has been introduced implicitly by Mike Boyle in the early 1980’s for Z-subshifts.</p>
<p>In a suitable natural formulation, in the context of subshifts, it turns out to coincide with the notion of an absolute retract, introduced by Borsuk in the 1930’s.</p>
<p>The map extension property is a stronger property than strong irreducibly, but it still holds for a variety of ``reasonable’’ subshifts such as any subshift with a safe symbol or proper colorings of (the standard Cayley graph of) Z^2 with 5 or more colors.</p>
<p>A Z-subshift has the map extension property if and only if it is a mixing subshift of finite type.</p>
<p>The map extension property allows a meaningful complete multidimensional generalization of both Kreiger’s embedding theorem and of Boyle’s lower entropy factor theorem (partial generalization have been obtained in previous work for other classes).</p></div>Tom MeyerovitchBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10242023-12-24T16:21:13+02:002023-12-26T12:23:50+02:00<span class="mathjax">Or Landesberg: On the denseness of horospheres in higher-rank</span>December 28, 11:10—12:00, 2023, -101<div class="mathjax"><p>In this talk I will discuss a necessary and sufficient condition for denseness of horopherical orbits in the non-wandering set of a higher-rank homogeneous space $G / \Gamma$, for a Zariski dense discrete subgroup $\Gamma < G$, possibly of infinite covolume. In rank one this condition (established in this setting by Eberlein and Dal’bo) implies in particular that the horospherical subgroup acts minimally on the non-wandering set if and only if the discrete group $\Gamma$ is convex co-compact. In contrast, we show that Schottky groups in higher-rank can support non-minimal horospherical actions. This distinction between rank-one and higher-rank is due to the role that Benoist’s limit cone plays in the analysis. Based on joint work with Hee Oh.</p></div>Or LandesbergYaletag:www.math.bgu.ac.il,2005:MeetingDecorator/10232023-12-24T16:09:59+02:002023-12-24T16:09:59+02:00<span class="mathjax">Or Landesberg: On the denseness of horospheres in higher-rank</span>December 28, 11:10—12:00, 2023, -101<div class="mathjax"><p>In this talk I will discuss a necessary and sufficient condition for denseness of horopherical orbits in the non-wandering set of a higher-rank homogeneous space $G / \Gamma$, for a Zariski dense discrete subgroup $\Gamma < G$, possibly of infinite covolume. In rank one this condition (established in this setting by Eberlein and Dal’bo) implies in particular that the horospherical subgroup acts minimally on the non-wandering set if and only if the discrete group $\Gamma$ is convex co-compact. In contrast, we show that Schottky groups in higher-rank can support non-minimal horospherical actions. This distinction between rank-one and higher-rank is due to the role that Benoist’s limit cone plays in the analysis. Based on joint work with Hee Oh.</p></div>Or LandesbergYaletag:www.math.bgu.ac.il,2005:MeetingDecorator/10252023-12-28T13:55:56+02:002024-01-02T10:31:18+02:00<span class="mathjax">Liran Ron: Groups with Finitely Many Busemann Points</span>January 4, 11:10—12:00, 2024, -101<div class="mathjax"><p>Horofunction boundaries are a nice way to approach questions about the behavior of metric spaces at infinity and learn about their geodesics. In the case of Cayley graphs of finitely generated groups, they are also fruitful when studying group actions, algebraic properties and geometric properties (such as the growth rate of the group).</p>
<p>The basic construction is the embedding of the group G in a space of 1-Lipschitz functions on it, by the map sending x to the function b_x(y)=d(x,y)-d(x,1_G). This gives a compactification of G and a compact boundary. The elements in the boundary are called horofunctions. Some of the horofunctions (and in some cases, all of them) are realized as limits of geodesic rays in G, and these are called Busemann points.</p>
<p>The boundary depends on the metric on G, so different Cayley graphs can give rise to different (non-homeomorphic) boundaries. Thus, we are interested in finding out which properties of the boundary are invariants of the group, and we are mainly focused on the cardinality in a broad sense (i.e. finite, countable or uncountable boundary) and the existence of a finite orbit under the group action on the boundary.</p>
<p>In this talk we will review quickly the main definitions and examples and then focus on groups with finitely many Busemann points. We will hopefully go through the main steps of proving that a group with finitely many Busemann points in every Cayley graph horofunction boundary are virtually-cyclic, and in that case every horofunction is a Busemann point.</p>
