2016 Jun 02

# Groups & dynamics: Todor Tsankov (Paris-Diderot): On metrizable universal minimal flows

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
2016 Mar 29

# Dynamics lunch seminar: Brandon Seward (HUJI): Entropy theory for non-amenable groups (part IV)

12:00pm to 1:45pm

Ross 70
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 12

# Groups & dynamics: Elon Lindenstrauss (HUJI), "Rigidity of higher rank diagonalizable actions in positive characteristic"

10:00am to 11:00am

## Location:

Ross 70
Title: Rigidity of higher rank diagonalizable actions in positive characteristic
2017 Dec 12

# T&G: Yoel Groman (Columbia), Generation of the Fukaya category of a Lagrangian torus fibration by a section

1:00pm to 2:30pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
The (wrapped) Fukaya category of a symplectic manifold is a category whose objects are Lagrangian submanifolds and which contains a wealth of information about the symplectic topology. I will discuss the construction of the wrapped Fukaya category for certain completely integrable Hamiltonian systems. These are 2n-dimensional symplectic manifolds carrying a system of n commuting Hamiltonians surjecting onto Euclidean space. This gives rise to a Lagrangian torus fibration with singularities.
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 lens spaces which may be of independent interest.
2016 Mar 15

# Dynamics lunch seminar: Brandon Seward (HUJI): Entropy theory for non-amenable groups (part II)

12:00pm to 1:45pm

## Location:

Ross 70
"Entropy theory for non-amenable groups (part II)"
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 May 18

# Basic notions: Ehud de Shalit - The Loxton - van der Poorten conjecture

4:00pm to 5:00pm

Abstract: Adamczewski and Bell proved in the 2013 the Loxton - van der Poorten conjecture. It says the following. Let f be a Laurent power series (with complex coefficients) and let \sigma_p be the operator substituting x^p for x in f. Suppose that f satisfies a homogenous polynomial equation in the operator \sigma_p with coefficients which are rational functions, and a similar equation in the operator \sigma_q where p and q are multiplicatively independent natural numbers. Then f is a rational function.
2017 May 25

# Basic notions: Ehud de Shalit - The Loxton - van der Poorten conjecture

4:00pm to 5:00pm

Abstract: Adamczewski and Bell proved in the 2013 the Loxton - van der Poorten conjecture. It says the following. Let f be a Laurent power series (with complex coefficients) and let \sigma_p be the operator substituting x^p for x in f. Suppose that f satisfies a homogenous polynomial equation in the operator \sigma_p with coefficients which are rational functions, and a similar equation in the operator \sigma_q where p and q are multiplicatively independent natural numbers. Then f is a rational function.
2017 May 21

# Combinatorics: 2 TALKS: Ilan Karpas (HUJI) "Two results about union-closed families" and Michael Simkin (HUJI) "The Threshold for the Appearance of Latin Square-Like Objects in Random Arrays"

11:00am to 1:00pm

## Location:

Rothberg B221 (CS building)
First talk (11:00--11:50): Speaker: Ilan Karpas, HU Tilte: Two results about union-closed families
2015 Dec 24

# Amitsur Algebra: Michael Larsen (Indiana U)

12:00pm to 1:15pm

## Location:

Manchester Building (room 209), Jerusalem, Israel
Title: Character values on compact simple Lie groups Abstract: This work is part of a joint project with Aner and others to find upper bounds for values of irreducible characters in two related settings: compact simple Lie groups and finite groups of Lie type. I will discuss the first case, presenting bounds of the form $$|\chi(g)| = O(\chi(1)^\alpha),$$
2015 Nov 19

# Amitsur Algebra: Avinoam Mann (HUJI), "Irreducible characters of some p-groups"

12:00pm to 1:15pm

## Location:

Manchester Building (room 209), Jerusalem, Israel
Abstract: We will discuss the characters of some classes of finite p-groups, in particular groups of maximal class and generalizations, and normally monomial groups.