2018
Jan
16

# Dynamical & Probability

2018
Jan
02

# Dynamics Seminar: Ilya Khayutin (Princeton / IAS) - CM Points, Joinings and Intermediate Measures

2:15pm to 3:15pm

## Location:

Ross 70

A celebrated theorem of Duke states that Picard/Galois orbits of CM points on a complex modular curve, e.g. SL2(Z)\SL2(R)/SO2(R), equidistribute in the limit when the absolute value of the discriminant goes to infinity. Michel and Venkatesh have conjectured that a sequence of some 2-fold self-joinings of CM orbits equidistributes in the product space as long as it escapes any closed orbit of an intermediate subgroup, i.e. Hecke correspondences.

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

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

2015
Nov
03

# Dynamics & probability: Asaf Nachmias (Tel Aviv)

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)

Title: Indistinguishability of trees in uniform spanning forests
Abstract:
The uniform spanning forest (USF) of an infinite connected graph G is the weak limit of the uniform spanning tree measure taken on exhausting finite subgraphs of G. It is easy to see that it is supported on spanning graphs of G with no cycles, but it need not be connected. Indeed, a classical result of Pemantle ('91) asserts that when G=Zd, the USF is almost surely a connected tree if and only if d=1,2,3,4.

2015
Dec
29

2015
Dec
08

# Dynamics & probability: Brandon Seward (HUJI): "Positive entropy actions of countable groups factor onto Bernoulli shifts"

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)

Title: Positive entropy actions of countable groups factor onto Bernoulli shifts
Abstract: I will prove that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well-known Sinai factor theorem from classical entropy theory. As an application, I will show that for a large
class of non-amenable groups, every positive entropy free ergodic action satisfies the measurable von Neumann conjecture.

2015
Dec
22

# Dynamics & probability: Naomi Feldheim (Stanford), "New results on zeroes of stationary Gaussian functions"

2:00pm to 3:00pm

## Location:

Math 209 (Manchester building)

We consider (complex) Gaussian analytic functions on a horizontal strip, whose distribution is invariant with respect to horizontal shifts (i.e., "stationary"). Let N(T) be the number of zeroes in [0,T] x [a,b]. We present an extension of a result by Wiener, concerning the existence and characterization of the limit N(T)/T as T approaches infinity, as well as characterize the growth of the variance of N(T).

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.

2016
Apr
10

# Dvoretzky lecture 2: Lai-Sang Young (Courant) "Proving the positivity of Lyapunov exponents"

4:00pm to 5:00pm

## Location:

Lecture hall 2

A signature of chaotic behavior in dynamical systems is sensitive dependence on initial conditions, and Lyapunov exponents measure the rates at which nearby orbits diverge. One might expect that geometric expansion or stretching in a map would lead to positive Lyapunov exponents. This, however, is very difficult to prove - except for maps with invariant cones (or a priori separation of expanding and contracting directions).

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.

2017
May
16

# Special dynamics seminar: Ian Morris (Surrey): Equilibrium states of affine iterated function systems

(All day)

## Location:

Equilibrium states of affine iterated function systems

Motivated by the long-standing problem of finding sharp lower estimates for the Hausdorff dimension of self-affine sets, I will describe some recent results on the equilibrium states of the singular value function. These equilibrium states arise as candidates for the measures of maximal Hausdorff dimension on self-affine sets. In particular I will discuss a sufficient condition for uniqueness of the equilibrium state (from joint work with Antti Käenmäki) and an unconditional bound for the number of ergodic equilibrium states (from joint work with Jairo Bochi).

2017
Feb
09

2017
Dec
19

# Dynamics Seminar: Asaf Katz (Chicago): "Quantitative disjointness of nilflows and horospherical flows."

2:15pm to 3:15pm

## Location:

Ross 70

In his influential disjointness paper, H. Furstenberg proved that weakly-mixing systems are disjoint from irrational rotations (and in general, Kronecker systems), a result that inspired much of the modern
research in dynamics. Recently, A. Venkatesh managed to prove a quantitative version of this
disjointness theorem for the case of the horocyclic flow on a compact Riemann surface.
I will discuss Venkatesh's disjointness result and present a generalization of this result to more general actions of nilpotent groups, utilizing structural results about nilflows proven by Green-Tao-Ziegler.

2017
Jun
06