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
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.
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 Apr 07

Colloquium: Lai-Sang Young (Courant) "Measuring Dynamical Complexity"

2:30pm to 3:30pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
I will discuss, for differentiable dynamical systems, three ways to capture dynamical complexity:
hyperbolicity, which measures the sensitivity of dependence on initial conditions.
entropy, which measures the predictability of future dynamical events in the sense of information theory.
the speed of correlation decay or equivalently the rate at which memory is lost.
2016 Nov 24

Colloquium: Dan Freed (University of Texas) "Bordism and topological phases of matter"

2:00pm to 3:00pm

Location:

Manchester Building (Hall 2), Hebrew University Jerusalem
Topological ideas have at various times played an important role in condensed matter physics. This year's Nobel Prize recognized the origins of a particular application of great current interest: the classification of phases of a quantum mechanical system. Mathematically, we would like describe them as path components of a moduli space, but that is not rigorously defined as of now. In joint work with Mike Hopkins we apply
stable homotopy theory (Adams spectral sequence) to compute the group of
topological phases of "invertible" systems. We posit a continuum field