BGU BGU Probability and Ergodic Theory (PET) seminarBGU Math<span class="mathjax">Tom Meyerovitch: On pointwise periodicity and expansiveness</span>March 20, 11:00—12:00, 2018, 2012018-03-12T23:38:17+02:002018-03-12T23:38:13+02:00BGU MathTom MeyerovitchBGU<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><span class="mathjax">Jeremias Epperlein: Derivative Algebras and Topological Conjugacies Between Cellular Automata</span>March 27, 11:10—12:00, 2018, 2012018-03-20T13:32:27+02:002018-02-28T08:56:31+02:00BGU MathJeremias EpperleinBGU<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><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, 2012018-04-08T18:53:06+03:002018-03-01T10:09:41+02:00BGU MathMatan HarelTel Aviv University<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><span class="mathjax">Gady Kozma : Irreducibility of random polynomials</span>April 17, 11:00—12:00, 2018, 2012018-04-10T09:23:52+03:002018-03-01T10:11:42+02:00BGU MathGady Kozma Weizmann Institute<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><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, 2012018-04-18T14:52:55+03:002018-03-04T21:53:06+02:00BGU MathRon PeledTel Aviv University<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 finite systems. This is known to decay exponentially fast for a strong random field. 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><span class="mathjax">Sebastián Donoso: Good lower bounds for multiple recurrence</span>April 30, 11:00—12:00, 2018, -1012018-04-24T15:50:28+03:002018-04-24T14:24:08+03:00BGU Math Sebastián DonosoUniversidad de O’Higgins<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><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, 2012018-04-09T13:31:02+03:002018-03-18T17:11:38+02:00BGU MathChen DubiBGU<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><span class="mathjax">Erez Nesharim: The t-adic Littlewood conjecture is false</span>May 8, 11:00—12:00, 2018, 2012018-04-22T10:36:06+03:002018-04-15T10:33:41+03:00BGU MathErez NesharimUniversity of York<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><span class="mathjax">Idan Perl: Harmonic functions on locally compact groups</span>May 22, 11:00—12:00, 2018, 2012018-05-14T20:42:30+03:002018-05-09T21:16:36+03:00BGU MathIdan PerlBGU<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><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, 2012018-04-29T17:48:53+03:002018-04-22T10:37:45+03:00BGU MathTal HoreshIHES<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><span class="mathjax">Yotam Smilansky: Kakutani’s splitting procedure for multiscale substitution schemes</span>June 12, 11:00—12:00, 2018, 2012018-05-29T09:33:46+03:002018-04-15T10:38:11+03:00BGU MathYotam Smilansky<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><span class="mathjax">Ofer Busani: The Multi-Lane Totally Asymmetric Simple Exclusion Process</span>June 19, 11:00—12:00, 2018, 2012018-05-28T16:11:43+03:002018-05-27T13:04:49+03:00BGU MathOfer BusaniBar Ilan<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><span class="mathjax">Rachel Skipper: Quasi-isometry classes of simple groups</span>October 18, 11:00—12:00, 2018, -1012018-10-10T12:39:25+03:002018-10-09T09:42:12+03:00BGU MathRachel SkipperGeorg-August-University, Göttingen<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><span class="mathjax">Yair Hartman: Stationary C*-Dynamical Systems</span>October 25, 11:00—12:00, 2018, -1012018-10-18T14:34:28+03:002018-10-03T10:21:31+03:00BGU MathYair HartmanBen-Gurion University <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><span class="mathjax">J.C. Saunders: Sieve Methods in Random Graph Theory</span>November 1, 11:00—12:00, 2018, -1012018-10-10T09:09:22+03:002018-10-06T21:17:37+03:00BGU Math J.C. SaundersBen-Gurion University<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><span class="mathjax">הסמינר מבוטל בשל סדנא על stack: TBA</span>November 8, 11:00—12:00, 2018, -1012018-10-24T11:36:54+03:002018-10-07T11:57:19+03:00BGU Mathהסמינר מבוטל בשל סדנא על stack<span class="mathjax">Jeremias Epperlein: Sheltered sets, dead ends and