<p>Joint work with Ariel Yadin</p></div>Liran RonBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10092023-09-18T11:29:29+03:002024-01-07T11:28:33+02:00<span class="mathjax">Izhar Oppenheim: Banach Fixed Point Properties of Higher Rank Groups</span>January 11, 11:10—12:00, 2024, -101<div class="mathjax"><p>A classical Theorem of Delorme-Guichardet states that a group G has property (T) if and only if every continuous affine isometric action of G on a Hilbert space has a fixed point.</p>
<p>There was a conjecture (attributed to Margulis) that for simple higher rank algebraic groups, this result has the following far reaching generalization: For a simple higher rank algebraic group with a finite center G, every continuous affine isometric action of G on a uniformly convex space has a fixed point.</p>
<p>This conjecture was recently settled by the joint works of V. Lafforgue, Liao for the non-Archimedean case, and myself, and de Laat and de la Salle in the real case.</p>
<p>In my lecture, I will discuss the history of the conjecture mentioned above and a further generalization of its solution beyond algebraic groups (namely, for higher rank universal lattices and Steinberg groups).</p></div>Izhar OppenheimBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10142023-09-26T09:04:37+03:002024-01-16T14:38:26+02:00<span class="mathjax">Elyasheev Leibtag: Images of Algebraic Groups and Mixing Properties</span>January 18, 11:10—12:00, 2024, -101<div class="mathjax"><p>Let G be an algebraic group over a local field.
We will show that the image of G under an arbitrary continuous homomorphism into any (Hausdorff) topological group is closed if and only if the center of G is compact. We will show how mixing properties for unitary representations follow from this topological property.</p></div>Elyasheev LeibtagWeizmann Institute of Science tag:www.math.bgu.ac.il,2005:MeetingDecorator/10132023-09-26T08:53:55+03:002024-01-21T11:49:07+02:00<span class="mathjax">Elad Tsalik (postponed): Algebra and Geometry of q-Simplicial Complexes</span>January 25, 11:10—12:00, 2024, -101<div class="mathjax"><p>A Grassmannian complex is a family of linear subspaces of a given linear space, closed under inclusion. In the talk we will explore the properties of Grassmannian complexes over a finite field and define boundary maps that give rise to notions of connectivity and high dimensional expansion. In contrast to the simplex, where all the homology groups are trivial, the complete Grassmannian (consisting of all subspaces of a given linear space) may have a non-trivial homology, and other exciting phenomena.</p>
<p>We will show analogues to the theorems of Linial, Meshulam and Wallach on the expansion of the complete Grassmannian, and to the phase transition of the connectivity of a random complex.</p>
<p>If time permits, we will discuss related extremal problems and topological overlap.</p>
<p>Based on joint work with Ran Tessler.</p></div>Elad Tsalik (postponed)Weizmann Institute of Science tag:www.math.bgu.ac.il,2005:MeetingDecorator/10292024-01-21T11:50:21+02:002024-01-28T16:19:58+02:00<span class="mathjax">Yair Glasner: Finer Topologies and Stronger Rigidity for some Higher Rank Lattices</span>February 1, 11:10—12:00, 2024, -101<div class="mathjax"><p>(A joint work with Waltraud Lederle) In order to avoid technicalities I will focus on one specific example for a higher $\mathbb{Q}$-rank lattice: the group $\Gamma = \mathrm{SL}_3(\mathbb{Z})$. This group exhibits strong rigidity properties, some of which are naturally expressed in topological terms. For example, one of the earliest rigidity results, the congruence subgroup property which was established independently by Mennicke and Bass-Milnor-Serre, can be expressed as an equality between two group topologies on $\Gamma$: The profinite and the congruence topologies. Margulis’ celebrated normal subgroup theorem can be thought of as the statement that even the normal topology coincides with these two. Here the normal topology is defined by taking all infinite normal subgroups as a basis of identity neighborhoods for a topology on $\Gamma$. Together with Waltraud Lederle we introduce an a-priori much finer topology on $\Gamma$ called the boomerang topology and show that in fact even this topology coincides with the congruence topology. As a result we obtain a generalization of a rigidity theorem for probability measure preserving actions due to Nevo-Stuck-Zimmer.</p></div>Yair GlasnerBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10302024-01-21T11:50:42+02:002024-02-06T09:40:50+02:00<span class="mathjax">Yair Hartman: Sale on Boundaries: 1+1</span>February 8, 11:10—12:00, 2024, -101<div class="mathjax"><p>During the 60,s and the 70,s Furstenberg developed two parallel theories regarding boundaries of groups of different flavours. One is topological, and the other is measurable and relates to random walks. The research of these two theories and their connections with rigidity theory and operator algebra theory is still very active, yet many questions are open.
