tag:www.math.bgu.ac.il,2005:/en/research/seminars/colloquium/meetingsBGU ColloquiumBGU Mathtag:www.math.bgu.ac.il,2005:MeetingDecorator/492015-10-05T14:33:01+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Asaf Nachmias: Unimodular hyperbolic planar graphs</span>March 24, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>We study random hyperbolic planar graphs by using their circle packing embedding to connect their geometry to that of the hyperbolic plane. This leads to several results: Identification of the Poisson and geometric boundaries, a connection between hyperbolicity and a form of non-amenability, and a new proof of the Benjamini-Schramm recurrence result.
Based on works with subsets of Omer Angel, Martin Barlow, Ori Gurel-Gurevich, Tom Hutchcroft and Gourab Ray.</p></div>Asaf NachmiasTel Avivtag:www.math.bgu.ac.il,2005:MeetingDecorator/502015-10-05T14:33:01+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Boaz Tsaban: Algebra, selections, and additive Ramsey theory</span>April 14, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>Improving upon theorems of Hilbert, Schur, and others, and establishing a longstanding conjecture, Hindman proved that, for each finite coloring of the natural numbers, there is an infinite set such that all finite sums of elements from the set have the same color.
Galvin and Glazer used the algebraic and topological structure of the set of ultrafilters (to be defined in the lecture) to provide a very clear and elegant proof of Hindman’s Theorem. This soon became the leading method for establishing coloring theorems in arithmetic and related fields.</p>
<p>We will survey the Galvin-Glazer method and proof, and indicate a surprising recent discovery, that Hindman’s theorem is a special (in a sense, degenerate) case of a theorem about open covers of topological spaces with a property introduced by Karl Menger. The proof uses, in addition to extensions of the Galvin-Glazer theory, infinite games and selection principles.</p>
<p>The talk will be aimed at a general mathematical audience. In particular, we do not assume familiarity with any of the concepts mentioned above. The price is that we will not provide proof details; these are too subtle and laborious for a colloquium talk. The emphasis will be on the introduction to this beautiful connection.</p></div>Boaz TsabanBar Ilan Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/512015-10-05T14:33:01+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Marek Bozejko: Non-commutative Brownian motions and Levy processes with applications to free probability and von Neumann algebras</span>April 21, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>The subject of my talk will be the following topics:
1. Classical and non-commutative Brownian motions with realization on some Fock spaces.</p>
<ol>
<li>
<p>q-Brownian motions,q-CCR relations (a a<em>- qa</em> a =1) and theta functions of Jacobi.</p>
</li>
<li>
<p>Meixner-Levy processes and relation to the free Levy processes.</p>
</li>
</ol>
<p>4.Factorial q-von Neumann algebras and ultracontractivity of q-Ornstein-Uhlenbeck semigroup.</p></div>Marek BozejkoUniversity of Wroclawtag:www.math.bgu.ac.il,2005:MeetingDecorator/522015-10-05T14:33:01+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Nir Lev: Quasicrystals and Poisson summation formula</span>April 28, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>The subject of this talk is the analysis of discrete distributions of masses that have a pure point spectrum. A new peak of interest in this subject has appeared after the experimental discovery of quasicrystalline materials in the middle of 80’s. I will present the relevant background and discuss some recent results obtained in joint work with Alexander Olevskii.</p></div>Nir LevBar Ilan Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/532015-10-05T14:33:01+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Jerzy Kakol: SELECTED TOPICS ON THE WEAK TOPOLOGY OF BANACH SPACES</span>May 5, 14:30—15:30, 2015, Math -101Jerzy KakolUniversity of Poznantag:www.math.bgu.ac.il,2005:MeetingDecorator/542015-10-05T14:33:01+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Amir Dembo: Statistical physics on sparse random graphs: mathematical perspective</span>May 19, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>Theoretical models of disordered materials lead to challenging mathematical problems with applications to random combinatorial problems and coding theory. The underlying structure is that of many discrete variables that are strongly interacting according to a mean field model determined by a random sparse graph. Focusing on random finite graphs that converge locally to trees we review recent progress in validating the `cavity’ prediction for the limiting free energy per vertex and the approximation of local marginals by the belief propagation algorithm.
This talk is based on joint works with Anirban Basak, Andrea Montanari, Allan Sly and Nike Sun.</p></div>Amir DemboStanford Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/552015-10-05T14:33:01+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Emanuel Milman: Curvature-Dimension Condition for Non-Conventional Dimensions</span>May 26, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>Given an n-dimensional Riemannian manifold endowed with a probability density, we are interested in studying its isoperimetric, spectral and concentration properties. To this end, the Curvature-Dimension condition CD(K,N), introduced by Bakry and Emery in the 80’s, is a very useful tool. Roughly put, the parameter K serves as a lower bound on the weighted manifold’s “generalized Ricci curvature”, whereas N serves as an upper bound on its “generalized dimension”. Traditionally, the range of admissible values for the generalized dimension N has been confined to [n,infty]. In this talk, we present some recent developments in extending this range to N < 1, allowing in particular negative (!) generalized dimensions.
We will mostly be concerned with obtaining sharp isoperimetric inequalities under the Curvature-Dimension condition, identifying new one-dimensional model-spaces for the isoperimetric problem. Of particular interest is when curvature is strictly positive, yielding a new single model space (besides the previously known N-sphere and Gaussian measure): the sphere of (possibly negative) dimension N<1, which enjoys a spectral-gap and improved exponential concentration.</p>
<p>Time permitting, we will also discuss the case when curvature is only assumed non-negative. When N is negative, we confirm that such spaces always satisfy an N-dimensional Cheeger isoperimetric inequality and N-degree polynomial concentration, and establish that these properties are in fact equivalent. In particular, this renders equivalent various weak Sobolev and Nash inequalities for different exponents on such spaces.</p></div>Emanuel MilmanTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/132015-10-05T14:33:00+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Eran Shmaya: Expert testing</span>June 2, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>An expert provides probabilistic predictions about a sequence of future outcomes (for example, an outcome can be the daily price of a stock and the expert provides the distribution of the price). An inspector reviews the predictions made by the expert and the observed outcomes and applies some test to decide on the validity of the expert’s predictions. The expert testing literature asks whether there exists some test that distinguishes a “true expert”, who provided the correct predictions from a “charlatan”, who concoct predictions strategically to pass the test. I will give a survey of the literature, heavily biased towards my own papers.</p></div>Eran ShmayaTel Aviv University and Kellogg School of Managementtag:www.math.bgu.ac.il,2005:MeetingDecorator/122015-10-05T14:33:00+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Amnon Yekutieli: Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers</span>June 9, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>The story of Pythagorean triples is an ancient one, as the name suggests. We are looking for triples (a, b, c) of positive integers that are the sides of a right angled triangle; namely they satisfy the Pythagorean Theorem.
In this talk I will explain how to find all Pythagorean triples (reduced and ordered) with a given hypotenuse c. The method is simple and constructive. For instance, we will be able to find (by hand) the only triple with hypotenuse 289, and the only two triples with hypotenuse 85.</p>
<p>The relation between Pythagorean triples and complex numbers, prime numbers and Gauss integers is well-known. What might be new in the talk (but I can’t vouch for it) is the connection to abelian group theory.</p></div>Amnon Yekutielihttp://www.math.bgu.ac.il/~amyekutBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/142015-10-05T14:33:00+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Antoine Ducros: Geometry over p-adic fields: Berkovich’s approach</span>June 16, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>p-adic fields have been introduced by number theorists for arithmetic purposes. Such a field is complete with respect to an absolute value with some strange behaviour: for example, every closed ball with positive radius is open, and every point of such a ball is a center. Because of those properties, to develop a relevant geometric theory over p-adic fields is non-trivial: one can not naively mimic what is done in real or complex geometry, and one has to use a more subtle approach.
In this talk we will present that of Berkovich. His main idea consists in “adding a lot of points to naive p-adic spaces” in order to get good topological properties, like local compactness or local path-connectedness. After having given the basic definitions, we will investigate some significant examples, and give a survey of some of the (numerous) applications of the theory has had in various areas (spectral theory, dynamics, algebraic and arithmetic geometry…).</p></div>Antoine DucrosParis 6tag:www.math.bgu.ac.il,2005:MeetingDecorator/152015-10-05T14:33:00+03:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Jake Salomon: TBA</span>June 23, 14:30—15:30, 2015, Math -101Jake SalomonHUJItag:www.math.bgu.ac.il,2005:MeetingDecorator/1032016-02-26T08:33:39+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Kobi Peterzil: Applications of model theory to diophantine geometry</span>November 3, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>A family of problems in diophantine geometry has the following form: We fix a collection of “special” algebraic varieties where the 0-dimensional are called “special points”. In general, if V is a sepcial variety then the special points are Zariski dense in V, and one would like to prove the converse: If V is an irreducible algebraic variety and the special points are Zariski dense in V then V itself is special.
Particular cases of the above are the Manin-Mumford conjecture, the Mordell-Lang conjecture, and others. In 1990’s Hrushovski showed how model theoretic techniques could be applied to solve certain such problems. In 2008 Pila and Zannier developed a different framework. which allows to apply model theory and especially the theory of o-minimal structures, in order to tackle questions of this nature over the complex numbers. Pila himself used these methods to prove some open cases of the Andre-Oort conjecture and since then there was an influx of articles which use similar techniques. At the heart of the Pila-Zannier method lies a theorem of Pila and Wilkie on rational points on definable sets in o-minimal structures.
In this survey-like talk I will describe the basic ingredients of the Pila-Zannier method and its applications, in one or two simple cases.</p></div>Kobi Peterzilhttp://math.haifa.ac.il/kobi/Haifatag:www.math.bgu.ac.il,2005:MeetingDecorator/1072016-02-26T08:33:39+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Daniel Moskovich: Low dimensional topology of information fusion</span>November 10, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>It has been suggested that every good mathematical pattern
ought to be manifest in nature. This talk surveys the speaker’s work
with A.Y. Carmi on a manifestation of low-dimensional topology’s
diagrammatic calculus of tangles in the theory of information fusion
networks e.g. sensor networks and complex systems. It turns out that
various sets of information-theoretic quantities such as sets of
entropies naturally admit an algebraic structure called a quandle. The
topological toolbox is completely different from the toolbox of
statistical inference. Our diagrams are similar but not identical to
classical tangle diagrams, and our work involves studying their
diagrammatic algebra.
The talk is planned to be accessible to a general mathematical audience.</p></div>Daniel MoskovichBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1102016-02-26T08:33:39+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Yaar Solomon: The Danzer problem and a solution to a related problem of Gowers</span>November 17, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>Is there a point set $Y$ in $R^d$, and $C>0$, such that every convex set of volume 1 contains at least one point of $Y$ and at most $C$? This discrete geometry problem was posed by Gowers in 2000, and it is a special case of an open problem posed by Danzer in 1965. I will present two proofs that answers Gowers’ question with a NO. The first approach is dynamical; we introduce a dynamical system and classify its minimal subsystems. This classification in particular yields the negative answer to Gowers’ question. The second proof is direct and it has nice applications in combinatorics. [This is a joint work with Omri Solan and Barak Weiss].</p></div>Yaar Solomonhttp://www.math.stonybrook.edu/~yaars/Stony Brook universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/1142016-02-26T08:33:39+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Brandon Seward: Entropy for actions of non-amenable groups</span>November 24, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>Within the field of dynamics, entropy is a real number which measures the amount of chaos or complexity in a dynamical system. Entropy was first introduced for actions of the integers by Kolmogorov in 1958, and it led to huge advances in the field. During the 1970’s and 80’s entropy theory was largely extended to actions of amenable groups (such as abelian groups and solvable groups). In 2008, Lewis Bowen made a dramatic breakthrough by extending the notion of entropy to actions of sofic groups (such as linear groups and free groups). A new chapter in entropy theory is now unfolding. In this talk, I will discuss some of the history of classical entropy theory and then discuss some recent breakthroughs.</p></div>Brandon Sewardhttp://math.huji.ac.il/~bseward/Hebrew U. and Courant Institute of Mathematical Sciencestag:www.math.bgu.ac.il,2005:MeetingDecorator/872016-02-26T07:30:25+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Tomer Schlank: Ultra-Products and Chromatic Homotopy Theory</span>December 1, 14:30—15:30, 2015, Math -101<div class="mathjax"><p>The category of spectra is one of the most important constructions in modern
algebraic topology. It appears naturally in the study of cobordism classes of
manifolds, aa the classification of generalized cohomology theories and also can be
thought of as a homotopical analog of abelian groups. In the last years J. Lurie and
other authors began redeveloping algebra with Spectra taking the role of abelian
groups. Analogs of commutative and non-commutative rings , modules, lie-algebras
and many others developed, and many theorems where proved that are analogs of
the classical case. I’ll describe some of the tools and the ideas appearing in this
constructions and sketch some applications. The same way one can do algebra in
different characteristics (a prime $p$ or zero) which appear as points of the scheme
$Spec(\mathbb{Z})$, One can find all possible “characteristics” of Spectra. Those are classified by
a pair $(p, n)$ where $p$ is a prime and $n$ is a natural number called a height. Working
in a given characteristic $(n, p)$ one obtains what is called the $K(n)$-local category
at height $n$ and prime $p$. It is a well known observation that for a given height
$n$ certain “special” phenomena happen only for small enough primes. Further, in
some sense, the categories $C_{p,n}$ become more regular and algebraic as $p$ goes to
infinity for a fixed $n$. The goal of this talk is to make this intuition precise.</p>
<p>Given an infinite sequence of mathematical structures, logicians have a method to
construct a limiting one by using ultra-product. We shall define a notion of “ultraproduct
of categories” and then describe a collection of categories $D_{n,p}$ which will
serve as algebro-geometric analogs of the $K(n)$-local category at the prime $p$.</p>
<p>Then for a fixed height $n$ we prove:</p>
<div class="kdmath">$$
\prod_{p}^{\mathrm{Ultra}}C_{n,p}\cong\prod_{p}^{\mathrm{Ultra}}D_{n,p}
$$</div>
<p>If time permits we shall describe our ongoing attempts to use these methods to
get a version of the $K(n)$-local category corresponding to formal Drinfeld modules
(instead of formal groups).</p>
<p>This is a joint project with N. Stapleton and T. Barthel.</p></div>Tomer SchlankHebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/912016-02-26T07:30:25+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Eitan Sayag: Recent Developments in analysis on Spherical spaces</span>December 8, 14:30—15:30, 2015, Math -101<div class="mathjax">
<p>I will overview recent developments in harmonic analysis on spherical spaces. This class of spaces
includes the class of symmetric spaces and recently became relevant for variations on the Langlands program<br />
due to its relation to periods of automorphic forms.</p>
<p>
I will introduce some basic geometric properties of these spaces and then focus on two issues:
the decay of generalized matrix coefficients on real spherical spaces and the
regularity of generalized (spherical) characters.
</p>
<p>
After reviewing the necessary background, we will discuss some of our results and elaborate on few applications of these results to problems originating in arithmetic.
In particular we will discuss some new results on the problem of counting lattice points in the realm of real spherical spaces.
</p>
<p>
The main results include quantitative generalizations of Howe-Moore phenomena in the real case and a qualitative generalizations of Howe/Harish-Chandra character expansions in the p-adic case.
Our techniques relies on systematic usage of the action of Bernstein center in the p-adic case and the
theory of ODE in the real case (using the z-finite action of the center of the universal enveloping algebra).
</p>
<p>
The lecture is based on recent works with various collaborators (A. Aizenbud, D. Gourevtich, B. Kroetz, F. Knop, H. Schlichtkrull). </p></div>Eitan SayagBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/942016-02-26T07:30:25+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Allen Tannenbaum: Graph Curvature for Differentiating Cancer Networks</span>December 15, 14:30—15:30, 2015, Math -101<div class="mathjax">
<p>Cellular interactions can be modeled as complex dynamical systems represented by weighted graphs. The functionality of such networks, including measures of robustness, reliability, performance, and efficiency, are intrinsically tied to the topology and geometry of the underlying graph. Utilizing recently proposed geometric notions of curvature on weighted graphs, we investigate the features of gene co-expression networks derived from large-scale genomic studies of cancer. We find that the curvature of these networks reliably distinguishes between cancer and normal samples, with cancer networks exhibiting higher curvature than their normal counterparts. We establish a quantitative relationship between our findings and prior investigations of network entropy. Furthermore, we demonstrate how our approach yields additional, non-trivial pair-wise (i.e. gene-gene) interactions which may be disrupted in cancer samples. The mathematical formulation of our approach yields an exact solution to calculating pair-wise changes in curvature which was computationally infeasible using prior methods. As such, our findings lay the foundation for an analytical approach to studying complex biological networks.</p></div>Allen TannenbaumStony Brook Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/972016-02-26T07:30:25+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Omer Tamuz: What does a typical dynamical system look like?</span>December 22, 14:30—15:30, 2015, Math -101<div class="mathjax">
<p>The study of generic dynamical systems has lead to some important discoveries in the past. In this talk I will explain the topological notion of a “generic dynamical system”, survey some historical results and describe a new one, regarding the entropy of symbolic dynamics on amenable groups.