horoballs in groups</span>November 15, 11:00—12:00, 2018, -1012018-11-06T15:55:02+02:002018-10-08T15:39:50+03:00BGU MathJeremias EpperleinBen-Gurion University <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><span class="mathjax">Yiftach Dayan: Diophantine approximations on random fractals</span>November 22, 11:00—12:00, 2018, -1012018-11-18T20:45:33+02:002018-10-10T09:10:51+03:00BGU MathYiftach DayanTel-Aviv University<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><span class="mathjax">Daniel Luckhardt: Benjamini-Schramm Continuity of Normalized Characteristic numbers on Riemannian manifolds</span>November 29, 11:00—12:00, 2018, -1012018-11-26T09:01:01+02:002018-10-10T09:11:42+03:00BGU MathDaniel LuckhardtBen-Gurion University <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><span class="mathjax">חנוכה: TBA</span>December 6, 11:00—12:00, 2018, -1012018-10-11T20:36:42+03:002018-10-10T09:27:47+03:00BGU Mathחנוכה<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, -1012018-12-10T08:37:28+02:002018-10-10T09:27:07+03:00BGU MathRon PeledTel-Aviv University<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><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, -1012018-12-13T09:17:52+02:002018-10-10T09:27:58+03:00BGU MathRoss Pinskyhttp://www2.math.technion.ac.il/~pinsky/index.htmlTechnion<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><span class="mathjax">The talk has been cancelled: TBA</span>December 27, 11:00—12:00, 2018, -1012018-12-12T15:22:23+02:002018-10-10T09:28:08+03:00BGU MathThe talk has been cancelled<span class="mathjax">Chandrika Sadanand: You can hear the shape of a polygonal billiard table</span>January 3, 11:00—12:00, 2019, -1012018-10-22T14:12:41+03:002018-10-10T09:28:15+03:00BGU MathChandrika SadanandThe Hebrew University of Jerusalem<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><span class="mathjax">Nishant Chandgotia: Universal models for Z^d actions</span>January 10, 11:00—12:00, 2019, -1012019-01-06T23:40:33+02:002018-10-10T09:28:21+03:00BGU MathNishant Chandgotiahttp://math.huji.ac.il/~nishant/The Hebrew University of Jerusalem<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><span class="mathjax">Dirk Frettlöh: Bounded distance equivalence of aperiodic Delone sets and bounded remainder sets</span>February 28, 11:10—12:00, 2019, -1012019-02-24T12:03:19+02:002018-11-01T15:33:10+02:00BGU MathDirk Frettlöhhttps://www.math.uni-bielefeld.de/~frettloe/Bielefeld university<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><span class="mathjax">Omri Sarig: Local limit theorem for inhomogeneous Markov chains (joint with Dolgopyat)</span>March 7, 11:10—12:00, 2019, -1012019-02-11T14:18:37+02:002018-12-01T21:03:57+02:00BGU MathOmri Sarighttp://www.weizmann.ac.il/math/sarigo/Weizmann Institute<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><span class="mathjax">David Lipshutz: Pathwise derivatives of reflected diffusions</span>March 14, 11:10—12:00, 2019, -1012019-03-05T08:56:56+02:002018-12-01T21:04:04+02:00BGU MathDavid Lipshutzhttps://sites.google.com/view/lipshutz/homeTechnion<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><span class="mathjax">Holiday: Purim</span>March 21, 11:10—12:00, 2019, -1012018-12-01T21:13:03+02:002018-12-01T21:04:11+02:00BGU MathHoliday<span class="mathjax">Wojciech Samotij: The lower tail for triangles in sparse random graphs</span>March 28, 11:10—12:00, 2019, -1012019-01-09T14:43:45+02:002018-12-01T21:04:18+02:00BGU MathWojciech Samotijhttp://www.math.tau.ac.il/~samotij/Tel-Aviv University<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><span class="mathjax">Felix Pogorzelski: New developments on non-commutative quasicrystals</span>April 4, 11:10—12:00, 2019, -1012019-03-26T23:25:04+02:002018-12-01T21:04:28+02:00BGU Math Felix Pogorzelskihttp://www.math.uni-leipzig.de/~pogorzelski/Universität Leipzig<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><span class="mathjax">Federico Vigolo: An introduction to warped cones</span>April 11, 11:10—12:00, 2019, -1012019-04-08T09:05:18+03:002018-12-01T21:04:35+02:00BGU MathFederico