2018
Jan
25

# Events & Seminars

2018
Jan
10

# Jerusalem Analysis Seminar - Michael Aizenman (Princeton)

12:00pm to 1:00pm

## Location:

Room 70 in the Ross Building

Title: On the decay of correlations under quenched disorder

Read more about Jerusalem Analysis Seminar - Michael Aizenman (Princeton)

2017
Dec
06

# Analysis and PDEs - Victor Ivrii (Toronto)

12:00pm to 1:00pm

## Location:

Ross 70

Title: Asymptotics of the ground state energy for relativistic heavy atoms and molecules

2017
Nov
28

# Dynamics Seminar: Nattalie Tamam (TAU), "Divergent trajectories in arithmetic homogeneous spaces of rational rank two"

2:15pm to 3:15pm

## Location:

Ross 70

In the theory of Diophantine approximations, singular points are ones for which Dirichlet’s theorem can be infinitely improved. It is easy to see that all rational points are singular. In the special case of dimension one, the only singular points are the rational ones. In higher dimensions, points lying on a rational hyperplane are also obviously singular. However, in this case there are additional singular points. In the dynamical setting the singular points are related to divergent trajectories.

2017
Oct
31

# Dynamics Seminar: Weikun He (HUJI): Orthogonal projections of discretized sets

2:00pm to 3:00pm

## Location:

Ross 70

In this talk I will discuss a finitary version of projection theorems in fractal geometry. Roughly speaking, a projection theorem says that, given a subset in the Euclidean space, its orthogonal projection onto a subspace is large except for a small set of exceptional directions. There are several ways to quantify "large" and "small" in this statement. We will place ourself in a discretized setting where the size of a set is measured by its delta-covering number : the minimal number of balls of radius delta needed to cover the set, where delta > 0 is the scale.

2018
Jan
16

# Dynamics Seminar: Neil Dobbs (Univ. College, Dublin), "Birkhoff averages of perturbations."

2:15pm to 3:15pm

## Location:

Ross 70

Birkhoff averages (of an observable along orbits) are objects of interest when investigating statistical behaviour of a dynamical system. If there is a unique physical measure, the Birkhoff averages will converge, for almost every orbit, to the space average (i.e. the integral) of the observable, so the physical measure captures important statistical properties of the dynamical system. However, in the quadratic family, for

2017
Dec
12

# Dynamics Seminar: Jakub Konieczny, " Automatic sequences, nilsystems and higer order Fourier analysis."

2:15pm to 3:15pm

## Location:

Ross 70

Automatic sequences are one of the most basic models of computation, with remarkable links to dynamics, algebra and logic (among other fields). In the talk, we will explore a point of view inspired by higher order Fourier analysis. Specifically, we will investigate the behaviour of Gowers norms of some automatic sequences, and (almost) classify all automatic sequences given by generalised polynomial fomulas. The tools used will include some non-trivial results concerning dynamics of nilsystems and their connection

2017
Dec
05

# Dynamics Seminar: Micheal Hochman (HUJI): Dimension of self-affine sets and measures

2:15pm to 3:15pm

## Location:

Ross 70

I will discuss joint work with Balazs Barany and Ariel Rapaport on the dimension of self-affine sets and measures. We confirm that under mild irreducibility conditions on the generating maps, the dimension is "as expected", i.e. equal to the affinity or Lyapunov dimension. This completes a program started by Falconer in the 1980s. In the first part of the talk I will explain how the Lyapunov dimension arises from Ledrappier-Young formula for self-affine sets, and then explain how additive combinatorics methods can be used to prove that this is the correct dimension.

2017
Nov
21

# Dynamics Seminar: Yakov Pesin (PSU), “A geometric approach for constructing equilibrium measures in hyperbolic dynamics”

2:15pm to 3:15pm

## Location:

Ross 70

In the classical settings of Anosov diffeomorphisms or more general locally maximal hyperbolic sets I describe a new approach for constructing equilibrium measures corresponding to some continuous potentials and for studying some of their ergodic properties. This approach is pure geometrical in its nature and uses no symbolic representations of the system. As a result it can be used to effect thermodynamics formalism for systems for which no symbolic representation is available such as partially hyperbolic systems.

2018
Jan
09

# Dynamics seminar: Zemer Kosloff (HUJI), "Proving Ergodicity via divergence of ergodic sums"

2:15pm to 3:15pm

## Location:

Ross 70

Ergodicity of a nonsingular transformation is equivalent to divergence of ergodic sums of all indicator functions of positive measure. In practice this divergence condition is easy to verify for “nice” sets and hard to verify for general sets. In this talk we will show two different arguments of how to pass from a

2017
Oct
24

2017
Nov
14

# Dynamics Seminar: Jie Li (HUJI), "When are all closed subsets recurrent?" ??

2:15pm to 3:15pm

## Location:

Ross 70

In this talk I will introduce the relations of rigidity, equicontinuity and pointwise recurrence between an invertible topological dynamical system (X; T) and the dynamical system (K(X); T_K) induced on the hyperspace K(X) of all compact subsets of X, and show some

characterizations.

Based on joint work with Piotr Oprocha, Xiangdong Ye and Ruifeng Zhang.

characterizations.

Based on joint work with Piotr Oprocha, Xiangdong Ye and Ruifeng Zhang.

2017
Dec
26

# Dynamics Seminar: Yuval Peres (Microsoft), "Gravitational allocation to uniform points on the sphere"

2:15pm to 3:15pm

## Location:

Ross 70

Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them ? "Fairly" means that each region has the same area. It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins of attraction for the resulting gradient flow yield such a partition—with exactly equal areas, no matter how the points are distributed. (See the

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.

2017
Apr
30

# Combinatorics: Amir Yehudayoff (Technion) "An exposition to topological overlap in the plane"

11:00am to 1:00pm

## Location:

Rothberg B221 (CS building)

Speaker: Amir Yehudayoff (Technion)

Title: An exposition to topological overlap in the plane

Abstract: We shall discuss Gromov's proof for topological overlap in

the plane. We will also consider a weighted version of Gromov's

theorem and deduce a dual statement.

Title: An exposition to topological overlap in the plane

Abstract: We shall discuss Gromov's proof for topological overlap in

the plane. We will also consider a weighted version of Gromov's

theorem and deduce a dual statement.