Based on joint work with Joshua Frisch.</p></div>Omer Tamuzhttp://people.hss.caltech.edu/~tamuz/Caltechtag:www.math.bgu.ac.il,2005:MeetingDecorator/822016-02-26T07:29:44+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Uzi Vishne: Linkage of quadratic Pfister forms</span>January 5, 14:30—15:30, 2016, Math -101<div class="mathjax">
<p>The algebraic theory of quadratic forms connects fascinating topics, from Hurwitz’ theorem and Hilbert’s 17th problem, to the theorems of Voevodsky-Orlov-Vishik and Voevodsky-Rost on the Witt ring and Milnor’s K-theory, and beyond.</p>
<p>
After proving to the audience that this is a beautiful subject, I will try to explain why and how everything is harder in characteristic 2.
</p>
<p>
I will describe the effects of linkage of quadratic Pfister forms, in particularly in characteristic 2, where one has to distinguish between left- and right-linkage. I will describe a potential invariant (which fails), and construct sets of forms that should be linked, but aren't. </p></div>Uzi Vishnehttp://u.cs.biu.ac.il/~vishne/Bar Ilan Univeristytag:www.math.bgu.ac.il,2005:MeetingDecorator/832016-02-26T07:29:44+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Nir Avni: Counting points and representations</span>January 12, 14:30—15:30, 2016, Math -101<div class="mathjax">
<p>I will talk about the following questions:</p>
<p>
1) Given a system of polynomial equations with integer coefficients, how many solutions does it have in the ring Z/N?
</p>
<p>
2) Given a polynomial map f:R^a–>R^b and a smooth, compactly supported measure m on R^a, does the push-forward of m by f have bounded density?
</p>
<p>
3) Given a lattice in a higher rank Lie group (say, SL(n,Z) for n>2). How many d-dimensional representations does it have?
</p>
<p>
I will explain how these questions are related to the singularities of certain varieties. Along the way, I'll talk about canonical singularities, random commutators, and the moduli space of local systems.
</p>
<p>
This is a joint work with Rami Aizenbud </p></div>Nir Avnihttp://www.math.northwestern.edu/~nir/Northwestern U.tag:www.math.bgu.ac.il,2005:MeetingDecorator/852016-02-26T07:29:44+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Amnon Besser: Integral points on curves</span>January 19, 14:30—15:30, 2016, Math -101<div class="mathjax">
<p>The problem of finding the integral or rational solutions of polynomial equations is one of the oldest in mathematics. The simplest non-trivial case is that of one equation in two variables. While we know that for a sufficiently high degree equation there are only a finite number of solutions, an effective method for finding these solutions in general is not known to exist.</p>
<p>
Quite recently, a far reaching program for finding the solutions using fundamental groups and p-adic numbers was invented by Minhyong Kim. I will explain some of the background, and also report on some work with Jennifer Balakrishnan and Steffen Muller using similar ideas to solve a new class of equations. I will give some concrete examples. </p></div>Amnon Besserhttp://www.math.bgu.ac.il/~bessera/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/772016-02-26T07:29:01+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Sasha Sodin: Random matrix valued fields</span>March 8, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>Random matrix theory is a source of non-trivial constructions
of stochastic processes, which appear as limiting objects as
the matrix size goes to infinity. We shall discuss some of these
processes, starting with two classical ones and proceeding to
two of the less-studied ones.</p></div>Sasha Sodinhttp://www.math.tau.ac.il/~sashas1/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/782016-02-26T07:29:01+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Jarek Kedra: On conjugation invariant geometry of groups</span>March 15, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>I will discuss basic properties of conjugation invariant norms on groups.
I will explain why some groups are bounded (a group G is bounded if every
conjugation invariant norm on G has finite diameter). The examples will
include diffeomorphism groups of manifolds and some lattices in semisimple
Lie groups. I will discuss the stronger notion of uniform boundedness. I
will also provide examples of unbounded groups, some open problems and an
application to group actions on manifolds.</p></div>Jarek Kedrahttp://www.abdn.ac.uk/ncs/profiles/kedra/U. of Aberdeentag:www.math.bgu.ac.il,2005:MeetingDecorator/792016-02-26T07:29:01+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">MIcha Sharir: Eliminating cycles, cutting lenses, and bounding incidences</span>March 22, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>The talk covers two unrelated topics in combinatorial geometry that have recently reached a confluence:
incidences between points and curves in the plane, or surfaces in higher dimensions, and elimination of
cycles in the depth relation of lines in 3-space. Recent progress on the latter problem, inspired by
the new algebraic machinery of Guth and Katz, has yielded a nearly tight bound, of roughly $n^{3/2}$,
on the number of cuts needed to eliminate all cycles for a set of n lines, or simply-shaped algebraic
curves, in 3-space. This in turn leads to a similar bound on the number of cuts that are needed to turn
a collection of n constant-degree algebraic arcs in the plane into a collection of pseudo-segments
(i.e., each pair of the new subarcs intersect at most once). This leads, among several other applications,
to improved incidence bounds between points and algebraic arcs in the plane, which are better than the
older general bound of Pach and Sharir, for any number of “degrees of freedom” of the curves. It also leads
to several new bounds for incidences between points and planes or points and spheres in three dimensions.</p>
<p>Based on joint works with Boris Aronov, Noam Solomon, and Joshua Zahl.</p></div>MIcha Sharirhttp://www.math.tau.ac.il/~michas/TAUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1242016-03-10T15:50:26+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Mikhail Muzychuk: Isomorphism problem for Cayley combinatorial objects</span>March 29, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>A Cayley combinatorial object over a group $H$ is a relational structure on $H$ invariant under the group of right translations $H_R$. Cayley graphs over the group $H$ provide a well-known example of such objects. An isomorphism problem for Cayley graphs will be the central topic of my talk. I shall present Klin-Poeschel approach to this problem based on the method of Schur. In addition, some recent results about isomorphism problem for non-graphical Cayley objects will be discussed.
(This talk will be part of Yom iuyn on Algebraic Combinatorics on on the occasion of the retirement of Prof. Mikhail Klin)</p></div>Mikhail MuzychukNetanya Academic Collegetag:www.math.bgu.ac.il,2005:MeetingDecorator/1002016-02-26T08:16:19+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Minhyong Kim: Reciprocity laws, Diophantine equations, and fundamental groups</span>April 5, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>We give a brief survey of the interaction between class field theory and the theory of Diophantine equations, starting from the theorem of Hasse-Minkowski to recent work on non-abelian reciprocity laws.</p></div>Minhyong Kimhttp://people.maths.ox.ac.uk/kimm/Oxfordtag:www.math.bgu.ac.il,2005:MeetingDecorator/1012016-02-26T08:16:20+02:002016-04-19T20:58:53+03:00BGU Math<span class="mathjax">Tamar Ziegler: Concatenating cubic structures and patterns in primes</span>April 12, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>A major difficulty in finding polynomial patterns in primes is the need to understand their distribution properties at short scales. We describe how for some polynomial configurations one can overcome this problem by concatenating short scale behavior in “many directions” to long scale behavior.</p></div>Tamar Zieglerhttp://www.ma.huji.ac.il/~tamarz/Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/1482016-04-10T20:27:32+03:002016-04-26T09:57:25+03:00BGU Math<span class="mathjax">Ronen Eldan: Interplays between stochastic calculus and geometric inequalities</span>May 3, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>In this talk, we will try to illustrate the potential of stochastic calculus as a tool for proving inequalities with a geometric nature. We’ll do so by focusing on the proofs of two new bounds related to the Gaussian Ornstein-Uhlenbeck convolution operator, which heavily rely on the use of Ito calculus. The first bound is a sharp robust estimate for the Gaussian noise stability inequality of C. Borell (which is, in turn, a generalization of the Gaussian isoperimetric inequality). The second bound concerns with the regularization of $L_1$ functions under the convolution operator, and provides an affirmative answer to a 1989 question of Talagrand. If time allows, we will also mention an application of these methods to concentration inequalities for log-concave measures.</p></div>Ronen Eldanhttp://www.wisdom.weizmann.ac.il/~ronene/Weizmanntag:www.math.bgu.ac.il,2005:MeetingDecorator/1512016-05-04T20:58:16+03:002016-05-06T09:31:44+03:00BGU Math<span class="mathjax">Henri Darmon: Elliptic curves and explicit class field theory</span>May 10, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>The arithmetic of elliptic curves is related in multiple ways to explicit class field theory, notably through the theory of {\em complex multiplication}, one of the crown jewels of number theory. This connection plays a key role in recent progress in the recent theorem that there are positive proportions of elliptic curves of rank zero, and of rank one, for which the Birch and Swinnerton-Dyer conjecture is true, growing out of the work of Gross-Zagier, Kolyvagin, Bhargava-Shankar, Skinner-Urban-Wan, and Wei Zhang. I will discuss various relations that exist between elliptic curves and explicit class field theory, such as those above.</p></div>Henri Darmonhttp://www.math.mcgill.ca/darmon/ McGilltag:www.math.bgu.ac.il,2005:MeetingDecorator/1502016-05-04T20:56:09+03:002016-10-11T21:48:12+03:00BGU Math<span class="mathjax">Ido Efrat: Absolute Galois groups - old and new results</span>May 17, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>Galois theory investigates the symmetry patterns among roots of polynomials over a field. These symmetry patterns are described by the absolute Galois group of the field, whose structure is in general still a mystery.
We will describe what is known about this symmetry group: classical facts, consequences of the epochal work by Veovodsky and Rost, and very recent structural results and conjectures related to higher cohomology operations and intersection theorems.</p></div>Ido Efrathttps://www.math.bgu.ac.il//~efrat/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1532016-05-17T22:23:46+03:002016-05-18T20:30:28+03:00BGU Math<span class="mathjax">N. Christopher Phillips: The mean dimension of a homeomorphism and the radius of comparison of its C*-algebra</span>May 31, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>We describe a striking conjectured relation
between ``dimensions’’ in topological dynamics and C<em>-algebras.
(No previous knowledge
of C</em>-algebras or dimension theory will be assumed.)
Let $X$ be a compact metric space,
and let $h \colon X \to X$ be a minimal homeomorphism
(no nontrivial invariant closed subsets).
The <em>mean dimension</em>
${\mathit{mdim}} (h)$ of $h$ is a dynamical invariant,
which I will describe in the talk,
and which was invented
for purposes having nothing to do with C<em>-algebras.
One can also form a crossed product C</em>-algebra $C^* ({\mathbb{Z}}, X, h)$.
It is simple and unital,
and there is an explicit description
in terms of operators on Hilbert space,
which I will give in the talk.
The <em>radius of comparison</em>
${\mathit{rc}} (A)$ of a simple unital C<em>-algebra $A$
is an invariant introduced for reasons having nothing to do
with dynamics;
I will give the motivation for its definition in the talk
(but not the definition itself).
It has been conjectured,
originally on very thin evidence,
that the radius of comparison of $C^</em>({\mathbb{Z}},X,h)$
is equal to half the
mean dimension of $h$
for any minimal homeomorphism $h$.</p>
<p>In this talk,
I will give elementary introductions to mean dimension,
the crossed product construction,
and the ideas behind the radius of comparison.
I will then describe the motivation for the conjecture
and some partial results towards it.</p></div>N. Christopher Phillipshttp://pages.uoregon.edu/ncp/ University of Oregontag:www.math.bgu.ac.il,2005:MeetingDecorator/1522016-05-05T11:53:15+03:002016-10-11T21:47:15+03:00BGU Math<span class="mathjax">Shakhar Smorodinsky: Improved bounds on the Hadwiger Debrunner numbers</span>June 14, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>The classical Helly’s theorem states that if in a family of compact convex sets in R^d every $d+1$ members have a non-empty intersection then the whole family has a non-empty intersection.</p>
<p>In an attempt to generalize Helly’s theorem, in 1957 Hadwiger and Debrunner posed a conjecture that was proved more than 30 years later in a celebrated result of Alon and Kleitman: For any p,q (p >= q > d) there exists a constant C=C(p,q,d) such that the following holds: If in a family of compact convex sets, out of every p members some q intersect, then the whole family can be pierced with C points. Hadwiger and Debrunner themselves showed that if q is very close to p, then $C=p-q+1$ suffices.</p>
<p>The proof of Alon and Kleitman yields a huge bound $C=O(p^{d^2+d})$, and providing sharp upper bounds on the minimal possible C remains a wide open problem.</p>
<p>In this talk we show an improvement of the best known bound on C for all pairs $(p,q)$. In particular, for a wide range of values of q, we reduce C all the way to the almost optimal bound p-q+1<=C<=p-q+2. This is the first near tight estimate of C since the 1957 Hadwiger-Debrunner theorem.</p>
<p>Joint work with Chaya Keller and Gabor Tardos.</p></div> Shakhar Smorodinskyhttps://www.math.bgu.ac.il///www.cs.bgu.ac.il/~shakhar/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1582016-06-22T10:51:03+03:002019-05-02T17:03:11+03:00BGU Math<span class="mathjax">Michael Lin: Positive Ritt contractions on $L_p$</span>June 28, 14:30—15:30, 2016, Math -101Michael LinBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1602016-10-09T15:01:09+03:002019-05-02T17:03:11+03:00BGU Math<span class="mathjax">Alfred Inselberg: VISUALIZING <span class="kdmath">$\mathbb{R}^N$</span> AND SOME NEW DUALITIES</span>November 8, 14:30—15:30, 2016, Math -101Alfred Inselberghttp://www.math.tau.ac.il/~aiisreal/San Diego Supercomputing Center and Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/1622016-10-09T15:02:38+03:002016-11-06T20:58:22+02:00BGU Math<span class="mathjax">Karim Adiprasito: Combinatorial Hodge theory</span>November 15, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>I will discuss how Hodge theory, and positivity phenomena from algebraic geometry in general, can be used to resolve fundamental conjectures in combinatorics, including Rotas conjecture for log-concavity of Whitney numbers and beyond. I will also discuss how combinatorics can in turn be used to explain and prove such phenomena, such as the Hodge-Riemann relations for matroids.</p></div>Karim Adiprasitohttp://page.mi.fu-berlin.de/adiprasito/Hebrew University of Jerusalemtag:www.math.bgu.ac.il,2005:MeetingDecorator/1632016-10-09T15:04:24+03:002016-11-08T12:06:31+02:00BGU Math<span class="mathjax">Tali Pinsky: Could the Lorenz flow be hyperbolic?</span>November 22, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>I will describe the theory of hyperbolic flows on three manifolds, and then describe a new approach to chaotic flows using knot theory, allowing for topological analysis of singular flows. I’ll use this to show that, surprisingly, the famous Lorenz flow on R^3 can be related to the geodesic flow on the modular surface. When changing the parameters, we also find a new type of topological phases in the Lorenz system.
This will be an introductory talk.</p></div>Tali Pinskyhttp://www.math.tifr.res.in/~tali/TIFR, Indiatag:www.math.bgu.ac.il,2005:MeetingDecorator/1652016-10-09T15:11:22+03:002016-11-16T22:13:09+02:00BGU Math<span class="mathjax">Doron Puder: Random Matrices, Graphs on Surfaces and Mapping Class Group</span>November 29, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>This is joint work with Michael Magee.
Since the 1970’s, Physicists and Mathematicians who study random matrices in the standard models of GUE or GOE,
are aware of intriguing connections between integrals of such random matrices and the enumeration of graphs on surfaces.
We establish a new aspect of this theory: for random matrices sampled from the group U(n) of Unitary matrices. The group structure of these matrices allows us to go further and find surprising algebraic quantities hidden in the values of these integrals.
The talk will be aimed at graduate students, and all notions will be explained.</p></div>Doron Puderhttps://sites.google.com/site/doronpuder/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/1642016-10-09T15:08:10+03:002016-11-27T21:02:06+02:00BGU Math<span class="mathjax">Chloé Perin: First-order logic on the free group and geometry</span>December 6, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>We will give an overview of questions one might ask about the first-order theory of free groups and related groups: how much information can first-order formulas convey about these groups or their elements, what algebraic interpretation can be given for model theoretic notions such as forking independence, etc. It turns out that techniques from geometric group theory are very useful to tackle such problems. Some of these questions have been answered, others are still open - our aim is to give a feel for the techniques and directions of this field.