Vigolohttp://www.wisdom.weizmann.ac.il/~vigolo/Weizmann Istitute<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><span class="mathjax">Holiday: Passover</span>April 18, 11:10—12:00, 2019, -1012018-12-01T21:13:15+02:002018-12-01T21:04:43+02:00BGU MathHoliday<span class="mathjax">Holiday: Passover</span>April 25, 11:10—12:00, 2019, -1012018-12-01T21:13:23+02:002018-12-01T21:06:57+02:00BGU MathHoliday<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, -1012019-05-02T17:03:13+03:002018-12-01T21:07:38+02:00BGU MathMichael Lin Ben-Gurion University<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><span class="mathjax">Holiday: Independence Day</span>May 9, 11:10—12:00, 2019, -1012018-12-01T21:13:34+02:002018-12-01T21:09:51+02:00BGU MathHoliday<span class="mathjax">@ weizmann institute: students’ probability day - in memory of Oded Schramm</span>May 16, 11:10—12:00, 2019, -1012019-02-28T21:36:54+02:002018-12-01T21:10:27+02:00BGU Math @ weizmann institute<span class="mathjax">J.C. Saunders: On (a,b) Pairs in Random Fibonacci Sequences</span>May 23, 11:10—12:00, 2019, -1012019-03-05T09:28:51+02:002018-12-01T21:10:48+02:00BGU Math J.C. SaundersBen-Gurion University<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><span class="mathjax">(seminar is cancelled): Open day at the Math department</span>May 30, 11:10—12:00, 2019, -1012019-03-05T09:56:28+02:002018-12-01T21:10:54+02:00BGU Math(seminar is cancelled)<span class="mathjax">Eitan Bachmat: On the index of refraction of a distribution, lenses and probability.</span>June 6, 11:10—12:00, 2019, -1012019-06-04T09:31:53+03:002018-12-01T21:10:59+02:00BGU MathEitan Bachmathttps://www.cs.bgu.ac.il/~ebachmat/Ben-Gurion University<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><span class="mathjax">Dina Barak: Maximum of exponential random variables and Hurwitz’s zeta function</span>June 20, 11:10—12:00, 2019, -1012019-06-10T23:14:10+03:002018-12-01T21:11:08+02:00BGU MathDina BarakBen-Gurion University<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><span class="mathjax">Stanislav Molchanov: Random exponentials and Dickmann’s laws: survey and applications</span>June 27, 11:10—12:00, 2019, -1012019-04-11T09:00:42+03:002019-04-10T11:21:11+03:00BGU MathStanislav Molchanovhttp://math2.uncc.edu/~molchanov/University of North Carolina (UNC) at Charlotte; Higher School of Economics (HSE), Moscow<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><span class="mathjax">Itay Londner: Optimal arithmetic structure in interpolation sets</span>June 27, 14:10—15:10, 2019, -1012019-06-18T10:18:47+03:002018-12-01T21:11:03+02:00BGU MathItay Londnerhttp://www.math.ubc.ca/~itayl/University of British Columbia<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><span class="mathjax">Adam Dor-On: Problems on Markov chains arising from operator algebras</span>July 1, 13:10—14:00, 2019, -1012019-06-26T20:49:59+03:002019-06-26T12:25:55+03:00BGU MathAdam Dor-Onhttps://adoronmath.wordpress.com/University of Illinois at Urbana-Champaign<span class="mathjax">Davide Giraudo: Bounded law of the iterated logarithms for stationary random fields</span>September 18, 14:10—15:00, 2019, 2012019-09-08T12:22:46+03:002019-09-08T12:07:16+03:00BGU MathDavide Giraudohttps://sites.google.com/site/davidegiraudomathematics/Ruhr-Universität Bochum<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><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, -1012019-10-22T14:16:48+03:002019-07-30T13:18:08+03:00BGU MathBarak Weisshttp://www.math.tau.ac.il/~barakw/Tel-Aviv University<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><span class="mathjax">Tom Meyerovitch: Efficient finitary codings by Bernoulli processes</span>November 7, 11:10—12:00, 2019, -1012019-10-27T13:20:38+02:002019-07-30T13:19:12+03:00BGU MathTom Meyerovitchhttps://sites.google.com/site/tommeyerovitch/homeBen-Gurion University<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><span class="mathjax">Talk has been cancelled : TBA</span>November 14, 11:10—12:00, 2019, -1012019-11-13T22:03:33+02:002019-07-30T13:19:28+03:00BGU MathTalk has been cancelled <span class="mathjax">Uriel Gabor: On the failure of Ornstein’s theory in the finitary category.