2017 Mar 16

# Colloquium: Oren Becker (HUJI) Tzafriri Prize Lecture "Equations in permutations and group theoretic local testability"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract: Given two permutations A and B which "almost" commute, are they "close" to permutations A' and B' which really commute? This can be seen as a question about a property the equation XY=YX. Studying analogous problems for more general equations (or sets of equations) leads to the notion of "locally testable groups" (aka "stable groups").
2017 Jun 08

# Colloquium:  Vadim Kaloshin (Maryland) - "Birkhoff Conjecture for convex planar billiards and deformational spectral rigidity of planar domains"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
G.D.Birkhoff introduced a mathematical billiard inside of a convex domain as the motion of a massless particle with elastic reflection at the boundary. A theorem of Poncelet says that the billiard inside an ellipse is integrable, in the sense that the neighborhood of the boundary is foliated by smooth closed curves and each billiard orbit near the boundary is tangent to one and only one such curve (in this particular case, a confocal ellipse). A famous conjecture by Birkhoff claims that ellipses are the only domains with this
2018 May 17

# Colloquium - Tzafriri lecture: Amitay Kamber (Hebrew university) "Almost-Diameter of Quotient Spaces and Density Theorems"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
A recent result of Lubetzky and Peres showed that the random walk on a $q+1$-regular Ramanujan graph has $L^{1}$-cutoff, and that its “almost-diameter” is optimal. Similar optimal results were proven by other authors in various contexts, e.g. Parzanchevski-Sarnak for Golden Gates and Ghosh-Gorodnik-Nevo for Diophantine approximations. Those results rely in general on a naive Ramanujan conjecture, which is either very hard, unknown, or even false in some situations. We show that a general version of those results can be proven using the density hypothesis of Sarnak-Xue.
2017 Mar 02

# Colloquium - Joram seminar: Hugo Duminil-Copin (Universite de Geneve, IHES), "Proving conformal invariance using discrete holomorphicity"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Title: Proving conformal invariance using discrete holomorphicity Abstract:
2017 May 18

# Colloquium: Alex Eskin (Chicago) Dvoretzky Lecure Series, "Polygonal Billiards and Dynamics on Moduli Spaces."

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Billiards in polygons can exhibit some bizarre behavior, some of which can be explained by deep connections to several seemingly unrelated branches of mathematics. These include algebraic geometry (and in particular Hodge theory), Teichmuller theory and ergodic theory on homogeneous spaces. I will attempt to give a gentle introduction to the subject. A large part of this talk will be accessible to undergraduates.
2015 Nov 25

# Topology & geometry: Lara Simone Suárez (HUJI), "Exact Lagrangian cobordism and pseudo-isotopy"

11:00am to 12:45pm

## Location:

Ross building, Hebrew University (Seminar Room 70A)
Abstract: Consider two Lagrangian submanifolds L, L′ in a symplectic manifold (M,ω). A Lagrangian cobordism (W;L,L′) is a smooth cobordism between L and L′ admitting a Lagrangian embedding in (([0,1]×R)×M,(dx∧dy)⊕ω) that looks like [0,ϵ)×{1}×L and (1−ϵ,1]×{1}×L′ near the boundary. In this talk we will show that under some topological constrains, an exact Lagrangian cobordism (W;L,L′) with dim(W)>5 is diffeomorphic to [0,1]×L.
2017 Jun 01

# Group actions:Lei Yang - badly approximable points on curves and unipotent orbits in homogeneous spaces

10:30am to 11:30am

We will study n-dimensional badly approximable points on curves. Given an analytic non-degenerate curve in R^n, we will show that any countable intersection of the sets of weighted badly approximable points on the curve has full Hausdorff dimension. This strengthens a previous result of Beresnevich by removing the condition on weights. Compared with the work of Beresnevich, we study the problem through homogeneous dynamics. It turns out that the problem is closely related to the study of distribution of long pieces of unipotent orbits in homogeneous spaces.
2018 Jan 22