In an attempt to understand better the connections between them, I’ll show that they share the same driving force. We סwill develop one machinery to produce them both at the same time. Two Boundary Theories for the price of one.</p></div>Yair HartmanBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10312024-01-23T09:45:24+02:002024-01-23T09:45:24+02:00<span class="mathjax">Shlomo Hoory: On the Girth of Graph Lifts</span>February 15, 11:10—12:00, 2024, -101<div class="mathjax"><p>The size of the smallest $k$-regular graph of girth $g$ is denoted by the well studied function $n(k,g)$.
We suggest generalizing this function to $n(H,g)$, defined as the smallest size girth $g$ graph covering the, possibly non-regular, graph $H$.
We prove that the two main combinatorial bounds on $n(k,g)$, the Moore lower bound and the Erdos-Sachs upper bound,
carry over to the new setting of lifts, even in their non-asymptotic form.</p>
<p>We also consider two other generalizations of $n(k,g)$:
i) The smallest size girth $g$ graph sharing a universal cover with $H$. We prove that it is the same as $n(H,g)$ up to a multiplicative constant.
ii) The smallest size girth $g$ graph with a prescribed degree distribution. We discuss this known generalization and argue that the new suggested definitions are superior.</p>
<p>We conclude with experimental results for a specific base graph and with some conjectures and open problems.</p>
<p><a href="https://arxiv.org/abs/2401.01238">https://arxiv.org/abs/2401.01238</a></p></div>Shlomo Hoorytag:www.math.bgu.ac.il,2005:MeetingDecorator/10152023-09-26T09:38:53+03:002024-02-20T08:10:56+02:00<span class="mathjax">Michael Lin: Uniform ergodicity and the one-sided ergodic Hilbert transform</span>February 22, 11:10—12:00, 2024, -101<div class="mathjax"><p>Let $T$ be a bounded linear operator on a Banach space $X$ satisfying $\lVert T^n\rVert/n\rightarrow 0$. We prove that $T$ is uniformly ergodic if and only if the one-sided ergodic Hilbert transform $H(T)x:=\lim_{n\rightarrow \infty}\sum_{k=1}^nk^{-1}T^kx$ converges for every $x\in \overline{(I-T)X}$. When $T$ is a power-bounded (or more generally $(C,\alpha)$ bounded for some $0<\alpha<1$), then $T$ us uniformly ergodic if and only if the domain of $H$ equals $(I-T)X$.</p></div>Michael LinBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10432024-02-26T18:08:43+02:002024-02-26T18:20:26+02:00<span class="mathjax">Ariel Yadin: The Infrared Bound Without Reflection Positivity</span>February 29, 11:10—12:00, 2024, -101<div class="mathjax"><p>To shake things up a little we’ll talk about the Ising model.
I will explain a phenomenon in thermodynamics called the “infrared bound”, and what it is usually good for.
The only known way to prove this bound on a graph is using a property called “reflection positivity”. But this basically limits the graph in question to Z^d, the Euclidean lattice.</p>
<p>Recently with Tom Meyerovitch we have been thinking of a new method of proving the infrared bound on other (transitive) graphs.
I will present a necessary and sufficient condition for something called “Gaussian domination” which in turn implies the infrared bound.