</span>November 21, 11:10—12:00, 2019, -1012019-11-12T20:58:33+02:002019-07-30T13:19:45+03:00BGU MathUriel GaborThe Hebrew University<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><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, -1012019-11-24T08:43:55+02:002019-07-30T13:19:53+03:00BGU MathManuel Luethihttps://people.math.ethz.ch/~luethman/Tel-Aviv University<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><span class="mathjax">Amnon Yekutieti: An averaging process for unipotent group actions – in differential geometry</span>December 5, 11:10—12:00, 2019, -1012019-11-17T14:18:54+02:002019-07-30T13:20:03+03:00BGU MathAmnon Yekutietihttps://www.math.bgu.ac.il/~amyekut/Ben-Gurion University<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><span class="mathjax">Jeremias Epperlein: Automorphisms of topological Markov shifts and Wagoner’s complexes</span>December 12, 11:10—12:00, 2019, -1012019-11-28T13:48:15+02:002019-07-30T13:20:13+03:00BGU MathJeremias Epperleinhttps://www.math.bgu.ac.il/~jeremias/Ben-Gurion University<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><span class="mathjax">Rene Rühr: Cut-And-Project quasicrystals and their moduli spaces</span>December 19, 11:10—12:00, 2019, -1012019-12-03T13:51:58+02:002019-07-30T13:20:24+03:00BGU MathRene Rührhttps://sites.google.com/site/reneruehrTechnion<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><span class="mathjax">Asaf Katz: Measure rigidity for Anosov flows via the factorization method</span>December 26, 11:10—12:00, 2019, -1012019-12-10T21:42:49+02:002019-07-30T13:20:37+03:00BGU MathAsaf Katzhttps://sites.google.com/view/asafkatzUniversity of Chicago<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><span class="mathjax">Amitay Kamber: Cutoff on graphs and the Sarnak-Xue density of eigenvalues</span>January 2, 11:10—12:00, 2020, -1012019-12-30T09:43:22+02:002019-07-30T13:20:44+03:00BGU MathAmitay KamberThe Hebrew University<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><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, -1012020-01-06T11:57:15+02:002019-07-30T13:20:54+03:00BGU MathAron Wennmanhttps://people.kth.se/~aronw/Tel-Aviv University<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><span class="mathjax">Geoffrey Wolfer: Estimating the mixing time of non-reversible Markov chains</span>January 16, 11:10—12:00, 2020, -1012019-12-19T10:11:40+02:002019-07-30T13:21:12+03:00BGU MathGeoffrey Wolferhttp://web.dagama.org/resumeBen-Gurion University<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><span class="mathjax">Tom Gilat: Decomposition of random walk measures on the one-dimensional torus</span>January 23, 11:10—12:00, 2020, -1012020-01-15T10:21:03+02:002019-07-30T14:54:08+03:00BGU MathTom GilatBar-Ilan University<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><span class="mathjax">Sebastián Barbieri: On the relation between topological entropy and asymptotic pairs</span>January 27, 11:10—12:00, 2020, -1012020-01-26T09:21:07+02:002019-11-11T22:01:33+02:00BGU MathSebastián Barbierihttps://www.labri.fr/perso/sbarbieri/index.htmlUniversité de Bordeaux<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><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, -1012020-02-05T08:45:09+02:002020-02-05T08:45:09+02:00BGU MathYuqing (Frank) Linhttps://web.ma.utexas.edu/users/ylin/The University of Texas at Austin<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><span class="mathjax">Houcein Elabdalaoui: Sarnak’s Möbius disjointness conjecture for dendrites and Veech systems</span>February 20, 11:10—12:00, 2020, -1012020-02-06T10:28:20+02:002019-12-20T14:09:56+02:00BGU MathHoucein Elabdalaouihttp://elabdalaoui.perso.math.cnrs.fr/Université de Rouen<span class="mathjax">Bashir Abu Khalil: Extracting an invariant of conjugacy from independence entropy</span>September 3, 11:10—12:00, 2020, online2020-09-01T07:25:50+03:002020-08-14T11:34:37+03:00BGU MathBashir Abu KhalilBGU<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><span class="mathjax">Dor Bitan: Homomorphic operations over secret shares</span>October 22, 11:10—12:00, 2020, Online2021-10-28T09:05:22+03:002020-10-12T18:00:55+03:00BGU MathDor BitanBen-Gurion University<span class="mathjax">Yair Hartman: Random walks on dense subgroups</span>October 29, 11:10—12:00, 2020, Online2021-10-28T09:04:17+03:002020-10-12T21:28:00+03:00BGU MathYair Hartmanhttps://www.math.bgu.ac.il/~hartmany/Ben-Gurion University<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><span class="mathjax">Arielle Leitner: Deformations of generalized cusps on convex projective manifolds</span>November 5, 11:10—12:00, 2020, Online2021-10-28T09:06:57+03:002020-10-12T21:30:34+03:00BGU MathArielle Leitnerhttp://www.wisdom.weizmann.ac.il/~ariellel/Weizmann Institute<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><span class="mathjax">: TBA</span>November 12, 11:10—12:00, 2020, Online2021-10-28T08:29:15+03:002020-10-12T21:31:54+03:00BGU Math<span class="mathjax">Ariel Yadin: Non-trivial phase transition in percolation</span>November 19, 11:10—12:00, 2020, Online2021-10-28T09:08:49+03:002020-10-12T21:32:27+03:00BGU MathAriel Yadinhttps://www.math.bgu.ac.il/~yadina/Ben-Gurion University<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><span class="mathjax">Gil Goffer: Is invariable generation hereditary?</span>November 26, 11:10—12:00, 2020, Online2020-11-26T16:07:49+02:002020-10-12T21:32:55+03:00BGU MathGil Gofferhttps://www.weizmann.ac.il/pages/search/people?language=english&single=1&person_id=52900Weizmann Institute<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><span class="mathjax">Yaar Solomon: TBA</span>December 3, 16:00—17:00, 2020, Online2021-10-28T09:09:36+03:002020-10-12T21:33:15+03:00BGU MathYaar Solomon<span class="mathjax">Erez Nesharim: Approximation by algebraic numbers and homogeneous dynamics</span>December 10, 11:10—12:00, 2020, Online2021-10-28T09:08:14+03:002020-10-12T21:33:31+03:00BGU MathErez Nesharimhttp://math.huji.ac.il/~ereznesh/The Hebrew University<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><span class="mathjax">Yotam Smilansky: Multiscale substitution tilings</span>December 17, 15:30—16:30, 2020, Online2021-10-27T17:22:28+03:002020-10-12T21:33:46+03:00BGU MathYotam Smilanskyhttps://sites.math.rutgers.edu/~smilansky/Rutgers University<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><span class="mathjax">Zemer Kosloff: On the local limit theorem in dynamical systems</span>December 24, 11:10—12:00, 2020, Online2021-10-28T08:33:03+03:002020-10-12T21:34:04+03:00BGU MathZemer Kosloffhttp://math.huji.ac.il/~zemkos/The Hebrew University<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><span class="mathjax">Amir Algom: On the decay of the Fourier transform of self-conformal measures</span>December 31, 15:30—16:30, 2020, Online2021-10-28T08:27:58+03:002020-10-12T21:34:17+03:00BGU MathAmir Algomhttps://sites.psu.edu/amira/Penn State University<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><span class="mathjax">Guy Salomon: Amenability, proximality, and higher order syndeticity</span>January 7, 11:10—12:00, 2021, Online2021-06-27T08:43:13+03:002020-10-12T21:34:50+03:00BGU MathGuy SalomonWeizmann Institute<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><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, Online2021-01-15T09:19:07+02:002020-10-12T21:36:10+03:00BGU MathJeremias Epperleinhttps://www.fim.uni-passau.de/en/dynamical-systems/publications/dr-jeremias-epperlein/University of Passau<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><span class="mathjax">Shrey Sanadhya: Substitution on infinite alphabets and generalized Bratteli-Vershik models.