# NT&AG: Shaul Zemel (HUJI), "Heegner Divisors on Toroidal Compactifications of Orthogonal Shimura Varieties"

2:00pm to 3:00pm

## Location:

Room 70A, Ross Building, Jerusalem, Israel
2017 Apr 20

# Basic notions: Raz Kupferman (HUJI) - A geometric framework for continuum mechanics

4:00pm to 5:15pm

Abstract: The “geometrization" of mechanics (whether classical, relativistic or quantum) is almost as old as modern differential geometry, and it nowadays textbook material. The formulation of a mathematically-sound theory for the mechanics of continuum media is still a subject of ongoing research. In this lecture I will present a geometric formulation of continuum mechanics, starting with the definition of the fundamental physical observables, e.g., force, deformation, stress and traction. The outcome of this formulation is a generalization of Newton’s "F=ma” equation for continuous media.
2017 Jun 15

# Group actions: Nir Lazarovich (ETH Zurich): Detecting sphere boundaries of hyperbolic groups

10:00am to 11:00am

We show that the boundary of a one-ended simply connected at infinity hyperbolic group with enough codimension-1 surface subgroups is homeomorphic to a sphere. By works of Markovic and Kahn-Markovic our result gives a new characterization of groups which are virtually fundamental groups of hyperbolic 3-manifolds. Joint work with B. Beeker.
2017 May 04

# Group actions: Nicolas de Saxcé (Paris 13) - Diophantine approximation and diagonal flows on the space of lattices

10:00am to 11:00am

## Location:

Ross 70
For almost every real number x, the inequality |x-p/q|<1/q^a has finitely many solutions if and only if a>2. By Roth's theorem, any irrational algebraic number x also satisfies this property, so that from that point of view, algebraic numbers and random numbers behave similarly.
2016 Nov 17

# Colloquium: Boris Zilber (Oxford) " A model-theoretic semantics of algebraic quantum mechanics"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
We approach the formalism of quantum mechanics from the logician point of view and treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics. We then aim to establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states with the action of time evolution operators, which is a limit of finite models. The finitary nature of the space allows us to give a precise meaning and calculate various classical quantum mechanical quantities.
2015 Dec 03

# Colloquium: Ofer Zeitouni (Weizmann), "Extremes of logarithmically correlated fields"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Title: Extremes of logarithmically correlated fields Abstract: The general theory of Gaussian processes gives a recipe for estimating the maximum of a random field, which is neither easy to compute nor sharp enough for obtaining the law of the maximum. In recent years, much effort was invested in understanding the extrema of logarithmically correlated fields, both Gaussian and non-Gaussian. I will explain the motivation, and discuss some of the recent results and the techniques that have been involved in proving them.
2016 Mar 10

# Colloquium: Nati Linial (Hebrew University) "Higher dimensional permutations"

3:30pm to 4:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
This is part of our ongoing effort to develop what we call "High-dimensional combinatorics". We equate a permutation with its permutation matrix, namely an nxn array of zeros and ones in which every line (row or column) contains exactly one 1. In analogy, a two-dimensional permutation is an nxnxn array of zeros and ones in which every line (row, column or shaft) contains exactly one 1. It is not hard to see that a two-dimensional permutation is synonymous with a Latin square. It should be clear what a d-dimensional permutation is, and those are still very partially understood.
2016 Nov 03

# Colloquium: T.N.Venkataramana (Tata Institute) "Monodromy Groups and Arithmetic Groups"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
To a linear differential equation on the projective line with finitely many points of singularities, is associated a monodromy group; when the singularities are "reguar singular", then the monodromy group gives more or less complete information about the (asymptotics of the ) solutions. The cases of interest are the hypergeometric differential equations, and there is much recent work in this area, centred around a question of Peter Sarnak on the arithmeticity/thin-ness of these monodromy groups. I give a survey of these recent results.