The main idea of the talk is to present the different ideas that arise in these kinds of thermodynamic models.</p>
<p>No background is assumed.</p></div>Ariel YadinBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10412024-02-12T08:01:37+02:002024-03-10T09:28:00+02:00<span class="mathjax">Ariel Rapaport: Dimension of Bernoulli convolutions in R^d</span>March 14, 11:10—12:00, 2024, -101<div class="mathjax"><p>Let $(\lambda_{1},…,\lambda_{d})=\lambda\in(0,1)^{d}$ be with $\lambda_{1}>…>\lambda_{d}$ and let $\mu_{\lambda}$ be the distribution of the random vector $\sum_{n\ge0}\pm (\lambda_{1}^{n},…,\lambda_{d}^{n})$, where the $\pm$ are independent fair coin-tosses. Assuming $P(\lambda_{j})\ne 0$ for all $1\le j\le d$ and nonzero polynomials with coefficients $\pm1,0$, we show that $\operatorname{dim}\mu_{\lambda}=\min \big(d,\dim_{L}\mu_{\lambda} \big)$, where $\dim_{L}\mu_{\lambda}$ is the Lyapunov dimension. This extends to higher dimensions a result of Varjú from 2018 regarding the dimension of Bernoulli convolutions on the real line. Joint work with Haojie Ren.</p></div>Ariel RapaportTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/10052023-09-10T10:12:56+03:002024-01-03T10:14:31+02:00<span class="mathjax">Uri Bader: Higher Kazhdan Property and Unitary Cohomology of Arithmetic Groups (Postponed)</span>May 2, 11:10—12:00, 2024, -101Uri BaderWeizmann Institute of Science tag:www.math.bgu.ac.il,2005:MeetingDecorator/10542024-04-17T16:07:03+03:002024-05-03T19:23:36+03:00<span class="mathjax">Uri Bader: Higher Kazhdan Property and Unitary Cohomology of Arithmetic Groups</span>May 9, 11:10—12:00, 2024, -101Uri BaderBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10552024-04-17T16:07:24+03:002024-05-12T12:21:22+03:00<span class="mathjax">Omri Sarig: Equidistribution of Discrepancy Sequences (Joint with Dolgopyat)</span>May 16, 11:10—12:00, 2024, -101<div class="mathjax"><p>Let \alpha be an irrational number and let J be a sub interval of [0,1]. The discrepancy sequence of J is D(N), where</p>
<table>
<tbody>
<tr>
<td>D(N):=the number of visits of n\alpha mod 1 to J for 1<n<N minus N</td>
<td>J</td>
<td>.</td>
</tr>
</tbody>
</table>
<p>Weyl’s Equidistribution Theorem says that D(N)=o(N). But this sequence is not necessarily bounded.</p>
<p>I will characterize the irrationals \alpha of bounded type, for which the discrepancy sequence of the interval [0,1/2] is equidistributed on (1/2)Z . This is joint work with Dima Dolgopyat.</p></div>Omri SarigWeizmann Institute of Sciencetag:www.math.bgu.ac.il,2005:MeetingDecorator/10622024-05-08T08:08:54+03:002024-05-20T14:40:39+03:00<span class="mathjax">Adian Young: Random temporo-spatial differentiations</span>May 23, 11:10—12:00, 2024, -101<div class="mathjax"><p>Temporo-spatial differentiations are ergodic averages on a probabilistic dynamical system $(X, \mu, T)$ taking the form $\left( \frac{1}{\mu(C_k)} \int_{C_k} \frac{1}{k} \sum_{j = 0}^{k - 1} T^j f \mathrm{d} \mu \right)_{k = 1}^\infty $ where $C_k \subseteq X$ are measurable sets of positive measure, and $f \in L^\infty(X, \mu)$. These averages combine both the dynamics of the transformation and the structure of the underlying probability space $(X, \mu)$. We will discuss the motivations behind studying these averages, results concerning the limiting behavior of these averages and, time permitting, discuss generalizations to non-autonomous dynamical systems. Joint work with Idris Assani.</p></div>Adian Younghttps://us02web.zoom.us/j/81787996207?pwd=dVZFcEtBMGJkVWdHL0gyV2VoNGJlUT09BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/10592024-05-07T13:54:06+03:002024-05-07T13:54:06+03:00<span class="mathjax">Lior Tenenbaum: TBA</span>May 30, 11:10—12:00, 2024, -101Lior TenenbaumTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/10582024-05-06T13:35:43+03:002024-05-06T13:35:43+03:00<span class="mathjax">Gill Goffer: TBA</span>June 13, 11:10—12:00, 2024, -101Gill GofferUCSDtag:www.math.bgu.ac.il,2005:MeetingDecorator/10572024-05-03T19:29:57+03:002024-05-06T13:35:03+03:00<span class="mathjax">Ilya Gekhtman: TBA</span>June 27, 11:10—12:00, 2024, -101 Ilya GekhtmanTechnion