</span>February 11, 16:25—17:30, 2021, Online2021-02-14T21:35:16+02:002021-01-27T12:20:50+02:00BGU MathShrey Sanadhyahttps://sites.google.com/view/shrey-sanadhya/homeThe University of Iowa<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><span class="mathjax">: TBA</span>March 4, 11:10—12:00, 2021, Online2021-02-11T10:51:49+02:002021-02-11T10:51:24+02:00BGU Math<span class="mathjax">Nattalie Tamam: Effective equidistribution of horospherical flows in infinite volume</span>March 11, 16:00—17:00, 2021, Online2021-03-11T17:46:31+02:002021-02-11T10:52:06+02:00BGU MathNattalie Tamamhttps://www.math.ucsd.edu/~natamam/University of California, San Diego<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><span class="mathjax">Yuqing Frank Lin: A multiplicative ergodic theorem for von Neumann algebra valued cocycles</span>March 18, 11:10—12:00, 2021, Online2021-03-18T16:41:24+02:002021-02-11T10:52:18+02:00BGU MathYuqing Frank Linhttps://web.ma.utexas.edu/users/ylin/Ben-Gurion University<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><span class="mathjax">: Passover break</span>March 25, 11:10—12:00, 2021, -1012021-02-11T10:53:34+02:002021-02-11T10:53:19+02:00BGU Math<span class="mathjax">: Passover break</span>April 1, 11:10—12:00, 2021, -1012021-02-11T10:53:55+02:002021-02-11T10:53:55+02:00BGU Math<span class="mathjax">: Holocaust Memorial Day</span>April 8, 11:10—12:00, 2021, -1012021-02-11T10:54:47+02:002021-02-11T10:54:47+02:00BGU Math<span class="mathjax">: Memorial day for Israel’s fallen</span>April 15, 11:10—12:00, 2021, -1012021-02-11T10:56:05+02:002021-02-11T10:56:05+02:00BGU Math<span class="mathjax">Zohar Reizis: Random walks on finite partite simplicial complexes</span>April 22, 11:10—12:00, 2021, Online2021-04-22T12:06:52+03:002021-02-11T10:56:33+02:00BGU MathZohar ReizisBen-Gurion University<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><span class="mathjax">Nishant Chandgotia: About Borel and almost Borel embeddings for Z^d actions</span>April 29, 11:10—12:00, 2021, Online2021-04-29T13:40:56+03:002021-02-11T10:57:04+02:00BGU MathNishant Chandgotiahttp://math.huji.ac.il/~nishant/The Hebrew University<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><span class="mathjax">Tsachik Gelander: Infinite volume and infinite injectivity radius</span>May 6, 11:10—12:00, 2021, Online2021-05-06T14:35:57+03:002021-02-11T10:57:46+02:00BGU Math Tsachik Gelanderhttps://www.weizmann.ac.il/pages/search/people?language=english&single=1&person_id=48373Weizmann Institute<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><span class="mathjax">Faustin Adiceam: Around the Danzer problem and the construction of dense forests.</span>May 13, 11:10—12:00, 2021, Online2021-05-13T12:38:01+03:002021-02-11T10:57:58+02:00BGU MathFaustin Adiceamhttps://sites.google.com/site/fadiceammaths/The University of Manchester<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><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, Online2021-05-20T21:35:19+03:002021-02-11T10:58:22+02:00BGU MathYiftach DayanTechnion<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><span class="mathjax">Doron Puder: TBA</span>May 27, 10:00—10:45, 2021, Online2021-05-12T20:42:10+03:002021-02-11T10:58:08+02:00BGU MathDoron Puderhttps://sites.google.com/site/doronpuder/Tel-Aviv University<span class="mathjax">Daren Wei: Slow entropy of higher rank abelian unipotent actions</span>June 3, 11:10—12:00, 2021, Online2021-06-10T12:29:07+03:002021-02-11T10:58:47+02:00BGU MathDaren Weihttps://sites.google.com/view/darenweimath/The Hebrew University<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><span class="mathjax">Henna Koivusalo: Linear repetitivity in polytopal cut and project sets</span>June 10, 11:10—12:00, 2021, Online2021-06-10T14:52:48+03:002021-02-11T10:58:59+02:00BGU MathHenna Koivusalohttps://people.maths.bris.ac.uk/~te20281/University of Bristol<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><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)2021-06-24T14:40:04+03:002021-02-11T10:59:17+02:00BGU MathEitan Bachmathttps://www.cs.bgu.ac.il/~ebachmat/Ben-Gurion University<div class="mathjax"><p>We consider some conjectures (and a few results on maximal increasing subsequences) which are motivated by airplane boarding.