We will assume no special knowledge of model theory.</p></div>Chloé Perinhttp://math.huji.ac.il/~perin/Hebrew University of Jerusalemtag:www.math.bgu.ac.il,2005:MeetingDecorator/1842016-10-30T15:31:53+02:002016-12-05T16:37:58+02:00BGU Math<span class="mathjax">Boris Zilber: A geometric semantics of algebraic quantum mechanics</span>December 13, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>We approach the formalism of quantum mechanics from the logician point of view and treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics. We then aim to establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states with the action of time evolution operators, which is a limit of finite models. The finitary nature of the space allows us to give a precise meaning and calculate various classical quantum mechanical quantities.
This talk is based on my paper “The semantics of the canonical commutation relation” arxiv.org/abs/1604.07745</p></div>Boris Zilberhttps://people.maths.ox.ac.uk/zilber/Oxfordtag:www.math.bgu.ac.il,2005:MeetingDecorator/1662016-10-09T15:12:41+03:002016-11-27T21:07:04+02:00BGU Math<span class="mathjax">Adam Sheffer: Geometric Incidences and the Polynomial Method</span>December 20, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>While the topic of geometric incidences has existed for
several decades, in recent years it has been experiencing a
renaissance due to the introduction of new polynomial methods. This
progress involves a variety of new results and techniques, and also
interactions with fields such as algebraic geometry and harmonic
analysis.</p>
<p>A simple example of an incidences problem: Given a set of n points and
set of n lines, both in R^2, what is the maximum number of point-line
pairs such that the point is on the line. Studying incidence problems
often involves the uncovering of hidden structure and symmetries.</p>
<p>In this talk we introduce and survey the topic of geometric
incidences, focusing on the recent polynomial techniques and results
(some by the speaker). We will see how various algebraic and analysis
tools can be used to solve such combinatorial problems.</p></div>Adam Shefferhttp://www.its.caltech.edu/~adamsh/California Institute of Technology (Caltech)tag:www.math.bgu.ac.il,2005:MeetingDecorator/1772016-10-19T14:20:30+03:002016-12-14T21:00:50+02:00BGU Math<span class="mathjax">Alon Nishry: Gaussian complex zeros and eigenvalues - Rare events and the emergence of the ‘forbidden’ region</span>December 27, 14:30—15:30, 2016, Math -101<div class="mathjax"><p>The zeros of the Gaussian Entire Function and the infinite Ginibre ensemble are two natural examples of two-dimensional random point configurations whose distribution is invariant under rigid motions of the plane. Due to non-trivial correlations, the features of these two processes are quite different from the ones of the homogeneous Poisson point process. For this reason, these processes are of interest to analysts, probabilists, and mathematical physicists.</p>
<p>I will describe some of the things that we know about the structure and the statistics of these processes. Of particular interest are rare events, when the number of points in a certain domain is very different from its ‘typical’ value. An important example is the ‘hole’ event, when there are no zeros in a large disk. Conditioned on the hole event, the zeros exhibit a large forbidden region, outside the hole, where there are very few zeros asymptotically. This is a new phenomenon, which is in stark contrast to the corresponding result known to hold for the Ginibre ensemble.</p>
<p>Based on a joint work with S. Ghosh (arXiv:1609.00084).</p></div>Alon NishryUniversity of Michigantag:www.math.bgu.ac.il,2005:MeetingDecorator/2112016-12-15T16:44:45+02:002016-12-15T16:44:45+02:00BGU Math<span class="mathjax">Percy Deift : Universality in numerical computations with random data. Case studies</span>January 10, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>This is joint work with Govind Menon, Sheehan Olver and
Thomas Trogdon. The speaker will present evidence for universality in
numerical computations with random data. Given a (possibly stochastic)
numerical algorithm</p>
<p>with random input data, the time (or number of iterations) to
convergence (within a given tolerance) is a random variable, called the
halting time. Two-component universality is observed for the
fluctuations of the halting time, i.e., the</p>
<p>histogram for the halting times, centered by the sample average and
scaled by the sample variance, collapses to a universal curve,
independent of the input data distribution, as the dimension increases.
Thus, up to two components,</p>
<p>the sample average and the sample variance, the statistics for the
halting time are universally prescribed. The case studies include six
standard numerical algorithms, as well as a model of neural computation
and decision making.</p></div>Percy Deift http://math.nyu.edu/faculty/deift/NYUtag:www.math.bgu.ac.il,2005:MeetingDecorator/1672016-10-09T20:32:48+03:002017-01-05T11:25:39+02:00BGU Math<span class="mathjax">Ori Parzanchevski: New directions in Ramanujan graphs and complexes</span>January 17, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>A Ramanujan graph is a finite graph which behaves, in terms of expansion, like its universal cover (which is an infinite tree). In recent years a parallel theory has emerged for simplicial complexes of higher dimension, where the role of the tree is taken by Bruhat-Tits buildings. I will recall briefly the story of Ramanujan graphs, and then explain what are “Ramanujan complexes”, and survey some of the new results regarding their construction and their properties.</p></div>Ori Parzanchevskihttp://math.huji.ac.il/~parzan/Hebrew University of Jerusalemtag:www.math.bgu.ac.il,2005:MeetingDecorator/2202017-01-01T14:43:11+02:002017-01-19T15:51:59+02:00BGU Math<span class="mathjax">Zur Luria: Latin squares, designs, and high-dimensional expanders</span>January 24, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>Expander graphs have many wonderful properties: They are highly connected, pseudorandom, and random walks on expanders are rapidly mixing. The study of these objects has been immensely useful and fruitful for both applicative and theoretical fields. Recently, there has been a lot of interest in the study of generalizations of expander graphs to d-uniform hypergraphs. Several competing definitions have been proposed, each corresponding to a different property of expander graphs. Understanding these definitions, their applications, and the relations between them is the goal of this emerging field.</p>
<p>In a joint work with Alexander Lubotzky and Ron Rosenthal, we proved the existence of bounded degree coboundary expanders, a concept that generalizes high connectivity in graphs. Our work makes use of Peter Keevash’s recent construction of designs: We show that the union of a constant number of designs constructed according to Keevash’s random construction is with high probability a good coboundary expander.</p>
<p>The expander mixing lemma quantifies the extent to which an expander graph is pseudorandom. In a joint work with Nati Linial, we asked if there exist pseudorandom designs. In particular, we conjectured that a typical Latin square design is pseudorandom. This has implications for the Algebraic concept of quasirandom groups, introduced by Gowers. Our conjecture implies that there exist maximally quasirandom quasigroups, and we prove this fact.</p>
<p>There remain many promising directions for further research.</p></div>Zur Luriahttp://ethz.academia.edu/ZurLuriaETH tag:www.math.bgu.ac.il,2005:MeetingDecorator/2192016-12-25T14:48:52+02:002017-03-08T12:34:23+02:00BGU Math<span class="mathjax">Yosif Polterovich: Sloshing, Steklov and corners</span>March 21, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>The sloshing problem is a Steklov type eigenvalue problem describing small oscillations of an ideal fluid. We will give an overview of some latest advances in the study of Steklov and sloshing spectral asymptotics, highlighting the effects arising from corners, which appear naturally in the context of sloshing. In particular, we will outline an approach towards proving the conjectures posed by Fox and Kuttler back in 1983 on the asymptotics of sloshing frequencies in two dimensions. The talk is based on a joint work in progress with M. Levitin, L. Parnovski and D. Sher.</p></div>Yosif Polterovichhttp://www.dms.umontreal.ca/~iossif/Université de Montréaltag:www.math.bgu.ac.il,2005:MeetingDecorator/2372017-02-28T22:19:07+02:002017-02-28T22:20:21+02:00BGU Math<span class="mathjax">Vitali Milman : Some Fundamental Operator Relations in Convex Geometry and Classical Analysis</span>March 28, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>The main goal of the talk is to show how some classical
constructions in Geometry and Analysis appear (and in a unique way)
from elementary and very simple properties. For example, the polarity
relation and support functions are very important and well known
constructions in Convex Geometry, but some elementary properties
uniquely imply these constructions, and lead to their functional
versions, say, in the class of log-concave functions. It turns out
that they are uniquely defined also for this class, as well as for
many other classes of functions.
In this talk we will use these Geometric results as an introduction
to the main topic which involves the analogous results in Analysis. We
will start the Analysis part by characterizing the Fourier transform
(on the Schwartz class in R^n) as, essentially, the only map which
transforms the product to the convolution, and discuss a very
surprising rigidity of the Chain Rule Operator equation (which
characterizes the derivation operation). There will be more examples
pointing to an exciting continuation of this direction in Analysis.</p>
<p>The results of the geometric part are mostly joint work with Shiri
Artstein-Avidan, and of the second, Analysis part, are mostly joint
work with Hermann Koenig.</p>
<p>The talk will be easily accessible for graduate students.</p></div>Vitali Milman http://www.math.tau.ac.il/~milman/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/2382017-02-28T22:24:39+02:002019-05-02T17:03:12+03:00BGU Math<span class="mathjax">Victor Abrashkin: Galois groups of local fields, Lie algebras and ramification</span>April 4, 14:30—15:30, 2017, Math -101Victor Abrashkinhttp://www.maths.dur.ac.uk/~dma0va/U. of Durhamtag:www.math.bgu.ac.il,2005:MeetingDecorator/2392017-02-28T22:26:10+02:002017-04-12T16:07:32+03:00BGU Math<span class="mathjax">Inna Entova-Aizenbud: Stability in representation theory of the symmetric groups</span>April 25, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>In the finite-dimensional representation theory of the symmetric groups <span class="kdmath">$S_n$</span> over the base field <span class="kdmath">$\mathbb{C}$</span>, there is an an interesting phenomena of “stabilization” as <span class="kdmath">$n \to \infty$</span>: some representations of <span class="kdmath">$S_n$</span> appear in sequences <span class="kdmath">$(V_n)_{n \geq 0}$</span>, where each <span class="kdmath">$V_n$</span> is a finite-dimensional representation of <span class="kdmath">$S_n$</span>, where <span class="kdmath">$V_n$</span> become “the same” in a certain sense for <span class="kdmath">$n >> 0$</span>.</p>
<p>One manifestation of this phenomena are sequences <span class="kdmath">$(V_n)_{n \geq 0}$</span> such that the characters of <span class="kdmath">$S_n$</span> on <span class="kdmath">$V_n$</span> are “polynomial in $n$”. More precisely, these sequences satisfy the condition: for <span class="kdmath">$n>>0$</span>, the trace (character) of the automorphism <span class="kdmath">$\sigma \in S_n$</span> of <span class="kdmath">$V_n$</span> is given by a polynomial in the variables <span class="kdmath">$x_i$</span>, where <span class="kdmath">$x_i(\sigma)$</span> is the number of cycles of length <span class="kdmath">$i$</span> in the permutation <span class="kdmath">$\sigma$</span>.</p>
<p>In particular, such sequences <span class="kdmath">$(V_n)_{n \geq 0}$</span> satisfy the agreeable property that <span class="kdmath">$\dim(V_n)$</span> is polynomial in <span class="kdmath">$n$</span>.</p>
<p>Such “polynomial sequences” are encountered in many contexts: cohomologies of configuration spaces of <span class="kdmath">$n$</span> distinct ordered points on a connected oriented manifold, spaces of polynomials on rank varieties of <span class="kdmath">$n \times n$</span> matrices, and more. These sequences are called <span class="kdmath">$FI$</span>-modules, and have been studied extensively by Church, Ellenberg, Farb and others, yielding many interesting results on polynomiality in <span class="kdmath">$n$</span> of dimensions of these spaces.</p>
<p>A stronger version of the stability phenomena is described by the following two settings:</p>
<ul>
<li> The algebraic representations of the infinite symmetric group $$S_{\infty} = \bigcup_{n} S_n,$$ where each representation of $$S_{\infty}$$ corresponds to a ``polynomial sequence'' $$(V_n)_{n \geq 0}$$.</li>
<li> The "polynomial" family of Deligne categories $$Rep(S_t), ~t \in \mathbb{C}$$, where the objects of the category $$Rep(S_t)$$ can be thought of as "continuations of sequences $$(V_n)_{n \geq 0}$$" to complex values of $$t=n$$. </li>
</ul>
<p>I will describe both settings, show that they are connected, and explain some applications in the representation theory of the symmetric groups.</p></div>Inna Entova-Aizenbudhttps://www.math.bgu.ac.il/~entova/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/2442017-03-15T12:21:09+02:002017-03-27T20:49:53+03:00BGU Math<span class="mathjax">Jozsef Solymosi: Geometric methods in additive combinatorics.</span>May 9, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>Many interesting problems in additive combinatorics have a translation to geometric questions. A classical example to this is when Elekes used point-line incidence bounds on the sum-product problem of Erdos and Szemeredi. In this talk we will see more examples and will list several open problems in additive combinatorics.</p></div> Jozsef Solymosihttp://www.math.ubc.ca/~solymosi/UBCtag:www.math.bgu.ac.il,2005:MeetingDecorator/2632017-04-12T16:12:21+03:002017-05-10T09:05:59+03:00BGU Math<span class="mathjax">Jon Aaronson: Rational ergodicity and distributional limits of infinite ergodic transformations.</span>May 16, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>In infinite ergodic theory, absolutely normalized pointwise convergence of
ergodic sums fails. Sometimes, this is replacable by weaker modes of convergence. Namely distributional limits and/or weak limits (as in e.g. “rational ergodicity”).
We’ll review the subject exhibiting “natural examples” and then see the “latest news” that every random variable on the positive reals occurs as the distributional limit of some infinite ergodic transformation. As a corollary, we obtain a complete exhibition of the possible “<span class="kdmath">$A$</span>-rational ergodicity properties” (<span class="kdmath">$0 < A \le \infty$</span>) for infinite ergodic transformations.
The main construction follows by “inversion” from a related construction showing that every random variable on the positive reals occurs as the distributional limit of the partial sums some positive, ergodic stationary process normalized by a 1-regularly varying normalizing sequence.</p>
<p>The “latest news” is joint work with Benjamin Weiss.
For further info. see arXiv:1604.03218.</p></div>Jon Aaronsonhttp://www.math.tau.ac.il/~aaro/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/2352017-02-28T22:16:42+02:002017-05-24T12:10:47+03:00BGU Math<span class="mathjax">Ishai Dan-Cohen: A fundamental group approach to the unit equation</span>June 6, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>Over the course of the last 15 years or so, Minhyong Kim has developed a method for making effective use of the fundamental group to bound sets of solutions to hyperbolic equations; his method opens a new avenue in the quest for an effective version of the Mordell conjecture. But although Kim’s approach has led to the construction of explicit bounds in special cases, the problem of realizing the potential effectivity of his methods remains a difficult and beautiful open problem. In the case of the unit equation, this problem may be approached via ``motivic’’ methods. Using these methods we are able to describe an algorithm; its output upon halting is provably the set of integral points, while its halting depends on conjectures. This will be a colloquium-version of a talk that I gave at the algebraic geometry seminar here in November of 2015.</p></div>Ishai Dan-Cohenhttps://www.math.bgu.ac.il/~ishida/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/2712017-05-10T09:03:24+03:002017-05-16T22:53:53+03:00BGU Math<span class="mathjax">Klaus Künnemann: The Calabi-Yau problem in archimedean and non-archimedean geometry</span>June 13, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>We describe the Calabi-Yau problem on complex manifolds and its analog in non-archimedean geometry. On complex manifolds the Calabi-Yau problem asks locally for solutions of a PDE of Monge-Ampère type. The complex Calabi-Yau problem was posed by Calabi in 1954 and solved by Yau in 1978.
