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

2:00pm to 3:00pm

Ross 70
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.
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.
2017 Dec 26

# T&G: Or Hershkovits (Stanford), Uniqueness of mean curvature flow through (some) singularities

1:00pm to 2:30pm

## Location:

Room 63, Ross Building, Jerusalem, Israel
Abstract: Given a smooth compact hypersurface in Euclidean space, one can show that there exists a unique smooth evolution starting from it, existing for some maximal time. But what happens after the flow becomes singular? There are several notions through which one can describe weak evolutions past singularities, with various relationship between them. One such notion is that of the level set flow.
2018 Jan 16

# T&G: Daniel Alvarez-Gavela (Stanford), Singularities of fronts: how to get rid of them and why

1:00pm to 2:30pm

## Location:

Room 63, Ross Building, Jerusalem, Israel
2017 Oct 31

# T&G: Pavel Giterman (Hebrew University), Descendant Invariants in Open Gromov Witten Theory

12:00pm to 1:30pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
In this talk we will consider the question of defining descendant invariants in open Gromov-Witten theory. In the closed Gromov-Witten theory, descendant invariants are constructed from Chern classes of certain tautological lines bundles which live on the moduli space of stable curves. The intersection numbers obtained from those classes (and other classes) can be incorporated in a generating function that satisfies various partial differential equations reflecting recurrence relations and which can sometimes be used to calculate the numbers explicitly.
2017 Nov 14

# T&G: Shmuel Weinberger (University of Chicago), Periodic transformations on aspherical manifolds

12:00pm to 1:30pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
Suppose Z/n acts on a manifold, then if it has a fixed point, the natural homomorphism Z/n --> Out(π) (π = the fundamental group) lifts to Aut(π). If π is centreless, and the aspherical manifold is locally symmetric and the action is isometric, the converse holds. We shall discuss the extent to which this observation is geometric and to what extent it's topological. (It will depend on M and it will depend on n).
לאירוע הזה יש שיחת וידאו.