</p></div><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 142021-10-22T21:58:12+03:002021-09-23T19:31:40+03:00BGU MathTattwamasi Amrutamhttps://www.math.uh.edu/~tamrutam/Ben-Gurion University<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><span class="mathjax">Matan Tal: Bohr Chaos and Invariant Measures</span>November 4, 11:10—12:00, 2021, Building 34, room 142021-11-04T15:56:27+02:002021-09-23T19:32:40+03:00BGU MathMatan TalThe Hebrew University<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><span class="mathjax">Matthieu Joseph: Allosteric actions of surface groups</span>November 11, 11:10—12:00, 2021, -1012021-11-11T15:12:47+02:002021-09-23T19:34:54+03:00BGU MathMatthieu Josephhttps://perso.ens-lyon.fr/matthieu.joseph/research.htmlÉcole normale supérieure de Lyon<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><span class="mathjax">Anton Hase: Introduction to bounded cohomology</span>November 18, 11:10—12:00, 2021, Building 34, room 142021-11-18T16:18:36+02:002021-09-23T19:35:04+03:00BGU MathAnton HaseBen-Gurion University<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><span class="mathjax">Trip to the desert of the PET seminar group!!: TBA</span>November 25, 11:10—12:00, 2021, -1012021-10-31T08:32:32+02:002021-09-23T19:35:19+03:00BGU MathTrip to the desert of the PET seminar group!!<span class="mathjax">Olga Lukina: Stabilizers in group Cantor actions and measures</span>December 2, 11:10—12:00, 2021, -1012021-12-02T15:20:52+02:002021-09-23T19:35:12+03:00BGU MathOlga Lukinahttps://sites.google.com/view/olgalukina/homeUniversity of Vienna<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><span class="mathjax">Valérie Berthé: Symbolic discrepancy and Pisot dynamics</span>December 9, 11:10—12:00, 2021, -1012021-12-09T13:05:16+02:002021-09-23T19:35:26+03:00BGU MathValérie Berthéhttps://www.irif.fr/~berthe/Université de Paris<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><span class="mathjax">Andreas Wieser: Linnik’s basic lemma with uniformity over the base field</span>December 16, 11:10—12:00, 2021, -1012021-12-18T11:40:57+02:002021-09-23T19:35:51+03:00BGU MathAndreas Wieserhttps://people.math.ethz.ch/~awieser/aboutThe Hebrew University<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><span class="mathjax">: TBA</span>December 23, 11:10—12:00, 2021, -1012021-11-28T10:56:11+02:002021-09-23T19:36:00+03:00BGU Math<span class="mathjax">Philipp Kunde: Non-classifiability of ergodic flows up to time change</span>December 30, 11:10—12:00, 2021, -1012021-12-30T15:13:17+02:002021-09-23T19:36:06+03:00BGU MathPhilipp Kundehttps://www.math.uni-hamburg.de/home/kunde/Universität Hamburg <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 142022-01-06T14:55:54+02:002021-09-23T19:36:13+03:00BGU MathNadav Ben-Davidhttps://emet.net.technion.ac.il/2019/02/27/nadav-ben-david/Ben-Gurion University<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><span class="mathjax">Dan Rust: Substitutions on compact alphabets</span>January 13, 11:10—12:00, 2022, -1012022-01-15T18:46:42+02:002021-09-23T19:36:45+03:00BGU MathDan Rusthttps://sites.google.com/view/danrust/The Open University (UK)<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><span class="mathjax">Elad Sayag: Entropy, ultralimits and Poisson boundaries</span>March 24, 11:10—12:00, 2022, -1012022-03-24T14:02:04+02:002021-11-08T21:01:04+02:00BGU MathElad SayagTel-Aviv University<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><span class="mathjax">Annette Karrer: The rigidity of lattices in products of trees</span>March 31, 11:10—12:00, 2022, -1012022-03-31T13:54:00+03:002021-11-08T21:01:13+02:00BGU MathAnnette KarrerTechnion<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><span class="mathjax">: TBA</span>April 7, 11:10—12:00, 2022, -1012022-03-31T13:52:45+03:002021-11-08T21:01:22+02:00BGU Math<span class="mathjax">Holiday: Passover break</span>April 14, 11:10—12:00, 2022, -1012021-11-08T21:06:11+02:002021-11-08T21:05:52+02:00BGU MathHoliday<span class="mathjax">Holiday: Passover break</span>April 21, 11:10—12:00, 2022, -1012021-11-08T21:06:35+02:002021-11-08T21:06:23+02:00BGU MathHoliday<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, -1012022-04-25T10:34:26+03:002021-11-08T21:06:43+02:00BGU MathChris Phillipshttps://pages.uoregon.edu/ncp/University of Oregon<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><span class="mathjax">Holiday: Yom Ha’Atzmaut</span>May 5, 11:10—12:00, 2022, -1012021-11-08T21:09:37+02:002021-11-08T21:09:10+02:00BGU MathHoliday<span class="mathjax">Ioannis Tsokanos: Density of oscillating sequences in the real line</span>May 12, 11:10—12:00, 2022, -1012022-05-12T13:29:26+03:002021-11-08T21:06:56+02:00BGU MathIoannis Tsokanoshttps://sites.google.com/view/ioannis-tsokanosThe University of Manchester<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><span class="mathjax">Arie Levit: Characters of groups, stability and sofic dynamical systems</span>May 19, 11:10—12:00, 2022, -1012022-05-19T15:19:46+03:002021-11-08T21:10:03+02:00BGU MathArie Levithttps://sites.google.com/site/arielevit/Tel-Aviv University<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><span class="mathjax">Shrey Sanadhya: Universality for R^d-flows</span>May 26, 11:10—12:00, 2022, -1012022-05-23T09:55:37+03:002021-11-08T21:10:13+02:00BGU MathShrey SanadhyaBen-Gurion University<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><span class="mathjax">Adam Śpiewak: Probabilistic Takens time-delay embeddings</span>June 2, 11:10—12:00, 2022, room 106, building 282022-06-02T13:32:47+03:002021-11-08T21:10:20+02:00BGU MathAdam Śpiewakhttps://adamspiewak.wordpress.com/Bar-Ilan University<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><span class="mathjax">Edgar Bering: Topological models of abstract commensurators</span>June 9, 11:10—12:00, 2022, room 106, building 282022-06-13T21:42:12+03:002021-11-08T21:10:28+02:00BGU MathEdgar BeringTechnion<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><span class="mathjax">Anton Hase: (Non-)Integrability of quaternion-Kähler symmetric spaces</span>June 16, 11:10—12:00, 2022, room 106, building 282022-06-21T12:28:40+03:002021-11-08T21:11:22+02:00BGU MathAnton HaseBen-Gurion University<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><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 282022-06-23T12:45:36+03:002021-11-08T21:11:29+02:00BGU MathDaniel Ingebretsonhttps://sites.google.com/view/dingebretson/Ben-Gurion University<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><span class="mathjax">Maksim Zhukovskii: Extremal independence in discrete random systems</span>June 30, 11:10—12:00, 2022, room 106, building 282022-06-30T13:49:35+03:002022-03-14T09:59:23+02:00BGU MathMaksim Zhukovskiihttps://combgeo.org/en/members/maksim-zhukovskii/Weizmann Institute<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><span class="mathjax">: TBA</span>October 27, 11:10—12:00, 2022, -1012022-08-11T17:14:52+03:002022-08-07T10:31:36+03:00BGU Math<span class="mathjax">: TBA</span>November 3, 11:10—12:00, 2022, -1012022-08-07T10:39:00+03:002022-08-07T10:31:52+03:00BGU Math<span class="mathjax">: TBA</span>November 10, 11:10—12:00, 2022, -1012022-08-07T10:39:07+03:002022-08-07T10:32:27+03:00BGU Math<span class="mathjax">: TBA</span>November 17, 11:10—12:00, 2022, -1012022-08-07T10:39:22+03:002022-08-07T10:33:08+03:00BGU Math<span class="mathjax">: TBA</span>November 24, 11:10—12:00, 2022, -1012022-08-07T10:39:14+03:002022-08-07T10:33:21+03:00BGU Math<span class="mathjax">: TBA</span>December 1, 11:10—12:00, 2022, -1012022-08-07T10:39:30+03:002022-08-07T10:33:31+03:00BGU Math<span class="mathjax">: TBA</span>December 8, 11:10—12:00, 2022, -1012022-08-07T10:39:38+03:002022-08-07T10:33:54+03:00BGU Math<span class="mathjax">: TBA</span>December 15, 11:10—12:00, 2022, -1012022-08-07T10:39:45+03:002022-08-07T10:34:07+03:00BGU Math<span class="mathjax">: TBA</span>December 22, 11:10—12:00, 2022, -1012022-08-07T10:39:52+03:002022-08-07T10:34:14+03:00BGU Math<span class="mathjax">: TBA</span>December 29, 11:10—12:00, 2022, -1012022-08-07T10:40:00+03:002022-08-07T10:34:23+03:00BGU Math<span class="mathjax">: TBA</span>January 5, 11:10—12:00, 2023, -1012022-08-07T10:40:06+03:002022-08-07T10:34:36+03:00BGU Math<span class="mathjax">: TBA</span>January 12, 11:10—12:00, 2023, -1012022-08-07T10:40:15+03:002022-08-07T10:34:42+03:00BGU Math<span class="mathjax">: TBA</span>January 19, 11:10—12:00, 2023, -1012022-08-07T10:40:22+03:002022-08-07T10:34:49+03:00BGU Math