After a presentation of the complex case we give a brief introduction to non-archimedean geometry and report on the recent progress in the non-archimedean case.</p></div> Klaus Künnemannhttp://homepages.uni-regensburg.de/~kuk22111/Universität Regensburg tag:www.math.bgu.ac.il,2005:MeetingDecorator/2752017-05-24T12:12:11+03:002017-06-12T21:01:44+03:00BGU Math<span class="mathjax">Arkady Poliakovsky: Jumps detection in Besov spaces via a new BBM formula. Applications to Aviles-Giga type functionals</span>June 20, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>Motivated by the formula, due to Bourgain, Brezis and Mironescu,
<span class="kdmath">$\lim_{\varepsilon\to 0^+} \int_\Omega\int_\Omega
\frac{|u(x)-u(y)|^q}{|x-y|^q}\,\rho_{\varepsilon}(x-y)\,dx\,dy=K_{q,N}\|\nabla
u\|_{L^{q}}^q\,,$</span>
that characterizes the functions in <span class="kdmath">$L^q$</span> that belong to <span class="kdmath">$W^{1,q}$</span>
(for <span class="kdmath">$q>1$</span>) and <span class="kdmath">$BV$</span> (for <span class="kdmath">$q=1$</span>), respectively, we study what
happens when one replaces the denominator in the expression above by
<span class="kdmath">$|x-y|$</span>. It turns out that, for <span class="kdmath">$q>1$</span> the corresponding functionals
“see’’ only the jumps of the <span class="kdmath">$BV$</span> function. We further identify the
function space relevant to the study of these functionals, the space <span class="kdmath">$BV^q$</span>, as the
Besov space <span class="kdmath">$B^{1/q}_{q,\infty}$</span>. We show, among
other things, that <span class="kdmath">$BV^q(\Omega)$</span> contains both the spaces
<span class="kdmath">$BV(\Omega)\cap L^\infty(\Omega)$</span> and <span class="kdmath">$W^{1/q,q}(\Omega)$</span>. We also
present applications to the study of singular
perturbation problems of Aviles-Giga type.</p></div>Arkady PoliakovskyBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/2732017-05-17T12:15:17+03:002017-05-24T12:07:50+03:00BGU Math<span class="mathjax">Yair Glasner : Invariant random subgroups in combinatorics, dynamics and representation theory</span>June 27, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>Let G be a locally compact group. For example it could be a discrete group or a Lie group.
A random closed subgroup of G, whose distribution is invariant under conjugation by elements of G
is called an “invariant random subgroup of G” or IRS for short.</p>
<p>IRS turn out to be very useful in a surprisingly wide array of applications even outside of group theory.
Yielding significant contributions to a-priori unrelated subjects such as these mentioned in the title.</p>
<p>I will survey some of these developments by stating one theorem in each of these
subjects explaining exactly how IRS come into the picture.</p></div>Yair Glasner https://www.math.bgu.ac.il/~yairgl/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/2892017-09-11T17:53:31+03:002017-09-11T19:42:07+03:00BGU Math<span class="mathjax">Gabriel Katz: Holography of traversing flows and its applications to the inverse scattering problems</span>October 24, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>We study the non-vanishing gradient-like vector fields $v$ on smooth compact manifolds $X$ with boundary. We call such fields traversing.</p>
<p>With the help of a boundary generic field $v$, we divide the boundary $\d X$ of $X$ into two complementary compact manifolds, $\d^+X(v)$ and $\d^-X(v)$. Then we introduce the causality map $C_v: \d^+X(v) \to \d^-X(v)$, a distant relative of the Poincare return map.</p>
<p>Let $\mathcal F(v)$ denote the oriented 1-dimensional foliation on $X$, produced by a traversing $v$-flow.</p>
<p>Our main result, the Holography Theorem, claims that, for boundary generic traversing vector fields $v$, the knowledge of the causality map $C_v$ is allows for a reconstruction of the pair $(X, \mathcal F(v))$, up to a homeomorphism $\Phi: X \to X$ which is the identity on the boundary $\d X$. In other words, for a massive class of ODE’s, we show that the topology of their solutions, satisfying a given boundary value problem, is rigid. We call these results ``holographic” since the $(n+1)$-dimensional $X$ and the un-parameterized dynamics of the flow on it are captured by a single correspondence $C_v$ between two $n$-dimensional screens, $\d^+X(v)$ and $\d^-X(v)$.</p>
<p>This holography of traversing flows has numerous applications to the dynamics of general flows. Time permitting, we will discuss some applications of the Holography Theorem to the geodesic flows and the inverse scattering problems on Riemannian manifolds with boundary.</p></div>Gabriel KatzMITtag:www.math.bgu.ac.il,2005:MeetingDecorator/2902017-09-11T17:54:21+03:002017-09-11T17:54:24+03:00BGU Math<span class="mathjax">Faculty Meeting (no colloquium): TBA</span>October 31, 14:30—15:30, 2017, Math -101Faculty Meeting (no colloquium)tag:www.math.bgu.ac.il,2005:MeetingDecorator/2962017-09-29T17:19:47+03:002017-10-21T16:28:43+03:00BGU Math<span class="mathjax">Yakov Pesin: Path connectedness of the space of hyperbolic ergodic measures</span>November 7, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>In 1977 Sigmund proved that the space of ergodic measures supported on a basic set of an Axiom A diffeomorphism is path connected. In the talk I will describe a substantial generalization of this result to the space of hyperbolic ergodic measures supported on an isolated homoclinic class of a general diffeomorphism. Such homoclinic classes should be viewed as basic structural elements of any dynamics. Examples will be discussed. This is a joint work with A. Gorodetsky.</p></div>Yakov Pesinhttps://www.math.psu.edu/pesin/Penn State Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/2872017-09-07T14:37:05+03:002017-11-01T08:13:15+02:00BGU Math<span class="mathjax">Michael Entov: First steps of the symplectic function theory</span>November 14, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>Symplectic function theory studies the space of smooth (compactly supported) functions on a symplectic manifold. This space is equipped with two structures: the Poisson bracket and the $C^0$ (or uniform) norm of the functions. Interestingly enough, while the Poisson bracket of two functions depends on their first derivatives, there are non-trivial restrictions on its behavior with respect to the $C^0$-norm. We will discuss various results of this kind and their applications to Hamiltonian dynamics.</p></div>Michael Entovhttps://sites.google.com/site/michaelentov/Techniontag:www.math.bgu.ac.il,2005:MeetingDecorator/2942017-09-18T02:20:47+03:002017-10-29T20:23:47+02:00BGU Math<span class="mathjax">Alex Lubotzky: First order rigidity of high-rank arithmetic groups</span>November 21, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>The family of high rank arithmetic groups is class of groups which is playing an important role in various areas of mathematics. It includes SL(n,Z), for n>2 , SL(n, Z[1/p] ) for n>1, their finite index subgroups and many more. A number of remarkable results about them have been proven including; Mostow rigidity, Margulis Super rigidity and the Quasi-isometric rigidity. We will talk about a new type of rigidity : “first order rigidity”. Namely if D is such a non-uniform characteristic zero arithmetic group and E a finitely generated group which is elementary equivalent to it ( i.e., the same first order theory in the sense of model theory) then E is isomorphic to D. This stands in contrast with Zlil Sela’s remarkable work which implies that the free groups, surface groups and hyperbolic groups ( many of which are low-rank arithmetic groups) have many non isomorphic finitely generated groups which are elementary equivalent to them.
Joint work with Nir Avni and Chen Meiri.</p></div>Alex Lubotzkyhttp://www.ma.huji.ac.il/~alexlub/Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/2912017-09-12T18:50:54+03:002017-11-22T09:29:09+02:00BGU Math<span class="mathjax">Itay Kaplan: On dense subgroups of permutation groups</span>November 28, 14:30—15:30, 2017, Math -101<div class="mathjax"><p>Joint work with Pierre Simon.
I will present a criterion that ensures that Aut(M) has a 2-generated dense subgroup when M is a countable structure (which holds in many examples), and discuss related subjects.</p></div>Itay Kaplanhttps://sites.google.com/site/itay80/Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/2922017-09-16T21:37:50+03:002017-11-27T13:58:33+02:00BGU Math<span class="mathjax">Gal Binyamini: Effectivity in tame and diophantine geometry</span>December 5, 14:30—15:30, 2017, Math -101<div class="mathjax">
<p>I will describe a link between tame geometry and diophantine geometry that has been unfolding in the past decade following the fundamental theorem of Pila-Wilkie in the theory of o-minimal structures. In particular I will describe how this theorem has been used in proofs of the Manin-Mumford conjecture (by Pila-Zannier), the Andre-Oort conjecture for modular curves (by Pila) and many other questions of “unlikely intersections” in diophantine geometry.
I will then discuss questions related to effectivity of the Pila-Wilkie theorem and its implications for the diophantine applications. In particular I will discuss our recent proof (joint with Novikov) of the restricted form of Wilkie’s conjecture, and more recent results on effectivity for the larger class of semi-Noetherian sets.</p></div>Gal Binyaminihttps://binyamini.wordpress.com/Weizmanntag:www.math.bgu.ac.il,2005:MeetingDecorator/3222017-11-20T16:19:32+02:002017-12-11T13:27:50+02:00BGU Math<span class="mathjax">Math-Physics meeting: TBA</span>December 12, 14:15—17:00, 2017, Math -101<div class="mathjax"><p>14:15-14:30-coffee break</p>
<p>14:30-14:40 Inna Entova</p>
<p>Title: Superalgebras and tensor categories</p>
<p>Abstract: I will briefly describe what are Lie superalgebras, and present some questions on their representations which have been studied in the last few years.</p>
<p>14:45-14:55 Daniel Berend</p>
<p>Title: Applied Probability.</p>
<p>Abstract: We will present an example of a problem in this area.</p>
<p>15:00-15:10 Shelomo Ben Abraham</p>
<p>Aperiodic tilings – an overflight</p>
<p>15:15-15:25 Yair Glasner</p>
<p>Title: A probabilistic Kesten theorem and counting periodic orbits in finite graphs.</p>
<p>Abstract: I will describe the notion of Invariant ransom subgroups and how we used it to give precise estimates on the asymptotic number of closed (non-backtracking) circuits in finite graphs.</p>
<p>15:30-15:40 Tom Meyerovitch</p>
<p>Title:
Gibbs measures and Markov Random Fields</p>
<p>Abstract:
From an abstract mathematical point of view, a Markov Random Field is a random function on the vertices of some (finite or countable) graph, with a certain conditional independence property. Every Gibbs measure (for a local interaction) is a Markov random Field. An old theorem due to Hammersley and Clifford establishes the converse, under some extra assumptions. I will present these notions and state some (slightly more) recent results and questions.</p>
<p>Coffee break</p>
<p>16:00-16:10 Doron Cohen</p>
<p>Title: Stochastic Processes and Quantum Chaos</p>
<p>Abstract: Our recent study considers the dynamics of stochastic and quantum models, in particular ring geometry: (a) with classical particles that perform random walk in disordered environment; (b) with quantum Bose particles whose dynamics is coherent. One theme that arises in both cases is the Anderson-type localization of the eigenstates.</p>
<p>16:15-16:25 Ilan Hirshberg</p>
<p>Title: C*-dynamical systems and crossed products.
Abstract: I’ll briefly say a few words on what the words above mean, and loosely what kinds of problems I tend to look at.</p>
<p>16:30-16:40 Victor Vinnikov
Noncommutative Function Theory</p>
<p>One of my main interests in recent years have been in developing a theory of functions of several noncommuting variables. It turns out, following the pioneering ideas of Joseph L. Taylor in the early 1970s, that such functions can be naturally viewed as functions on tuples of square matrices of all sizes that satisfy certain compatibility conditions as we vary the size of matrices. Noncommutative functions are related, among other things, to the theory of operator spaces (including such topics as complete positivity and matrix convexity) and to free probability.</p>
<p>Some other topics that I am interested in, and that I can discuss in case of interest, are function theory on the unit ball and on the polydisc in C^n and related operator theory, line and vector bundles on compact Riemann surface, especially theta functions and Cauchy kernels, determinantal representations of algebraic varieties, and various topics on convexity in real algebraic geometry related to hyperbolic polynomials.</p>
<p>16:45-16:55 David Eichler</p>
<p>Vortex-based, zero conflict routing in networks</p>
<p>Abstract: A novel approach is suggested for reducing traffic conflict in 2D spatial networks. Intersections without primary conflicts are defined as zero traffic conflict (ZTC) designs. A provably complete classification of maximal ZTC designs is presented. It is shown that there are 9 four-way and 3 three-way maximal ZTC intersection designs, to within mirror, rotation, and arrow reversal symmetry. Vortices are used to design networks where all or most intersections are ZTC. Increases in average travel distance, relative to unrestricted intersecting flow, are modest, and represent a worthwhile cost of reducing traffic conflict.</p></div>Math-Physics meetingtag:www.math.bgu.ac.il,2005:MeetingDecorator/2982017-10-18T10:00:23+03:002017-12-13T09:17:30+02:00BGU Math<span class="mathjax">Boaz Slomka: Approximations of convex bodies by measure-generated sets</span>December 19, 13:00—14:00, 2017, Math -101<div class="mathjax"><p>Problems pertaining to approximation and their applications have been extensively studied in the theory of convex bodies. In this talk we discuss several such problems, and focus on their extension to the realm of measures. In particular, we discuss variations of problems concerning the approximation of convex bodies by polytopes with a given number of vertices. This is done by introducing a natural construction of convex sets from Borel measures. We provide several estimates concerning these problems, and describe an application to bounding certain average norms.</p>
<p>Based on joint work with Han Huang</p></div>Boaz Slomkahttp://www-personal.umich.edu/~bslomka/University of Michigantag:www.math.bgu.ac.il,2005:MeetingDecorator/3362017-12-21T11:52:19+02:002017-12-21T11:52:32+02:00BGU Math<span class="mathjax">Benny Sudakov: Equiangular lines and spherical codes in Euclidean spaces</span>January 2, 13:00—14:00, 2018, Math -101<div class="mathjax"><p>A family of lines through the origin in Euclidean space is called
equiangular if any pair of lines defines the same angle. The problem
of estimating the maximum cardinality of such a family in $R^n$ was
extensively studied for the last 70 years. Answering a question of
Lemmens and Seidel from 1973, in this talk we show that for every
fixed angle$\theta$ and sufficiently large $n$ there are at most
$2n-2$ lines in$R^n$ with common angle $\theta$. Moreover, this is
achievable only when $\theta =\arccos \frac{1}{3}$. Various extensions
of this result to the more general settings of lines with $k$ fixed
angles and of spherical codes will be discussed as well. Joint work
with I. Balla, F. Drexler and P. Keevash.</p></div>Benny Sudakovhttps://people.math.ethz.ch/~sudakovb/ETHtag:www.math.bgu.ac.il,2005:MeetingDecorator/3112017-11-06T07:53:43+02:002017-12-17T13:06:46+02:00BGU Math<span class="mathjax">Naomi Feldheim: Gaussian stationary processes: a spectral perspective</span>January 2, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>A Gaussian stationary process is a random function f:R–>R or f:C–>C,
whose distribution is invariant under real shifts, and whose evaluation at
any finite number of points is a centered Gaussian random vector.
The mathematical study of these random functions goes back at least 75 years,
with pioneering works by Kac, Rice and Wiener.
Nonethelss, many basic questions about them, such as the fluctuations of their number of zeroes,
or the probability of having no zeroes in a large region, remained unanswered for many years.</p>
<p>In this talk, we will give an introduction to Gaussian stationary processes, and
describe how a spectral perspective combined with tools from harmonic, real and complex analysis,
yields new results about such long-lasting questions.</p></div>Naomi Feldheimhttp://www.wisdom.weizmann.ac.il/~/naomifel/index.htmlWeizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/2972017-10-15T14:32:12+03:002018-01-07T14:59:21+02:00BGU Math<span class="mathjax">George Glauberman: An analogue of Borel’s Fixed Point Theorem for finite p-groups</span>January 9, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>Borel’s Fixed Point Theorem states that a solvable connected
algebraic group G acting on a non-empty complete variety V
must have a fixed point. Thus, if V consists of subgroups of G,
and G acts on V by conjugation, then some subgroup in V is normal
in G.</p>
<p>Although G is infinite or trivial here, we can use the method of proof
to obtain applications to finite p-groups. We plan to discuss some
applications and some open problems. No previous knowledge of
algebraic groups is needed.</p></div> George Glaubermanhttp://math.uchicago.edu/~gg/University of Chicagotag:www.math.bgu.ac.il,2005:MeetingDecorator/3022017-10-31T13:02:48+02:002017-11-30T15:28:37+02:00BGU Math<span class="mathjax">David Evans: The Search for the Exotic : Subfactors and Conformal Field Theory</span>January 16, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>I will discuss the programme to understand conformal field theory via
subfactors and twisted equivariant K-theory.
