2017 Apr 27

# Colloquium: Gal Binyamini (Weizmann), " Differential equations and algebraic points on transcendental varieties"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
The problem of bounding the number of rational or algebraic points of a given height in a transcendental set has a long history. In 2006 Pila and Wilkie made fundamental progress in this area by establishing a sub-polynomial asymptotic estimate for a very wide class of transcendental sets. This result plays a key role in Pila-Zannier's proof of the Manin-Mumford conjecture, Pila's proof of the Andre-Oort conjecture for modular curves, Masser-Zannier's work on torsion anomalous points in elliptic families, and many more recent developments.
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 23

# Colloquium: Asaf Shapira (Tel Aviv) - "Removal Lemmas with Polynomial Bounds"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
A common theme in many extremal problems in graph theory is the
relation between local and global properties of graphs. We will
consider the following variant of this theme: suppose a graph G
is far (in some well defined sense) from satisfying property P.
Must G contain a small proof of this fact? We will show that
for many natural graph properties the answer is Yes. In particular,
we will show that the answer is Yes whenever P is a semi-algebraic
graph property, thus conforming a conjecture of Alon.
Joint work with L. Gishboliner
2017 Jun 22

# Colloquium: Zohovitzki prize lecture - Ariel Rapaport, "Self-affine measures with equal Hausdorff and Lyapunov dimensions"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
A measure on the plane is called self-affine if it is stationary with respect to a finitely supported measure on the affine group of R^2. Under certain randomization, it is known that the Hausdorff dimension of these measures is almost surely equal to the Lyapunov dimension, which is a quantity defined in terms of the linear parts of the affine maps. I will present a result which provides conditions for equality between these two dimensions, and connects the theory of random matrix products with the dimension of self-affine measures.
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
A well-known result of Borcherds yields the modularity of Heegner divisors on complex orthogonal Shimura varieties (i.e. Grassmannian quotients). These varieties are typically non-compact, and one way of completing them to compact varieties is via toroidal compactifications. However, the boundary components there also contain divisors. We show how to extend the Heegner divisors to such compactifications in such a manner that the modularity result of Borcherds still holds. This is joint work with J. Bruinier.
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.
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.
2015 Nov 19

# Colloquium: Shmuel Weinberger (Chicago), "The Quantitative challenge to topology"

2:30pm to 3:30pm

## Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Serre's thesis and its aftermath rolled in a golden age of algebraic topology which led to the impression that we can really understand (necessarily highly nonlinear) maps from one space to another. With the work of Thom on cobordism and Smale on immersions and the Poincare conjecture, a paradigm developed where geometric problems would be solved by reduction to algebraic topological ones.