Groups & Dynamics

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
2015 Nov 19

Groups & dynamics: Lei Yang (HUJI) "Equidistribution of expanding translates of curves in homogeneous spaces and Diophantine approximation"

10:00am to 11:00am

Location: 

Ross 70
Title: Equidistribution of expanding translates of curves in homogeneous spaces and Diophantine approximation.
Abstract:
We consider an analytic curve $\varphi: I \rightarrow \mathbb{M}(n\times m, \mathbb{R}) \hookrightarrow \mathrm{SL}(n+m, \mathbb{R})$ and embed it into some homogeneous space $G/\Gamma$, and translate it via some diagonal flow
2016 Nov 03

Groups and dynamics - Misha Belolipetsky

10:30am to 11:30am

Location: 

Ross 70
Speaker: Misha Belolipetsky
Title: Arithmetic Kleinian groups generated by elements of finite order
Abstract:
We show that up to commensurability there are only finitely many
cocompact arithmetic Kleinian groups generated by rotations. The proof
is based on a generalised Gromov-Guth inequality and bounds for the
hyperbolic and tube volumes of the quotient orbifolds. To estimate the
hyperbolic volume we take advantage of known results towards Lehmer's
problem. The tube volume estimate requires study of triangulations of
2015 Dec 17

Groups & dynamics: Robert Hough (IAS) - Mixing and cut-off on cyclic groups

12:00pm to 1:00pm

Location: 

Einstein 110
Consider a sequence of random walks on $\mathbb{Z}/p\mathbb{Z}$ with symmetric generating sets $A= A(p)$. I will describe known and new results regarding the mixing time and cut-off. For instance, if the sequence $|A(p)|$ is bounded then the cut-off phenomenon does not occur, and more precisely I give a lower bound on the size of the cut-off window in terms of $|A(p)|$. A natural conjecture from random walk on a graph is that the total variation mixing time is bounded by maximum degree times diameter squared.
2015 Nov 05

Groups & Dynamics : Ilya Khayutin (HUJI)

9:45am to 11:00am

Location: 

Manchester building, Hebrew University of Jerusalem, (Room 209)
Title: Arithmetic of Double Torus Quotients and the Distribution of Periodic Torus Orbits
Abstract:
In this talk I will describe some new arithmetic invariants for pairs of torus orbits on inner forms of PGLn and SLn. These invariants allow us to significantly strengthen results towards the equidistribution of packets of periodic torus orbits on higher rank S-arithmetic quotients. An important aspect of our method is that it applies to packets of periodic orbits of maximal tori which are only partially split.
2017 Jun 01

Group actions:Lei Yang - badly approximable points on curves and unipotent orbits in homogeneous spaces

10:30am to 11:30am

We will study n-dimensional badly approximable points on curves. Given an analytic non-degenerate curve in R^n, we will show that any countable intersection of the sets of weighted badly approximable points on the curve has full Hausdorff dimension. This strengthens a previous result of Beresnevich by removing the condition on weights. Compared with the work of Beresnevich, we study the problem through homogeneous dynamics. It turns out that the problem is closely related to the study of distribution of long pieces of unipotent orbits in homogeneous spaces.
2016 Nov 03

Groups and dynamics - Misha Belolipetsky

10:30am to 11:30am

Location: 

Ross 70
Arithmetic Kleinian groups generated by elements of finite order Abstract: We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. The proof is based on a generalised Gromov-Guth inequality and bounds for the hyperbolic and tube volumes of the quotient orbifolds. To estimate the hyperbolic volume we take advantage of known results towards Lehmer's problem. The tube volume estimate requires study of triangulations of lens spaces which may be of independent interest.
2016 Nov 17

Groups and dynamics: Arie Levit

10:30am to 11:30am

Location: 

Ross 70
Speaker: Arie Levit
Weizmann Institute
Title: Local rigidity of uniform lattices
Abstract: A lattice is topologically locally rigid (t.l.r) if small deformations of it are isomorphic lattices. Uniform lattices in Lie groups were shown to be t.l.r by Weil [60']. We show that uniform lattices are t.l.r in any compactly generated topological group.
2016 Mar 03

Groups & dynamics: Karim Adiprasito (HUJI) - Contractible manifolds, hyperbolicity and the fundamental pro-group at infinity

10:00am to 11:00am

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
2015 Dec 31

Groups & dynamics: Thang Neguyen (Weizmann) - Rigidity of quasi-isometric embeddings

10:00am to 11:00am

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

Pages