This has also resulted in a better understanding of the
double of the Haagerup subfactor, which was previously thought to be
exotic and un-related to known models.</p></div>David Evanshttps://profdavideevans.wordpress.com/Cardiff Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4222018-08-24T16:00:01+03:002018-08-24T16:00:05+03:00BGU Math<span class="mathjax">Faculty meeting: TBA</span>October 16, 14:30—15:30, 2018, Math -101Faculty meetingtag:www.math.bgu.ac.il,2005:MeetingDecorator/4282018-08-27T14:04:15+03:002018-10-16T08:26:23+03:00BGU Math<span class="mathjax">Meny Shlossberg: Algebraic entropy on strongly compactly covered groups</span>October 23, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups G such that every element of G is contained in a compact open normal subgroup of G. For continuous endomorphisms ϕ:G→G of these groups we compute the algebraic entropy and study its properties. Also an Addition Theorem is available under suitable conditions.</p>
<p>This is joint work with Anna Giordano Bruno and Daniele Toller.</p></div>Meny Shlossberghttp://www.shlossberg.com/doku.phpUniversity of Udinetag:www.math.bgu.ac.il,2005:MeetingDecorator/4232018-08-24T16:01:40+03:002018-11-04T09:53:54+02:00BGU Math<span class="mathjax">Yair Hartman: Which groups have bounded harmonic functions?</span>November 6, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>Bounded harmonic functions on groups are closely related to random walks on groups. It has long been known that all abelian groups, and more generally, virtually nilpotent groups are “Choquet-Deny groups”: these groups cannot support non-trivial bounded harmonic functions. Equivalently, their Furstenberg-Poisson boundary is trivial, for any random walk.
I will present a recent result where we complete the classification of discrete countable Choquet-Deny groups, proving a conjuncture of Kaimanovich-Vershik. We show that any finitely generated group which is not virtually nilpotent, is not Choquet-Deny. Surprisingly, the key is not the growth rate of the group, but rather the algebraic infinite conjugacy class property (ICC).</p>
<p>This is joint work with Joshua Frisch, Omer Tamuz and Pooya Vahidi Ferdowsi.</p></div>Yair HartmanBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/4242018-08-24T16:03:52+03:002018-11-11T20:17:19+02:00BGU Math<span class="mathjax">Stefan Friedl: Recent developments in 3-manifold topology</span>November 13, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>We will explain the Geometrization Theorem proved by Perelman in 2003 and we will talk about the Virtual Fibering Theorem proved several years ago by Ian Agol and Dani Wise. I will not assume any previous knowledge of 3-manifold topology.</p></div>Stefan Friedlhttps://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/friedl/Regensburg Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4252018-08-24T16:04:44+03:002018-11-19T07:54:33+02:00BGU Math<span class="mathjax">Gili Golan: Invariable generation of Thompson groups</span>November 20, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>A subset S of a group G invariably generates G if for every choice of $g(s)\in G$ ,$s\in S$ the set ${s^g(s):s\in S}$ is a generating set of G. We say that a group G is invariably generated if such S exists, or equivalently if S=G invariably generates G. In this talk, we study invariable generation of Thompson groups. We show that Thompson group F is invariably generated by a finite set, whereas Thompson groups T and V are not invariable generated. This is joint work with Tsachik Gelander and Kate Juschenko.</p></div>Gili GolanBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/4302018-10-02T14:43:40+03:002018-11-18T12:45:33+02:00BGU Math<span class="mathjax">Michal Marcinkowski: 3rd bounded cohomology of volume preserving transformation groups.</span>November 27, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>Let M be a Riemannian manifold with a given volume form and hyperbolic fundamental group. We will explain how to construct coclasses in the cohomology of the group of volume preserving diffeomorphisms (or homeomorphisms) of M. As an application, we show that the 3rd bounded cohomology of those groups
is highly non-trivial.</p></div>Michal Marcinkowskihttp://www.math.uni.wroc.pl/~marcinkow/Regensburg Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4572018-10-23T18:48:32+03:002018-12-02T13:20:02+02:00BGU Math<span class="mathjax">Boaz Slomka: Improved bounds for Hadwiger’s covering problem</span>December 4, 13:00—14:00, 2018, Math -101<div class="mathjax"><p>A long-standing open problem, known as Hadwiger’s covering problem, asks what is the smallest natural number N(n) such that every convex body in $R^n$ can be covered by a union of the interiors of at most N(n) of its translates. Despite continuous efforts, the best general upper bound known for this number remains as it was more than sixty years ago, of the order of $\binom{2n}{n}n\ln n$.</p>
<p>In this talk, I will discuss some history of this problem and present a new result in which we improve this bound by a sub-exponential factor. Our approach combines ideas from previous work, with tools from Asymptotic Geometric Analysis. Namely, we make use of measure concentration in the form of thin-shell estimates for isotropic log-concave measures.</p>
<p>If time permits we shall discuss some other methods and results concerning this problem and its relatives.</p>
<p>Joint work with H. Huang, B. Vritsiou, and T. Tkocz</p></div>Boaz Slomkahttp://www.wisdom.weizmann.ac.il/~boazsl/Weizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/4532018-10-14T09:38:02+03:002018-12-02T09:03:29+02:00BGU Math<span class="mathjax">Eli Shamovich: Operator algebras and noncommutative analytic geometry</span>December 11, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>The Hardy space $H^2(\mathbb{D})$ is the Hilbert space of analytic functions on the unit disc with square summable Taylor coefficients is a fundamental object both in function theory and in operator algebras. The operator of multiplication by the coordinate function turns $H^2(\mathbb{D})$ into a module over the polynomial ring $\mathbb{C}[z]$. Moreover, this space is universal, in the sense that whenever we have a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z]$, such that $z$ acts by a pure row contraction, we have that $\cH$ is a quotient of several copies of $H^2(\mathbb{D})$ by a submodule.</p>
<p>There are two multivariable generalizations of this property, one commutative and one free. I will show why the free generalization is in several ways the correct one. We will then discuss quotients of the noncommutative Hardy space and their associated universal operator algebras. Each such quotient naturally gives rise to a noncommutative analytic variety and it is a natural question to what extent does the geometric data determine the operator algebraic one. I will provide several answers to this question.</p>
<p>Only basic familiarity with operators on Hilbert spaces and complex analysis is assumed.</p></div>Eli Shamovichhttps://uwaterloo.ca/scholar/eshamoviWaterloo Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4292018-09-11T16:20:11+03:002018-09-11T16:21:36+03:00BGU Math<span class="mathjax">Eyal Subag: Symmetries of the hydrogen atom and algebraic families</span>December 18, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.</p></div>Eyal Subaghttp://www.personal.psu.edu/eus25/Penn Statetag:www.math.bgu.ac.il,2005:MeetingDecorator/4262018-08-24T16:07:30+03:002018-12-24T21:50:58+02:00BGU Math<span class="mathjax">Vera Serganova: Borel-Weil-Bott theorem for algebraic supergroups and weak BGG reciprocity</span>December 25, 14:30—15:30, 2018, Math -101<div class="mathjax"><p>We will review some results about superanalogue of Borel-Weil-Bott theorem, explain the role of Weyl groupoid and prove a weak version of BGG reciprocity. Then we illustrate how BGG reciprocity can be used for computing the Cartan matrix of the category of finite dimensional representations of the nontivial central extension of the periplectic supergroup P(4).</p></div>Vera Serganovahttps://math.berkeley.edu/people/faculty/vera-serganovaUniversity of California, Berkeleytag:www.math.bgu.ac.il,2005:MeetingDecorator/4272018-08-24T16:13:28+03:002019-01-06T09:42:29+02:00BGU Math<span class="mathjax">Dmitry Batenkov: Stability of some super-resolution problems</span>January 8, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>The problem of computational super-resolution asks to recover fine
features of a signal from inaccurate and bandlimited data, using an
a-priori model as a regularization. I will describe several
situations for which sharp bounds for stable reconstruction are known,
depending on signal complexity, noise/uncertainty level, and available
data bandwidth. I will also discuss optimal recovery algorithms, and
some open questions.</p></div>Dmitry Batenkovhttps://dimabatenkov.info/MITtag:www.math.bgu.ac.il,2005:MeetingDecorator/4992019-01-09T14:26:53+02:002019-01-09T14:26:55+02:00BGU Math<span class="mathjax">Faculty meeting: TBA</span>February 26, 14:30—15:30, 2019, Math -101Faculty meetingtag:www.math.bgu.ac.il,2005:MeetingDecorator/4332018-10-07T08:38:53+03:002019-02-28T09:33:45+02:00BGU Math<span class="mathjax">Lev Buhovski: Critical points of eigenfunctions</span>March 5, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>On a closed Riemannian manifold, the Courant nodal domain theorem gives an upper bound on the number of nodal domains of n-th eigenfunction of the Laplacian. In contrast to that, there does not exist such bound on the number of isolated critical points of an eigenfunction. I will try to sketch a proof of the existence of a Riemannian metric on the 2-dimensional torus, whose Laplacian has infinitely many eigenfunctions, each of which has infinitely many isolated critical points. Based on a joint work with A. Logunov and M. Sodin.</p></div>Lev Buhovskihttp://www.math.tau.ac.il/~levbuh/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/4392018-10-09T16:05:13+03:002019-01-09T14:26:27+02:00BGU Math<span class="mathjax">Wojciech Samotij: Large deviations in random graphs</span>March 12, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>Suppose that Y_1, …, Y_N are i.i.d. (independent identically distributed) random variables and let X = Y_1 + … + Y_N. The classical theory of large deviations allows one to accurately estimate the probability of the tail events X < (1-c)E[X] and X > (1+c)E[X] for any positive c. However, the methods involved strongly rely on the fact that X is a linear function of the independent variables Y_1, …, Y_N. There has been considerable interest—both theoretical and practical—in developing tools for estimating such tail probabilities also when X is a nonlinear function of the Y_i. One archetypal example studied by both the combinatorics and the probability communities is when X is the number of triangles in the binomial random graph G(n,p). I will discuss two recent developments in the study of the tail probabilities of this random variable. The talk is based on joint works with Matan Harel and Frank Mousset and with Gady Kozma.</p></div>Wojciech Samotijhttp://www.math.tau.ac.il/~samotij/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5072019-03-03T14:57:56+02:002019-03-26T17:14:12+02:00BGU Math<span class="mathjax">Scott Edward Schmieding: The stabilized automorphism group of a subshift</span>April 2, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>The automorphism group $Aut(\sigma)$ of a subshift $(X,\sigma)$ consists of all homeomorphisms $\phi\colon X\to X$ such that $\phi\sigma=\sigma\phi$. When $(X,\sigma)$ is a shift of finite type, $Aut(\sigma)$ is known to have a rich group structure, and we’ll discuss some background and problems related to the study of $Aut(\sigma)$. Finally, we’ll introduce a certain stabilized automorphism group and outline results which, among other things, provide new cases in which we can distinguish (up to isomorphism) the stabilized groups of certain full shifts. This is joint work with Yair Hartman and Bryna Kra.</p></div>Scott Edward Schmiedinghttps://www.scholars.northwestern.edu/en/persons/scott-edward-schmiedingNorthwestern Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5152019-03-07T12:06:20+02:002019-04-28T14:01:18+03:00BGU Math<span class="mathjax">Assaf Rinot: Hindman’s theorem and uncountable groups</span>April 30, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>In the early 1970’s, Hindman proved a beautiful theorem in
additive Ramsey theory asserting that for any partition of the set of
natural numbers into finitely many cells, there exists some infinite set
such that all of its finite sums belong to a single cell.</p>
<p>In this talk, we shall address generalizations of this statement to the
realm of the uncountable. Among others, we shall present a new theorem
concerning the real line which simultaneously generalizes a recent
theorem of Hindman, Leader and Strauss, and a classic theorem of Galvin
and Shelah.</p>
<p>This is joint work with David Fernandez-Breton.</p></div>Assaf Rinothttp://u.math.biu.ac.il/~rinotas/BIUtag:www.math.bgu.ac.il,2005:MeetingDecorator/5062019-03-03T14:56:30+02:002019-05-06T08:38:31+03:00BGU Math<span class="mathjax">Jean-Pierre Conze: Stationary random walks: recurrence, diffusion, examples, billiards</span>May 7, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>The billiards in the plane with periodic obstacles are dynamical systems with a simple description but intricate features in their behavior. A specific example, introduced by Paul and Tatania Ehrenfest in 1912, is the so-called “wind-tree” model, where a ball reduced to a point moves on the plane and collides with parallel rectangular scatters according to the usual law of geometric optics.</p>
<p>Natural questions are: does the ball return close to its starting point (recurrence), how fast the ball goes far from it? (diffusion), what is the set of scatters reached by the ball?</p>
<p>These billiards can be modeled as dynamical systems with an infinite invariant measure. The
position of the particle can be viewed as a stationary random walk, sum of a stationary
sequence of random variables with values in $R^2$, analogous to the classical random walks. For the billiard the increments are the displacement vectors between two collisions, while for the classical random walks the increments are independent random variables.</p>
<p>In the talk, after some general facts about systems with infinite invariant measure, the notions of recurrence and growth (or diffusion) of a stationary random walk will be illustrated by examples, in particular the “wind-tree” model.</p></div>Jean-Pierre Conzehttps://perso.univ-rennes1.fr/jean-pierre.conze/University of Rennestag:www.math.bgu.ac.il,2005:MeetingDecorator/5202019-03-12T16:54:06+02:002019-03-19T15:46:07+02:00BGU Math<span class="mathjax">Orr Shalit: Dilation theory: fresh directions with new applications</span>May 14, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>Dilation theory is a paradigm for understanding a general class of objects in terms of a better understood class of objects, by way of exhibiting every general object as ``a part of” a special, well understood object.
