Groups & Dynamics

2019 Apr 11

Groups & Dynamics Seminar: Erez Nesharim (Technion) - The t-adic Littlewood conjecture is false

10:00am to 11:00am

Location: 

Ross 70
The Littlewood and the p-adic Littlewood conjectures are famous open problems on the border between number theory and dynamics. In a joint work with Faustin Adiceam and Fred Lunnon we show that the analogue of the p-adic Littlewood conjecture over \mathbb{F}_3((1/t)) is false. The counterexample is given by the Laurent series whose coefficients are the regular paper folding sequence, and the method of proof is by reduction to the non vanishing of certain Hankel determinants.
2019 May 02

Kobi Peterzil (Haifa) - Closure of o-minimal flows on nilmanifolds

10:00am to 11:00am

I will discuss joint work with S. Starchenko, which combines dynamical systems in the nilmanifold setting with definable objects in o-minimal structures (e.g. semi-algebraic sets): Let G be a real algebraic unipotent group and let L be a lattice in G with p:G->G/L the quotient map. Given a subset X of G which is semi-algerbaic, or more generally definable in an o-minimal structure, we describe the closure of p(X) in terms of finitely many definable families of cosets of positive dimensional algebraic subgroups of G.
2019 Mar 14

Manuel Luethi (ETH) : Effective equidistribution of primitive rational points along long horocycle orbits and disjointness to Kloosterman sums

10:00am to 11:30am

Location: 

Ross 70
Abstract: An observation by Jens Marklof shows that the primitive rational points of a fixed denominator along the periodic unipotent orbit of volume equal to the square of the denominator equidistribute inside a proper submanifold of the modular surface. This concentration as well as the equidistribution are intimately related to classical questions of number theoretic origin. We discuss the distribution of the primitive rational points along periodic orbits of intermediate size. In this case, we can show joint equidistribution with polynomial rate in the modular surface and in the torus.
2018 May 31

Groups & Dynamics: Anish Gosh (TIFR) - The metric theory of dense lattice orbits

10:30am to 11:30am

Abstract: The classical theory of metric Diophantine approximation is very well developed and has, in recent years, seen significant advances, partly due to connections with homogeneous dynamics. Several problems in this subject can be viewed as particular examples of a very general setup, that of lattice actions on homogeneous varieties of semisimple groups. The latter setup presents significant challenges, including but not limited to, the non-abelian nature of the objects under study.
2018 Jun 14

Groups & Dynamics seminar. Mark Sapir (Vanderbilt): S-machines and their applications

10:30am to 12:00pm

Location: 

Ross 70
Title: S-machines and their applications
Abstract: I will discuss applications of S-machines which were first introduced in 1996. The applications include
* Description of possible Dehn functions of groups
* Various Higman-like embedding theorems
* Finitely presented non-amenable torsion-by-cyclic groups
* Aspherical manifolds containing expanders
* Groups with quadratic Dehn functions and undecidable conjugacy problem
2017 Apr 27

Group actions: Yair Glasner (BGU) - On Highly transitive permutation representations of groups. 

10:30am to 11:30am

Location: 

Ross 70
Abstract: A permutation representation of a group G is called highly transitive if it is transitive on k-tuples of points for every k. Until just a few years ago groups admitting such permutation representations were thought of as rare. I will focus on three rather recent papers: G-Garion, Hall-Osin, Gelander-G-Meiri (in preparation) showing that such groups are in fact very common.
2017 Nov 02

Group actions: Remi Coulon (Rennes) - Growth gap in hyperbolic groups and amenability

10:30am to 11:30am

Location: 

hyperbolic groups and amenability
(joint work with Françoise Dal'Bo and Andrea Sambusetti)
Given a finitely generated group G acting properly on a metric space X,
the exponential growth rate of G with respect to X measures "how big"
the orbits of G are. If H is a subgroup of G, its exponential growth
rate is bounded above by the one of G. In this work we are interested in
the following question: what can we say if H and G have the same
exponential growth rate? This problem has both a combinatorial and a
geometric origin. For the combinatorial part, Grigorchuck and Cohen
2018 May 10

Groups & dynamics: Sanghoon Kwon (Kwandong University) - A combinatorial approach to the Littlewood conjecture in positive characteristic

10:30am to 11:30am

Location: 

Ross 70
The Littlewood conjecture is an open problem in simultaneous Diophantine approximation of two real numbers. Similar problem in a field K of formal series over finite fields is also still open. This positive characteristic version of problem is equivalent to whether there is a certain bounded orbit of diagonal semigroup action on Bruhat-Tits building of PGL(3,K).
2015 Dec 17

Groups & dynamics: Rene Rühr, Distribution of Shapes of Orthogonal Lattices

10:00am to 11:30am

Location: 

Ross building, Hebrew University of Jerusalem, (Room 70)
To every topological group, one can associate a unique universal
minimal flow (UMF): a flow that maps onto every minimal flow of the
group. For some groups (for example, the locally compact ones), this
flow is not metrizable and does not admit a concrete description.
However, for many "large" Polish groups, the UMF is metrizable, can be
computed, and carries interesting combinatorial information. The talk
will concentrate on some new results that give a characterization of
metrizable UMFs of Polish groups. It is based on two papers, one joint

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