Events & Seminars

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.
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.
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
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 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 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. הצטרף: https://meet.google.com/mcs-bwxr-iza
2018 Jan 02

T&G: Shaofeng Wang (Hebrew University), GIT, symplectic reduction and the Kempf-Ness theorem

1:00pm to 2:30pm

Location: 

Room 63, Ross Building, Jerusalem, Israel
Let G be a group acting on a projective variety. If G is noncompact, the quotient space X/G is in general "bad". In this talk I will discuss two methods to make this quotient "good", i.e. GIT and symplectic reduction. Both methods include the idea of keeping "good orbits" and throwing away "bad orbits". Hilbert-Mumford criterion provides a way to distinguish good orbits (which are called stable orbits) and the Kempf-Ness theorem tells us two methods produce the same quotient space. I will use several examples to show how Hilbert-Mumford criterion and the Kempf-Ness theorem work.
2017 Oct 24

T&G: Asaf Shachar (Hebrew University), Riemannian embeddings of minimal distortion

12:00pm to 1:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
This talk revolves around the question of how close is one Riemannian manifold to being isometrically immersible in another. We associate with every mapping $f:(M,g) \to (N,h)$ a measure of distortion - an average distance of $df$ from being an isometry. Reshetnyak's theorem states that a sequence of mappings between Euclidean domains whose distortion tends to zero has a subsequence converging to an isometry. I will present a generalization of Reshetnyak’s theorem to the general Riemannian setting.
2017 Nov 07

T&G: Ran Tessler (ETH - ITS), Open (CP^1,RP^1) intersection theory: properties, calculations and open Gromov-Witten/Hurwitz corrspondence.

1:00pm to 2:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
We will start be explaining the difficulties in constructing enumerative open Gromov-Witten theories, and mention cases we can overcome these difficulties and obtain a rich enumerative structure. We then restrict to one such case, and define the full genus 0 stationary open Gromov-Witten theory of maps to CP^1 with boundary conditions on RP^1, including descendents, together with its equivariant extension. We fully compute the theory.
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.

Pages