In the first part of this talk I will discuss both classical and contemporary results and applications of dilation theory in operator theory. Then I will describe a dilation theoretic problem that we got interested in very recently: what is the optimal constant $c = c_{\theta,\theta’}$, such that every pair of unitaries $U,V$ satisfying $VU = e^{i\theta} UV$ can be dilated to a pair of $cU’, cV’$, where $U’,V’$ are unitaries that satisfy the commutation relation $V’U’ =e^{i\theta’} U’V’$?</p>
<p>I will present the solution of this problem, as well as a new application (which came to us as a pleasant surprise) of dilation theory to the continuity of the spectrum of the almost Mathieu operator from mathematical physics.</p>
<p>Based on a joint work with Malte Gerhold.</p></div>Orr Shalithttps://oshalit.net.technion.ac.il/Techniontag:www.math.bgu.ac.il,2005:MeetingDecorator/4712018-11-26T21:33:19+02:002019-01-19T14:24:27+02:00BGU Math<span class="mathjax">Noriko Sakurai and Gauchman events. Speaker: Sergei Fomin: TBA</span>May 21, 14:30—15:30, 2019, Math -101Noriko Sakurai and Gauchman events. Speaker: Sergei Fomintag:www.math.bgu.ac.il,2005:MeetingDecorator/5372019-05-08T09:35:59+03:002019-05-26T08:02:34+03:00BGU Math<span class="mathjax">Dan Florentin: New Functional Polarity Inequalities</span>June 11, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>Several functional analogs of fundamental geometric inequalities have appeared in recent decades, beginning with the works of Prekopa and Leindler in the 1970’s. In this talk I will, after discussing the method of functionalization of geometry, present new functional extensions of the Brunn Minkowski inequality and their consequences.</p></div>Dan Florentinhttp://www.math.kent.edu/~dflorent/Kent State Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/5042019-02-24T09:22:15+02:002019-06-16T12:35:02+03:00BGU Math<span class="mathjax">Eran Nevo: On face numbers of polytopes</span>June 18, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>A polytope is called simplicial if all its proper faces are simplices. The celebrated g-theorem gives a complete characterization of the possible face numbers (a.k.a. f-vector) of simplicial polytopes, conjectured by McMullen ’70 and proved by Billera-Lee (sufficiency) and by Stanley (necessity) ’80. The latter uses deep relations with commutative algebra and algebraic geometry. Moving to general polytopes, a finer information than the f-vector is given by the flag-f-vector, counting chains of faces according to their dimensions. Here much less is known, or even conjectured.</p>
<p>I will discuss what works and what breaks, at least conjecturally, when passing from simplicial to general polytopes, or subfamilies of interest.</p></div>Eran Nevohttp://math.huji.ac.il/~nevo/HUJItag:www.math.bgu.ac.il,2005:MeetingDecorator/5602019-09-19T17:47:38+03:002019-09-19T17:49:26+03:00BGU Math<span class="mathjax">Faculty meeting: Faculty meeting</span>October 29, 14:30—15:30, 2019, Math -101Faculty meetingtag:www.math.bgu.ac.il,2005:MeetingDecorator/5612019-09-19T17:50:13+03:002019-10-23T09:59:20+03:00BGU Math<span class="mathjax">GERT-MARTIN GREUEL: Simultaneous normalization of families of isolated singularities</span>November 5, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>A singularity refers always to a special situation, something that is not true in general. The term “singularity” is often used in a philosophical sense to describe a frightening or catastrophically situation which is often unknown. Singularity theory in mathematics is a well defined discipline with the aim to tame the “catastrophe”. I will give a general introduction to singularity theory with some examples from real life. Then I consider a special kind of taming a singularity, the normalization, and give an overview of classical and recent results on simultaneous normalization of families of algebraic and analytic varieties. I will also discuss some open problems.</p></div>GERT-MARTIN GREUELhttps://www.mathematik.uni-kl.de/en/greuel/Technische Universitat Kaiserslauterntag:www.math.bgu.ac.il,2005:MeetingDecorator/5622019-09-19T17:55:32+03:002019-10-23T10:00:25+03:00BGU Math<span class="mathjax">GERT-MARTIN GREUEL: Classification of Singularities in positive characteristic</span>November 12, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>The classification of hypersurface singularities aims at writing down a normal form of the defining power series with respect to some equivalence relation, and to give list of normal forms for a distinguished class of singularities. Arnold’s famous ADE-classification of singularities over the complex numbers had an enormous influence on singularity theory and beyond. I will report on some of the impact of his work to other disciplines and to some real-life applications of the classification. Stimulated by Arnold’s work, the classification has been carried on to singularities over fields of positive characteristic, partly with surprising differences. I will report on recent results about this classification and about related problems.</p></div>GERT-MARTIN GREUELhttps://www.mathematik.uni-kl.de/en/greuel/Technische Universitat Kaiserslauterntag:www.math.bgu.ac.il,2005:MeetingDecorator/5682019-10-10T09:11:50+03:002019-11-17T12:40:20+02:00BGU Math<span class="mathjax">Arie Levit: On Benjamini-Schramm convergence</span>November 19, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>Benjamini-Schramm convergence is a probabilistic notion useful in studying the asymptotic behavior of sequences of metric spaces. The goal of this talk is to discuss this notion and some of its applications from various perspectives, e.g. for groups, graphs, hyperbolic manifolds and locally symmetric spaces, emphasizing the distinction between the hyperbolic rank-one case and the rigid high-rank case. Understanding the “sofic” part of the Benjamini-Schramm space, i.e. all limit points of “finitary” objects, will play an important role. From the group-theoretic perspective, I will talk about sofic groups, i.e. groups which admit a probabilistic finitary approximation, as well as a companion notion of permutation stability. Several results and open problems will be discussed.</p></div>Arie Levithttps://sites.google.com/site/arielevit/Yaletag:www.math.bgu.ac.il,2005:MeetingDecorator/5652019-09-22T22:24:32+03:002019-11-25T19:47:03+02:00BGU Math<span class="mathjax">Gregory Defel: On bounded continuous solutions of the archetypal equation with rescaling</span>November 26, 14:30—15:30, 2019, Math -101Gregory Defelhttps://www.math.bgu.ac.il/~derfel/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/5772019-10-22T13:24:43+03:002019-12-01T20:00:14+02:00BGU Math<span class="mathjax">Howard Nuer: Cubic Fourfolds: Rationality and Derived Categories</span>December 3, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>The question of determining if a given algebraic variety is rational is a notoriously difficult problem in algebraic geometry, and attempts to solve rationality problems have often produced powerful new techniques. A well-known open rationality problem is the determination of a criterion for when a cubic hypersurface of five-dimensional projective space is rational. After discussing the history of this problem, I will introduce the two conjectural rationality criteria that have been put forth and then discuss a package of tools I have developed with my collaborators to bring these two conjectures together. Our theory of Relative Bridgeland Stability has a number of other beautiful consequences such as a new proof of the integral Hodge Conjecture for Cubic Fourfolds and the construction of full-dimensional families of projective Hyper Kahler manifolds. Time permitting I’ll discuss a few of the many applications of the theory of relative stability conditions to problems other than cubic fourfolds.</p></div>Howard Nuerhttps://sites.google.com/site/howardnuermath/homeUICtag:www.math.bgu.ac.il,2005:MeetingDecorator/5662019-10-06T09:42:36+03:002019-12-02T15:31:34+02:00BGU Math<span class="mathjax">Uri Shapira: Geometry of integral vectors</span>December 10, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>Given an integral vector, there are several geometric and arithmetic objects one can attach to it. For example, its direction (as a point on the unit sphere), the lattice obtained by projecting the integers to the othonormal hyperplane to the vector, and the vector of residues modulo a prime p to name a few. In this talk I will discuss results pertaining to the statistical properties of these objects as we let the integral vector vary in natural ways.</p></div>Uri Shapirahttps://ushapira.net.technion.ac.il/Techniontag:www.math.bgu.ac.il,2005:MeetingDecorator/6042019-11-04T16:09:30+02:002019-11-04T16:09:30+02:00BGU Math<span class="mathjax">Shamgar Gurevitch: Harmonic Analysis on $GL(n)$ over Finite Fields.</span>December 17, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio:</p>
<p>Trace(ρ(g)) / dim(ρ),</p>
<p>for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.</p>
<p>Recently (https://www.youtube.com/watchv=EfVCWWWNxvg&feature=youtu.be), we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank.</p>
<p>Rank suggests a new organization of representations based on the very few “Small” ones. This stands in contrast to Harish-Chandra’s “philosophy of cusp forms” (P-of-CF), which is (since the 60’s) the main organization principle, and is based on the (huge collection) of “Large” representations.</p>
<p>This talk will discuss the notion of rank for the group GL(n) over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for random walks.</p>
<p>This is joint work with Roger Howe (Yale and Texas A&M). The numerics for this work was carried by Steve Goldstein (Madison).</p></div>Shamgar Gurevitchhttps://www.math.wisc.edu/~shamgar/University of Wisconsin - Madisontag:www.math.bgu.ac.il,2005:MeetingDecorator/5632019-09-19T17:58:09+03:002019-12-21T15:20:33+02:00BGU Math<span class="mathjax">Adam Dor On: Matrix convexity, Arveson boundaries and Tsirelson problems</span>December 24, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>Following work of Evert, Helton, Klep and McCullough on free linear matrix inequality domains, we ask when a matrix convex set is the closed convex hull of its (absolute) extreme points. This is a finite-dimensional version of Arveson’s non-commutative Krein-Milman theorem, which may generally fail completely since some matrix convex sets have no (absolute) extreme points. In this talk we will explain why the Arveson-Krein-Milman property for a given matrix convex set is difficult to determine. More precisely, we show that this property for certain commuting tensor products of matrix convex sets is equivalent to a weak version of Tsirelson’s problem from quantum information. This weak variant of Tsirelson’s problem was shown, by a combination of results of Kirchberg, Junge et. al., Fritz and Ozawa, to be equivalent to Connes’ embedding conjecture; considered to be one of the most important open problems in operator algebras. We do more than just provide another equivalent formulation of Connes’ embedding conjecture. Our approach provides new matrix-geometric variants of weak Tsirelson type problems for pairs of convex polytopes, which may be easier to rule out than the original weak Tsirelson problem.</p>
<p>Based on joint work with Roy Araiza and Thomas Sinclair</p></div>Adam Dor Onhttps://adoronmath.wordpress.com/University of Copenhagentag:www.math.bgu.ac.il,2005:MeetingDecorator/5642019-09-19T18:08:12+03:002019-12-16T14:07:23+02:00BGU Math<span class="mathjax">Sergei Tabachnikov: Flavors of bicycle mathematics</span>December 31, 14:30—15:30, 2019, Math -101<div class="mathjax"><p>This talk concerns a naive model of bicycle motion: a bicycle is a segment of fixed length that can move so that the velocity of the rear end is always aligned with the segment. Surprisingly, this simple model is quite rich and has connections with several areas of research, including completely integrable systems. Here is a sampler of problems that I hope to touch upon:</p>
<p>1) The trajectory of the front wheel and the initial position of the bicycle uniquely determine its motion and its terminal position; the monodromy map sending the initial position to the terminal one arises. This mapping is a Moebius transformation, a remarkable fact that has various geometrical and dynamical consequences.</p>
<p>2) The rear wheel track and a choice of the direction of motion uniquely determine the front wheel track; changing the direction to the opposite, yields another front track. These two front tracks are related by the bicycle (Backlund, Darboux) correspondence, which defines a discrete time dynamical system on the space of curves. This system is completely integrable and it is closely related with another, well studied, completely integrable dynamical system, the filament (a.k.a binormal, smoke ring, local induction) equation.</p>
<p>3) Given the rear and front tracks of a bicycle, can one tell which way the bicycle went? Usually, one can, but sometimes one cannot. The description of these ambiguous tire tracks is an open problem, intimately related with Ulam’s problem in flotation theory (in dimension two): is the round ball the only body that floats in equilibrium in all positions? This problem is also related to the motion of a charge in a magnetic field of a special kind. It turns out that the known solutions are solitons of the planar version of the filament equation.</p></div>Sergei Tabachnikovhttp://www.personal.psu.edu/sot2/Penn State Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/6122019-11-25T19:54:55+02:002019-12-30T14:14:56+02:00BGU Math<span class="mathjax">Tom Meyerovitch: Universal models in ergodic theory and topological dynamics</span>January 7, 14:30—15:30, 2020, Math -101<div class="mathjax"><p>A number of of important results in modern mathematics involve an understanding the space of invariant probability measures for a homeomorphism, a flow, or group of homeomorphisms.</p>
<p>In this talk we will focus on finding situations where the space of invariant probability measures is
essentially ``as big as possible’’:
A topological dynamical system is $(X,S)$ \emph{universal} in the ergodic sense if any measure preserving system $(Y,T,\mu)$, there exists an S-invariant probability measure $\nu$ so that $(X,S,\nu)$ is isomorphic to $(Y,T,\mu)$ as measure preserving systems, assuming that the entropy of (Y,T,\mu) is strictly lower than the topological entropy of $(X,S)$.
Krieger’s generator theorem (1970) states that the shift map on the space bi-infinite of $N$-letter sequences is universal.
Lind and Thouvenot (1977) used Kreiger’s theorem to prove that Measure-preserving homeomorphisms of the torus represent
all finite entropy ergodic transformations. Recent conditions for universality of Soo-Quas (2016) and David Burguet (2019) imply that any ergodic automorphism of a compact group is universal. Together with Nishant Chandgotia we recently established a new and more general sufficient condition for ergodic universality.</p>
<p>Some new consequences include:
- A generic homeomorphism of a compact manifold (having dimension at least 2) can model any aperiodic measure preserving transformation.
- Any aperiodic measure preserving transformation can be modeled by a homeomorphism of the 2-torus which preserves Lebesgue measure.
- The space of 3-colorings of the standard Cayley graph of $\mathbb{Z}^d$, with $\mathbb{Z}^d$ acting by translations is universal. <br />
In this talk I will discus and explain some of the older and newer results.
No specific background in ergodic theory will be assumed.</p></div>Tom Meyerovitchhttps://sites.google.com/site/tommeyerovitch/homeBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/5782019-10-23T09:01:50+03:002020-01-12T12:01:15+02:00BGU Math<span class="mathjax">Michael Polyak: Enumerative geometry and Lie (super)algebras</span>January 14, 14:30—15:30, 2020, Math -101<div class="mathjax"><p>One of the classical enumerative problems in algebraic geometry is that of
counting of complex or real rational curves through a collection of points
in a toric variety.</p>
<p>We explain this counting procedure as a construction of certain cycles on
moduli of rigid tropical curves. Cycles on these moduli turn out to be
closely related to Lie algebras.</p>
<p>In particular, counting of both complex and real curves is related to the
quantum torus Lie algebra. More complicated counting invariants (the
so-called Gromov-Witten descendants) are similarly related to the
super-Lie structure on the quantum torus.</p>
<p>[No preliminary knowledge of tropical geometry or the quantum torus
algebra is expected.]</p></div>Michael Polyakhttp://www2.math.technion.ac.il/~polyak/Techniontag:www.math.bgu.ac.il,2005:MeetingDecorator/6252020-02-01T10:19:44+02:002020-03-08T10:54:57+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/6222020-01-22T16:47:46+02:002020-01-22T16:47:46+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/6452020-02-24T10:28:12+02:002020-02-24T10:28:12+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/6202019-12-30T14:17:27+02:002019-12-30T14:17:27+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/6242020-01-30T13:32:39+02:002020-01-30T13:32:39+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/6442020-02-22T21:08:43+02:002020-02-27T10:24:08+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/6052019-11-06T14:54:50+02:002020-02-27T11:21:07+02:00tag:www.math.bgu.ac.il,2005:MeetingDecorator/7842021-09-12T10:49:05+03:002021-09-12T10:49:05+03:00BGU Math<span class="mathjax">Departamental meeting: TBA</span>October 19, 14:30—15:30, 2021, Math -101Departamental meetingtag:www.math.bgu.ac.il,2005:MeetingDecorator/7882021-09-14T15:32:35+03:002021-10-24T11:50:54+03:00BGU Math<span class="mathjax">Dmitry Faifman: Integral geometry and valuation theory in pseudo-Riemannian spaces</span>October 26, 14:30—15:30, 2021, Math -101<div class="mathjax"><p>We will discuss the Blaschke branch of integral geometry and its manifestations in pseudo-Riemannian space forms. First we will recall the fundamental notion of intrinsic volumes, known as quermassintegrals in convex geometry. Those notions were extended later to Riemannian manifolds by H. Weyl, who discovered a remarkable fact: given a manifold M embedded in Euclidean space, the volume of the epsilon-tube around it is an invariant of the Riemannian metric on M. We then discuss Alesker’s theory of smooth valuations, which provides a framework and a powerful toolset to study integral geometry, in particular in the presence of various symmetry groups.
Finally, we will use those ideas to explain some recent results in the integral geometry of pseudo-Riemannian manifolds, in particular a collection of principal Crofton formulas in all space forms, and a Chern-Gauss-Bonnet formula for metrics of varying signature.
Partially based on joint works with S. Alesker, A. Bernig, G. Solanes.</p></div>Dmitry Faifmanhttps://sites.google.com/site/faifmand/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7852021-09-13T10:27:39+03:002021-10-25T08:43:48+03:00BGU Math<span class="mathjax">Cy Maor: Riemannian metrics on diffeomorphism groups — the good, the bad, and the unknown</span>November 2, 14:30—15:30, 2021, Math -101<div class="mathjax"><p>In finite dimensional Riemannian geometry, everything behaves nicely — the Riemannian metric induces a distance function, geodesics exist (at least for some time), and so on. In infinite dimensional Riemannian geometry, however, chaos reigns. In this talk I will focus on diffeomorphism groups, and on a particularly important hierarchy of Riemannian metrics on them: right-invariant Sobolev metrics. These arise in many different contexts, from purely mathematical ones, to applications in hydrodynamics and imaging. I will give a brief introduction to these metrics, why we care about them, and what we know (and don’t know) about their properties.
Parts of the talk will be based on joint works with Bob Jerrard and Martin Bauer.</p></div>Cy Maorhttp://www.math.huji.ac.il/~cmaor/Hebrew Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7822021-08-31T12:16:53+03:002021-11-09T09:45:21+02:00BGU Math<span class="mathjax">Yotam Smilansky: Order and disorder in multiscale substitution tilings</span>November 9, 14:30—15:30, 2021, Math -101<div class="mathjax"><p>The study of aperiodic order and mathematical models of quasicrystals is concerned with ways in which disordered structures can nevertheless manifest aspects of order. In the talk I will describe examples such as the aperiodic Penrose and pinwheel tilings, together with several geometric, functional, dynamical and spectral properties that enable us to measure how far such constructions are from demonstrating lattice-like behavior. A particular focus will be given to new results on multiscale substitution tilings, a class of tilings that was recently introduced jointly with Yaar Solomon.</p></div>Yotam Smilanskyhttps://sites.math.rutgers.edu/~smilansky/Rutgers Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7832021-09-02T08:44:51+03:002021-11-08T14:45:03+02:00BGU Math<span class="mathjax">Yaniv Ganor: Big Fiber Theorems and Ideal-Valued Measures in Symplectic Topology</span>November 16, 14:30—15:30, 2021, Math -101<div class="mathjax"><p>In various areas of mathematics there exist “big fiber theorems”, these are theorems of the following type: “For any map in a certain class, there exists a ‘big’ fiber”, where the class of maps and the notion of size changes from case to case.</p>
<p>We will discuss three examples of such theorems, coming from combinatorics, topology and symplectic topology from a unified viewpoint provided by Gromov’s notion of ideal-valued measures.</p>
<p>We adapt the latter notion to the realm of symplectic topology, using an enhancement of a certain cohomology theory on symplectic manifolds introduced by Varolgunes, allowing us to prove symplectic analogues for the first two theorems, yielding new symplectic rigidity results.</p>
<p>Necessary preliminaries will be explained.
The talk is based on a joint work with Adi Dickstein, Leonid Polterovich and Frol Zapolsky.</p></div>Yaniv Ganorhttps://sites.google.com/view/ganory/Techniontag:www.math.bgu.ac.il,2005:MeetingDecorator/8042021-10-03T10:24:19+03:002021-11-22T14:07:21+02:00BGU Math<span class="mathjax">Ilya Gekhtman: Randomness, genericity, and ubiquity of hyperbolic behavior in groups.</span>November 23, 14:30—15:30, 2021, Math -101<div class="mathjax"><p>Consider an infinite group G acting by isometries on some metric space X.<br />
How does a “typical” element act?
Consider a representation of G into some matrix group. What sort of matrix represents “typical” elements of G?</p>
<p>The answer depends on what we mean by the word “typical,” of which there are at least two reasonable notions. We may take a random walk on G and look where it lands after a large number of steps. We may also fix a generating set for G and look how large balls are distributed.</p>
<p>I will talk about how these two notions of genericity are related and how they differ, focusing on the setting of hyperbolic groups.
I will also explain that the following is true with respect to both notions:
For a group acting on a Gromov hyperbolic metric space typical elements act loxodromically, i.e. with north-south dynamics.</p>
<p>For a representation of a large class of groups (including hyperbolic groups) into SL_n R, typical elements map to matrices whose eigenvalues are all simple and have distinct moduli.</p></div>Ilya Gekhtmanhttps://sites.google.com/site/ilyagekhtman/Techniontag:www.math.bgu.ac.il,2005:MeetingDecorator/8092021-10-17T12:57:05+03:002021-11-24T09:50:00+02:00BGU Math<span class="mathjax">Itay Londner: Tiling the integers with translates of one tile: the Coven-Meyerowitz tiling conditions for three prime factors</span>November 30, 14:30—15:30, 2021, Math -101<div class="mathjax"><p>It is well known that if a finite set of integers A tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a factorization A+B=Z_M of a finite cyclic group. Coven and Meyerowitz (1998) proved that when the tiling period M has at most two distinct prime factors, each of the sets A and B can be replaced by a highly ordered “standard” tiling complement. It is not known whether this behaviour persists for all tilings with no restrictions on the number of prime factors of M.
In joint work with Izabella Laba (UBC), we proved that this is true when M=(pqr)^2. In my talk I will discuss this problem and introduce some ingredients from the proof.</p></div>Itay LondnerUBCtag:www.math.bgu.ac.il,2005:MeetingDecorator/8122021-10-24T11:59:36+03:002021-12-01T09:41:27+02:00BGU Math<span class="mathjax">Oren Becker: Character varieties of random groups</span>December 7, 14:30—15:30, 2021, Math -101<div class="mathjax"><p>The space Hom(\Gamma,G) of homomorphisms from a finitely-generated group \Gamma to a complex semisimple algebraic group G is known as the G-representation variety of \Gamma. We study this space when G is fixed and \Gamma is a random group in the few-relators model. That is, \Gamma is generated by k elements subject to r random relations of length L, where k and r are fixed and L tends to infinity.</p>
<p>More precisely, we study the subvariety Z of Hom(\Gamma,G), consisting of all homomorphisms whose images are Zariski dense in G. We give an explicit formula for the dimension of Z, valid with probability tending to 1, and study the Galois action on its geometric components. In particular, we show that in the case of deficiency 1 (i.e., k-r=1), the Zariski-dense G-representations of a typical \Gamma enjoy Galois rigidity.</p>
<p>Our methods assume the Generalized Riemann Hypothesis and exploit mixing of random walks and spectral gap estimates on finite groups.</p>
<p>Based on a joint work with E. Breuillard and P. Varju.</p></div>Oren Beckerhttps://sites.google.com/view/orenbecker/University of Cambridgetag:www.math.bgu.ac.il,2005:MeetingDecorator/8252021-10-25T19:56:27+03:002021-12-19T13:51:40+02:00BGU Math<span class="mathjax">Yariv Aizenbud: Non-Parametric Estimation of Manifolds from Noisy Data</span>December 21, 14:30—15:30, 2021, Math -101<div class="mathjax"><p>In many data-driven applications, the data follows some geometric structure, and the goal is to recover this structure. In many cases, the observed data is noisy and the recovery task is even more challenging. A common assumption is that the data lies on a low dimensional manifold. Estimating a manifold from noisy samples has proven to be a challenging task. Indeed, even after decades of research, there was no (computationally tractable) algorithm that accurately estimates a manifold from noisy samples with a constant level of noise.</p>
<p>In this talk, we will present a method that estimates a manifold and its tangent. Moreover, we establish convergence rates, which are essentially as good as existing convergence rates for function estimation.</p></div>Yariv Aizenbudhttps://math.yale.edu/people/yariv-aizenbudYale Univercitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8212021-10-25T14:39:07+03:002021-12-23T14:52:28+02:00BGU Math<span class="mathjax">Ron Levie: Wavelet-Plancherel: a new theory for analyzing and processing wavelet-based methods</span>December 28, 14:30—15:30, 2021, Math -101<div class="mathjax"><p>Continuous wavelet transforms are mappings that isometrically embed a signal space to a coefficient space over a locally compact group, based on so-called square integrable representations. For example, the 1D wavelet transform maps time signals to functions over the time-scale plane based on the affine group. When using wavelet transforms for signal processing, it is often useful to work interchangeably with the signal and the coefficient spaces. For example, we would like to know what operation in the signal domain is equivalent to multiplication in the coefficient space. While such a point of view is natural in classical Fourier analysis (i.e., “time convolution is equivalent to frequency multiplication”), it is not compatible with wavelet analysis, since wavelet transforms are not surjective.
In this talk, I will present the wavelet-Plancherel theory – an extension of classical wavelet theory in which the wavelet transform is canonically extended to an isometric isomorphism. The new theory allows formulating a variety of coefficient domain operations as signal domain operations, with closed form formulas. Using these so-called pull-back formulas, we are able to reduce the computational complexity of some wavelet-based signal processing methods. The theory is also useful for proving theorems in wavelet analysis. I will present an extension of the Heisenberg uncertainty principle to wavelet transforms and prove the existence of uncertainty minimizers using the wavelet-Plancherel theory.</p></div>Ron Leviehttps://sites.google.com/view/ronlevieLMUtag:www.math.bgu.ac.il,2005:MeetingDecorator/8272021-11-08T14:41:53+02:002022-01-02T20:47:30+02:00BGU Math<span class="mathjax">Dmitry Kerner: Finite determinacy of maps. Group orbits vs their tangent spaces</span>January 4, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>A function at a non-critical point can be converted to a linear form by a local coordinate change. At an isolated critical point one has the weaker statement: higher order perturbations do not change the group orbit. Namely, the function is determined (up to the local coordinate changes) by its (finite) Taylor polynomial.</p>
<p>This finite-determinacy property was one of the starting points of Singularity Theory. Traditionally such statements are proved by vector field integration. In particular, the group of local coordinate changes becomes a ``Lie-type” group.</p>
<p>I will show such determinacy results for maps of germs of (Noetherian) schemes. The essential tool is the “vector field integration” in any characteristic. This equips numerous groups acting on filtered modules with the ``Lie-type” structure.
(joint work with G. Belitskii, A.F. Boix, G.M. Greuel.)</p></div>Dmitry Kernerhttps://www.math.bgu.ac.il/~kernerdm/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/7862021-09-13T10:28:38+03:002022-03-13T12:51:38+02:00BGU Math<span class="mathjax">Leonid Polterovich: Symplectic maps: algebra, geometry, dynamics</span>March 22, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Symplectic maps can be considered as symmetries of a geometric structure
(a symplectic form) on a manifold, and as a mathematical model of admissible
motions of classical mechanics. I discuss a number of rigidity phenomena
of algebraic, geometric, and dynamical nature exhibited by these maps,
focusing on a recent work with Egor Shelukhin.</p></div>Leonid Polterovichhttps://sites.google.com/site/polterov/homeTel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/7872021-09-13T11:14:12+03:002022-03-27T11:00:53+03:00BGU Math<span class="mathjax">Izhar Oppenheim: Fixed-point properties for random groups</span>March 29, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>A group is said to have a fixed-point property with respect to some class of metric spaces if any isometric action of the group on any space in the class admits a fixed point.</p>
<p>In this talk, I will focus on fixed-point properties with respect to (classes of) Banach spaces. I will survey some results regarding groups with and without these fixed-point properties and then present a recent result of mine regarding fix-point properties for random groups with respect to l^p spaces.</p></div>Izhar Oppenheimhttps://izhar-oppenheim.com/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/8602022-02-03T11:08:43+02:002022-02-03T11:08:43+02:00BGU Math<span class="mathjax">Shlomo Hareli: About the Dynamics of Polydispersed Fuel</span>April 5, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>A poly disperse fuel spray consist of thousands of droplets in various volumes
and shapes. The Combustion of the poly disperse is a chemical process which
releases useful thermal energy. The poly disperse fuel droplets are described by
a discrete function - the particle (droplet) size distribution (PSD).</p>
<p>Models of the combustion process which accounts for each droplet are im-
practicable as they require a considerable amount of computations. As a result,
approximations are used to describe the combustion process. The approxima-
tions fail to describe the particle PSD adequately.</p>
<p>We propose a simpli�ed theoretical model which allow us to use continuous
distribution functions to approximate any PSD (experimental or theoretical)
during the combustion process much more accurately then previous ap-
proximations. The time depended distribution functions allow us to in-
vestigate the dynamics of the poly disperse fuel elegantly and even permit an
analytical study. The model provided some new theoretical insights.</p>
<p>Our main results show that during the self-ignition process, the radii of the
droplets decreased as expected, and the number of smaller droplets increased
in inverse proportion to the radius. An important novel result (visualized by
graphs) demonstrates that the mean radius of the droplets initially increases for
a relatively short period of time, which is followed by the expected decrease.</p></div>Shlomo HareliBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/8692022-03-20T11:48:25+02:002022-04-11T08:12:10+03:00BGU Math<span class="mathjax">Chris Phillips: Relations between dynamics and C*-algebras: Mean dimension and radius of comparison</span>April 12, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>This is joint work with Ilan Hirshberg.</p>
<p>For an action of an amenable group G on a compact metric space X, the mean dimension mdim (G, X) was introduced by Lindenstrauss and Weiss. It is designed so that the mean dimension of the shift on ([0, 1]^d)^G is d. Its motivation was unrelated to C*-algebras.</p>
<p>The radius of comparison rc (A) of a C*-algebra A was introduced by Toms to distinguish counterexamples in the Elliott classification program. The algebras he used have nothing to do with dynamics.</p>
<p>A construction called the crossed product C^* (G, X) associates a C<em>-algebra to a dynamical system. Despite the apparent lack of connection between these concepts, there is significant evidence for the conjecture that rc ( C^</em> (G, X) ) = (1/2) mdim (G, X) when the action is free and minimal. We will explain the concepts above; no previous knowledge of mean dimension, C<em>-algebras, or radius of comparison will be assumed. Then we describe some of the evidence. In particular, we give the first general partial results towards the direction rc ( C^</em> (G, X) ) \geq (1/2) mdim (G, X). We don’t get the exact conjectured bound, but we get nontrivial results for many of the known examples of free minimal systems with mdim (G, X) > 0.</p></div>Chris Phillipshttps://pages.uoregon.edu/ncp/University of Oregontag:www.math.bgu.ac.il,2005:MeetingDecorator/8612022-02-03T21:21:16+02:002022-04-22T18:48:04+03:00BGU Math<span class="mathjax">Maxim Gurevich: In between finite and p-adic groups - the case of permutations</span>April 26, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Using the Bruhat decomposition, a general linear group over a p-adic field may be thought of as a “quantum affine” version of a finite group of permutations. I would like to discuss some analogies and explore the implications of this point view on the spectral properties of the two groups.
For one, restriction of an irreducible smooth representation to its finite counterpart gives the correct notion of the wavefront set - an invariant of arithmetic
significance which is often approached using microlocal analysis.
From another perspective, the class of cyclotomic Hecke algebras is a natural interpolation between the finite and p-adic groups. I will show how the class of RSK representations (developed with Erez Lapid) serves as a bridge between the Langlands classification for the p-adic group and the classical Specht construction of the finite domain.</p></div>Maxim Gurevichhttps://sites.google.com/view/maxgur/homeTechniontag:www.math.bgu.ac.il,2005:MeetingDecorator/8622022-02-15T12:35:41+02:002022-02-15T12:35:41+02:00BGU Math<span class="mathjax">Faculty meeting: TBA</span>May 3, 14:30—15:30, 2022, Math -101Faculty meetingtag:www.math.bgu.ac.il,2005:MeetingDecorator/8652022-03-01T17:29:18+02:002022-05-09T11:47:07+03:00BGU Math<span class="mathjax">Nathan Keller: Can you hear the shape of a low-degree Boolean function?</span>May 10, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Analysis of Boolean functions aims at “hearing the shape” of functions on the discrete cube {-1,1}^n – namely, at understanding what the structure of the (discrete) Fourier transform tells us about the function.
In this talk, we focus on the structure of “low-degree” functions on the discrete cube, namely, on functions whose Fourier coefficients are concentrated on “low” frequencies. While such functions look very simple, we are surprisingly far from understanding them well, even in the most basic first-degree case.
We shall present several results on first-degree functions on the discrete cube, including the recent proof of Tomaszewski’s conjecture (1986) which asserts that any first-degree function (viewed as a random variable) lies within one standard deviation from its mean with probability at least 1/2. Then we shall discuss several core open questions, which boil down to understanding, what does the knowledge that a low-degree function is bounded, or is two-valued, tell us about its structure.</p>
<p>Based on joint work with Ohad Klein</p></div>Nathan Kellerhttps://u.math.biu.ac.il/~nkeller/BIUtag:www.math.bgu.ac.il,2005:MeetingDecorator/8702022-03-20T11:51:40+02:002022-05-11T14:27:27+03:00BGU Math<span class="mathjax">Shakhar Smorodinsky: A Solution to Ringel’s Circle Problem (1959)</span>May 17, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>In 1959 Gerhard Ringel posed the following problem which remained open for over 60 years.
Suppose we are given a finite family $\C$ of circles in the plane no three of which are pairwise tangent at the same point.
Is it possible to always color the circles with five colors so that tangent circles get distinct colors.</p>
<p>When the circles are not allowed to overlap (i.e., the discs bounded by the circles are pairwise interiorly disjoint) then the number of colors that always suffice
is four and this fact is equivalent to the Four-Color-Theorem for planar graphs.</p>
<p>We construct families of circles in the plane such that their tangency graphs have arbitrarily large
girth and chromatic number. Moreover, no two circles are internally tangent and no two circles are concentric.
This provides a strong negative answer to Ringel’s 1959 open problem.
The proof relies on a (multidimensional) version of Gallaiӳ theorem with polynomial constraints,
which we derive using tools from Ramsey-Theory.</p>
<p>Joint work with James Davis, Chaya Keller, Linda Kleist and Bartosz Walczak</p></div>Shakhar Smorodinskyhttps://www.math.bgu.ac.il/~shakhar/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/8892022-04-24T09:43:06+03:002022-05-22T11:54:14+03:00BGU Math<span class="mathjax">Arie Levit: Approximated and stable groups</span>May 24, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>In the study of infinite discrete groups it is useful to consider imperfect approximations by finitary models (either permutations or matrices). I will talk about the stability of such approximations, i.e. can it always be corrected to a perfect approximation, focusing mostly on amenable groups. The involved techniques include ergodic theory and dynamics as well as character theory of infinite groups. Some directions and open problems will be presented.</p></div>Arie Levithttps://sites.google.com/site/arielevit/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/8932022-05-24T11:54:52+03:002022-05-24T11:54:52+03:00BGU Math<span class="mathjax">Celebrating Michael Lin’s 80th birthday: A special day of lectures on dynamics and probability</span>May 31, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Celebrating Michael Lin’s 80th birthday.
Place: Ben-Gurion university of the Negev.
Room -103 in building 14 Mendel building (across from Aroma branch on the west side of the campus).
Time: Tuesday 31/5/2022 between 10:30-16:30.</p>
<p>Schedule:</p>
<p>10:00 - 10:30 Coffee
10:30 - 11:20 Omri Sarig (Weizmann institute)
11:40 - 13:00 Jon Aaronson (Tel-Aviv University)
13:00 - 14:30 Lunch (the lunch will take place in room -101 of the math building)
14:30 - 15:20 Eli Glasner (Tel-Aviv University, joint with Colloquium)
15:30 - 16:20 Ariel Yadin (Ben Gurion University)</p>
<p>Organizers: Yair Glasner, Tom Meyerovitch, and Guy Cohen
Zoom broadcasting LINK
Meeting ID: 820 8565 9434
The conference website: https://sites.google.com/view/michael-lins-80th-birthday/home</p></div>Celebrating Michael Lin's 80th birthdayhttps://sites.google.com/view/michael-lins-80th-birthday/homeBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/8882022-04-22T18:46:22+03:002022-06-07T12:01:51+03:00BGU Math<span class="mathjax">Uzi Vishne: Inclusion-exclusion, partial representations of semigroups, and nonassociative Specht polynomials</span>June 7, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>The dimension of the space of multilinear products of higher commutators is equal to the number of derangements, $[e^{-1}n!]$.
Our search for a combinatorial explanation for this fact led us to study representations of left regular bands, whose resolution is obtained through analysis of cubical partial representations. There are applications in combinatorics, probability, and nonassociative algebra.</p></div>Uzi Vishnehttps://u.math.biu.ac.il/~vishneu/BIUtag:www.math.bgu.ac.il,2005:MeetingDecorator/8912022-05-19T13:27:35+03:002022-06-13T14:09:00+03:00BGU Math<span class="mathjax">Natalia Tsilevich: Asymptotic representation theory, old and new</span>June 14, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Asymptotic representation theory is an important and quickly developing area of mathematics rich in connections to other fields, such as, e.g., probability, algebraic combinatorics, and mathematical physics. I will survey the basic ideas and results of asymptotic representation theory, mostly of symmetric groups, and then focus on some recent contributions.</p></div>Natalia Tsilevichhttp://www.pdmi.ras.ru/~natalia/PDMI, Saint Petersburg, Russiatag:www.math.bgu.ac.il,2005:MeetingDecorator/8872022-04-04T11:10:30+03:002022-06-20T11:12:43+03:00BGU Math<span class="mathjax">Barak Weiss: Horocycle flow on the moduli space of translation surfaces</span>June 21, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>By work of Ratner, Margulis, Dani and many others, unipotent flows on homogeneous spaces have strong measure theoretic and topological rigidity properties. By work of Eskin-Mirzakhani and Eskin-Mirzakhani-Mohommadi, the action of SL(2,R) and the upper triangular subgroup of SL(2,R) on strata of translation surfaces have similar rigidity properties. We will describe how some of these results fail for the horocycle flow on strata of translation surfaces. In particular, 1) There exist horocycle orbit closures with fractional Hausdorff dimension. 2) There exist points which do not equidistribute under the horocycle flow with respect to any measure. 3) There exist points which equidistribute distribute under the horocycle flow to a measure, but they are not in the topological support of that measure. This is joint work with Jon Chaika and John Smillie. The talk will be elementary and will require no prior background in dynamics.</p></div>Barak Weisshttp://www.math.tau.ac.il/~barakw/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9222022-10-20T11:25:46+03:002022-10-20T11:25:46+03:00BGU Math<span class="mathjax">Departamental meeting: TBA</span>October 25, 14:30—15:30, 2022, Math -101Departamental meetingtag:www.math.bgu.ac.il,2005:MeetingDecorator/9132022-09-04T15:00:42+03:002022-11-08T10:59:25+02:00BGU Math<span class="mathjax">Itay Glazer : Word maps and word measures: probability and geometry</span>November 8, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Given a word w in a free group F_r on a set of r elements (e.g. the commutator word w=xyx^(-1)y^(-1)), and a group G, one can associate a word map w:G^r–>G. For g in G, it is natural to ask whether the equation w(x1,…,xr)=g has a solution in G^r, and to estimate the “size” of this solution set, in a suitable sense. When G is finite, or more generally a compact group, this becomes a probabilistic problem of analyzing the distribution of w(x_1,…,x_r), for Haar-random elements x_1,…,x_r in G. When G is an algebraic group, such as SLn(C), it is natural to study the geometry of the fibers of w.
Such problems have been extensively studied in the last few decades, in various settings such as finite simple groups, compact p-adic groups, compact Lie groups, simple algebraic groups, and arithmetic groups. Analogous problems have been studied for Lie algebra word maps as well. In this talk, I will mention some of these results, and explain the tight connections between the probabilistic and algebraic approaches.</p>
<p>Based on joint works with Yotam Hendel and Nir Avni.</p></div>Itay Glazer https://sites.google.com/view/itay-glazerNorthwestern Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9142022-09-04T15:35:04+03:002022-11-14T08:19:02+02:00BGU Math<span class="mathjax">Yatir Halevi: Definably semisimple groups interpretable in p-adically closed fields (Joint work with Assaf Hasson and Ya’acov Peterzil)</span>November 15, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Identifying and characterizing the groups and fields one can define in various first order structures has had multiple applications within model theory and in other branches of mathematics. We focus here on p-adically closed fields.
Let K be a p-adically closed field (for example, Q_p). We will discuss some recent results regarding interpretable groups and interpretable fields in K:</p>
<p>1) Let G be an interpretable group. If G is definably semisimple (i.e.
G has no definable infinite normal abelian subgroups) group, then there exists a finite normal subgroup H such that G/H is definably isomorphic to a K-linear group.</p>
<p>2) Let F be an interpretable field. Then F is definably isomorphic to a finite extension of K.</p>
<p>No knowledge in model theory will be assumed, but some basic knowledge in logic will help.</p></div>Yatir Halevihttp://ma.huji.ac.il/~yatirh/Haifa Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9122022-09-04T14:57:29+03:002022-11-14T11:38:59+02:00BGU Math<span class="mathjax">Grigory Mashevitzky : On classification of semigroups by algebraic, logical and topological tools</span>November 22, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>ההרצאה תתקיים לכבוד פרישתו לגמלאות של פרופ’ גרגורי משביצקי.</p></div>Grigory Mashevitzky https://www.math.bgu.ac.il/en/people/users/gmashBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/9192022-09-20T11:06:08+03:002022-11-21T18:03:12+02:00BGU Math<span class="mathjax">Or Landesberg: Non-Rigidity of Horocycle Orbit Closures in Geometrically Infinite Surfaces</span>November 29, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Horospherical group actions on homogeneous spaces are famously known to be extremely rigid. In finite volume homogeneous spaces, it is a special case of Ratner’s theorems that all horospherical orbit closures are homogeneous. Rigidity further extends in rank-one to infinite volume but geometrically finite spaces. The geometrically infinite setting is far less understood.</p>
<p>We consider $\mathbb{Z}$-covers of compact hyperbolic surfaces and show that they support quite exotic horocycle orbit closures. Surprisingly, the topology of such orbit closures delicately depends on the choice of a hyperbolic metric on the covered compact surface. In particular, our constructions provide the first examples of geometrically infinite spaces where a complete description of horocycle orbit closures is known. Based on an ongoing joint work with James Farre and Yair Minsky.</p></div>Or Landesberghttps://landesberg.github.io/Yale Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9202022-09-22T21:04:45+03:002022-12-05T08:10:58+02:00BGU Math<span class="mathjax">Dmitry Kerner: Stable mappings of manifolds (stable mappings of henselian germs of schemes)</span>December 6, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Whitney studied the embeddings of (C^\infty) manifolds into R^N. A simple initial idea is: start from a map M-> R^N, and deform it generically. Hopefully one gets an embedding, at least an immersion. This fails totally because of the “stable maps”. They are non-immersions, but are preserved in small deformations.
The theory of stable maps was constructed in 50’s-60’s by Thom, Mather and others. The participating groups are infinite-dimensional, and the engine of the theory was vector fields integration. This chained all the results to the real/complex-analytic case.
I will discuss the classical case, then report on the new results, extending the theory to the arbitrary field (of any characteristic).</p></div>Dmitry Kernerhttps://www.math.bgu.ac.il/~kernerdm/BGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/9262022-10-23T08:59:21+03:002022-12-02T23:35:20+02:00BGU Math<span class="mathjax">Chaim Even Zohar: Random Manifolds and Knots</span>December 13, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>We introduce a combinatorial method of generating random submanifolds of a given manifold in all dimensions and codimensions. The method is based on associating random colors to vertices, as in recent work by Sheffield and Yadin on curves in 3-space. We determine conditions on which submanifolds can arise in which ambient manifolds, and study the properties of random submanifolds that typically arise. In particular, we investigate the knotting of random curves in 3-manifolds, and discuss some other applications.</p>
<p>Joint work with Joel Hass</p></div>Chaim Even Zoharhttps://history.math.technion.ac.il/sites/people-info/index.php?id=2400Techniontag:www.math.bgu.ac.il,2005:MeetingDecorator/9302022-10-30T08:42:40+02:002022-12-18T09:56:27+02:00BGU Math<span class="mathjax">Guy Salomon: New insights on the Nevo–Zimmer Theorem</span>December 20, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>Let G be a higher-rank Lie group (for example, SL_n(R) for n>2). Nevo and Zimmer’s structure theorem describes certain nonsingular actions that naturally arise when studying lattices. This theorem is very powerful and manifests rigidity phenomena. For example, it implies the celebrated Margulis Normal Subgroup Theorem, which classifies all normal subgroups of irreducible lattices of G. The original proof of Nevo–Zimmer Theorem heavily uses the structure of Lie groups.</p>
<p>In this talk, I will present a new theorem on general groups that immediately implies the Nevo–Zimmer Theorem (when restricting to the higher-rank Lie case). I will also explain how the generality of our theorem allows us to adapt it to the setup of normal unital completely positive maps on von Neumann algebras.</p>
<p>The talk is based on joint work with Uri Bader.</p></div>Guy Salomonhttps://www.guysalomon.com/Weizmann Institutetag:www.math.bgu.ac.il,2005:MeetingDecorator/9522022-12-22T12:59:10+02:002022-12-26T09:45:42+02:00BGU Math<span class="mathjax">Tobias Hartnick: Some recent developments in mathematical quasicrystals</span>December 27, 14:30—15:30, 2022, Math -101<div class="mathjax"><p>40 years after the discovery of quasicrystals, the mathematical theory around these objects is currently entering into a new phase. While the original goal of mathematical modelling of quasicrystalline materials has largely been achieved, many open questions remain.</p>
<p>One fundamental insight from the early days of quasicrystals is that questions about discrete structures can be attacked by methods from dynamical systems, ergodic theory and harmonic analysis. Over the last decade, attempts were made to use this dynamical approach in a broader context, for example to study quasicrystal-like discrete structures in non-Euclidean geometries. This has created new connections to different areas of mathematics, including rigidity theory of lattices, quasimorphisms, model theory, and non-abelian harmonic analysis, which as a byproduct also provide us with new tools to study classical problems. At the same time, recent progress in the theory of point processes has also lead to the discovery of new phenomena concerning classical quasicrystals, for example some surprising connections to diophantine approximation.</p>
<p>We thus believe that it is a good time to take another look at the classical theory of quasicrystals and see what modern methods have to say about some of the classical problems in the area. We will start from the early beginnings of the theory and then point out a few of the many recent discoveries.</p></div>Tobias Hartnickhttps://www.math.kit.edu/~hartnickKITtag:www.math.bgu.ac.il,2005:MeetingDecorator/9442022-11-21T08:32:40+02:002022-12-27T10:16:59+02:00BGU Math<span class="mathjax">Tsviqa Lakrec : THE AMPLITUHEDRON BCFW TRIANGULATION</span>January 3, 14:30—15:30, 2023, Math -101<div class="mathjax"><p>The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The talk is based on joint work with Chaim Even-Zohar and Ran Tessler.</p></div>Tsviqa Lakrec http://www.ma.huji.ac.il/~tsviqa/University of Zurichtag:www.math.bgu.ac.il,2005:MeetingDecorator/9282022-10-23T21:24:43+03:002023-01-09T07:55:56+02:00BGU Math<span class="mathjax">Emanuel Milman: Multi-Bubble Isoperimetric Problems - Old and New</span>January 10, 14:30—15:30, 2023, Math -101<div class="mathjax"><p>The classical isoperimetric inequality in Euclidean space $\mathbb{R}^n$ states that among all sets (“bubbles”) of prescribed volume, the Euclidean ball minimizes surface area. One may similarly consider isoperimetric problems for more general metric-measure spaces, such as on the $n$-sphere $\mathbb{S}^n$ and on $n$-dimensional Gaussian space $\mathbb{G}^n$ (i.e. $\mathbb{R}^n$ endowed with the standard Gaussian measure). Furthermore, one may consider the ``multi-bubble” isoperimetric problem, in which one prescribes the volume of $p \geq 2$ bubbles (possibly disconnected) and minimizes their total surface area – as any mutual interface will only be counted once, the bubbles are now incentivized to clump together. The classical case, referred to as the single-bubble isoperimetric problem, corresponds to $p=1$; the case $p=2$ is called the double-bubble problem, and so on.</p>
<p>In 2000, Hutchings, Morgan, Ritor'e and Ros resolved the double-bubble conjecture in Euclidean space $\mathbb{R}^3$ (and this was subsequently resolved in $\mathbb{R}^n$ as well) – the boundary of a minimizing double-bubble is given by three spherical caps meeting at $120^\circ$-degree angles. A more general conjecture of J.~Sullivan from the 1990’s asserts that when $p \leq n+1$, the optimal multi-bubble in $\mathbb{R}^n$ (as well as in $\mathbb{S}^n$) is obtained by taking the Voronoi cells of $p+1$ equidistant points in $\mathbb{S}^{n}$ and applying appropriate stereographic projections to $\mathbb{R}^n$ (and backwards).</p>
<p>In 2018, together with Joe Neeman, we resolved the analogous multi-bubble conjecture for $p \leq n$ bubbles in Gaussian space $\mathbb{G}^n$ – the unique partition which minimizes the total Gaussian surface area is given by the Voronoi cells of (appropriately translated) $p+1$ equidistant points. In the talk, we describe our approach in that work, as well as recent progress on the multi-bubble problem on $\mathbb{R}^n$ and $\mathbb{S}^n$. In particular, we show that minimizing bubbles in $\mathbb{R}^n$ and $\mathbb{S}^n$ are always spherical when $p \leq n$, and we resolve the latter conjectures when in addition $p \leq 5$ (e.g. the triple-bubble conjectures when $n\geq 3$ and the quadruple-bubble conjectures when $n\geq 4$).</p></div>Emanuel Milmanhttps://emilman.net.technion.ac.il/Techniontag:www.math.bgu.ac.il,2005:MeetingDecorator/9702023-01-26T12:42:54+02:002023-01-26T12:42:54+02:00BGU Math<span class="mathjax">Zeev Rudnick: TBA</span>March 28, 14:30—15:30, 2023, Math -101<div class="mathjax"><p>TBA</p></div>Zeev Rudnickhttp://www.math.tau.ac.il/~rudnick/Tel Aviv Universitytag:www.math.bgu.ac.il,2005:MeetingDecorator/9732023-02-22T16:16:24+02:002023-02-22T16:16:24+02:00BGU Math<span class="mathjax">Rahim Moosa: TBA</span>May 2, 14:30—15:30, 2023, Math -101<div class="mathjax"><p>TBA</p></div>Rahim Moosahttps://www.math.uwaterloo.ca/~rmoosa/University of Waterlootag:www.math.bgu.ac.il,2005:MeetingDecorator/9742023-02-22T19:28:08+02:002023-02-22T19:28:08+02:00BGU Math<span class="mathjax">Yair Glasner: TBA</span>May 16, 14:30—15:30, 2023, Math -101<div class="mathjax"><p>TBA</p></div>Yair Glasnerhttps://www.math.bgu.ac.il/en/people/users/yairglBGUtag:www.math.bgu.ac.il,2005:MeetingDecorator/9762023-03-05T17:19:54+02:002023-03-05T17:19:54+02:00BGU Math<span class="mathjax">Michael Entov: TBA</span>May 23, 14:30—15:30, 2023, Math -101<div class="mathjax"><p>TBA</p></div>Michael Entovhttps://sites.google.com/site/michaelentov/Techniontag:www.math.bgu.ac.il,2005:MeetingDecorator/9842023-03-19T22:07:56+02:002023-03-19T22:10:44+02:00BGU Math<span class="mathjax">Misha Verbitsky: TBA</span>June 6, 14:30—15:30, 2023, Math -101<div class="mathjax"><p>TBA</p></div>Misha Verbitskyhttp://verbit.ru/IMPAtag:www.math.bgu.ac.il,2005:MeetingDecorator/9852023-03-19T22:08:30+02:002023-03-19T22:08:30+02:00BGU Math<span class="mathjax">Misha Verbitsky: TBA</span>June 13, 14:30—15:30, 2023, Math -101<div class="mathjax"><p>TBA</p></div>Misha Verbitskyhttp://verbit.ru/IMPA