Seminars Sorted by Series

A very long random walk, seen from so far away that individual steps cannot be resolved, is the continuous random path called Brownian motion. This is a rough statement of Donsker's theorem and it is an example of how models in statistical mechanics...

I will report on a the following work in progress. Let X be a smooth connected curve over an algebraically closed field. Consider the dual pair H=SO_{2m}, G=Sp_{2n} over X with H split. Let Bun_G and Bun_H be the stacks of G-torsors and H-torsors on...

Color Coding is an algorithmic technique for deciding efficiently if a given input graph contains a path of a given length (or another small subgraph of a certain type). It illustrates well the phenomenon that probabilistic reasoning can be helpful...

Random waves have been investigated since the 1940's in connection with modeling telephone signals (Rice), to model sea waves (Longuet-Higgins), and since the 1970's by Berry and others to model quantum wave-functions of classically chaotic systems...

Motivated by some recent progress in the study of concentration phenomena for singularly perturbed elliptic nonlinear equations and the analogies with some problems in geometric analysis, we prove existence of new entire solutions of the focusing...

The Lubotzky-Sarnak Conjecture asserts that the fundamental group of a finite volume hyperbolic manifold does not have Property \tau. Put in a geometric context, this conjecture predicts a tower of finite sheeted covers for which the Cheeger...

What is the least surface area of a shape that tiles Rd under translations by Zd? Any such shape must have volume 1 and hence surface area at least that of the volume-1 ball, namely (–d). Our main result is a construction with surface area O(–d)...

Bose-Einstein condensation was predicted by Einstein in 1925 and was experimentally discovered 70 years later. This discovery was followed by a flurry of activity in the physics community with hundreds of papers published every year and with...

Trace formulae and relative trace formulae can be used to study the rich geometry of locally symmetric spaces. I will explain some illustrative examples coming from unitary groups in this talk.

This talk is intended for a general audience. We define and discuss a spectral invariant of closed Riemannian surfaces, namely the zeta regularized trace of inverse of the Laplacian. Physically this corresponds to the sum of squares of the...

(Joint work with Shiri Artstein-Avidan). We discuss in the talk an unexpected observation that very minimal basic properties essentially uniquely define some classical transforms which traditionally are defined in a concrete and quite involved form...

A pseudo-hermitian structure in 3-D is a contact form and an almost complex structure on the kernel of the contact form. There is a natural notion of area and mean curvature for a surface in such a geometry. I will discuss some work on the structure...

The classical isoperimetric inequality in Euclidean space asserts that among all sets of given Lebesgue measure; the Euclidean ball minimizes surface area. Using a suitable generalization of surface area, isoperimetric inequalities may be...

We will survey the role played by some classes of higher order integral conformal invariants in conformal geometry which include the integral of Q-curvature and those related to the Gauss-Bonnet integrand. We will also discuss a class of integral...

Sofic groups are the groups whose Cayley graph that can be approximated by finite graphs. This class of groups contains many known classes, e.g. profinite and amenable groups. Quite a few conjectures are known to hold for sofic groups. The most...

I will give an overview of a variational problem in conformal geometry/spectral theory. Beginning with a formula for the determinant of the laplacian for a surface and the work of Osgood-Phillips-Sarnak, I will explain some attempts to generalize...

If a closed subset X of the plane is projected orthogonally onto a line, then the Hausdorff dimension of the image is no larger than the dimension of X (since the projection is Lipschitz), and also no larger than 1 (since it is a subset of a line)...

We survey some of the points of contact between the two subjects of the title. The talk is intended for non-specialists.

What do the following seven things have in common: * zero-dimensional homogeneous polynomial ideals, * multivariate polynomial interpolation, * box splines, * hyperplane arrangements, * parking functions on graphs, * f-vectors of matroids, * integer...

Smectic liquid crystals correspond to certain foliations of Euclidean space. I will discuss the topology of defects in the smectics. Typically the index of these topological defects is characterized via the fundamental group of the manifold of...

In this talk we will relate some of the colorful history of one of the world's great math problems.

Quantum chaos is concerned with properties of eigenvalues and eigenfunctions of "quantized Hamiltonians". For instance, can classical chaos be detected by looking at the spacings between eigenvalues? Another problem is if classical ergodicity forces...

Semisimple Lie groups seem to be very rigid objects. In arithmetic situations the fact that a semisimple group may degenerate into a non-semisimple one in a family is well known. In geometric situations this phenomenon has not been applied that much...

I will report on a joint work with Ronny Hadani (UT Austin) and Amit Singer (Princeton). We give an algorithmic solution to the two problems that appear in the title. The input is the numerical data (roughly, random plane sections of the molecule)...

It has been recently observed that function spaces associated to a symplectic manifold exhibit unexpected properties and surprising structures, giving rise to new tools and intuition in symplectic topology. In the talk I shall discuss these...

The talk describes how pseudoholomorphic curve based techniques can be used to understand better the dynamics of autonomous Hamiltonian systems of two degrees of freedom restricted to a compact non-degenerate energy surface.

First I will introduce the notion of Gelfand pair and its connection to invariant functions and distributions on the group, and give some examples. We will start from finite groups and compact groups and then go on to reductive groups over local...

Following the brilliant insight of Riemann, that a good understanding of the distribution of prime numbers is equivalent to a good understanding of the location of zeros of pertinent L-functions, analytic number theory has traditionally centered on...

We establish a necessary and sufficient condition for an action of a lattice by homeomorphisms of the circle to extend continuously to the ambient locally compact group. This condition is expressed in terms of the real bounded Euler class of this...

I'll give a brief survey of Heegaard Floer homology, one of the latest and most powerful descendants of the Gauge theories of the 80's and 90's, and I'll discuss established and conjectured connections between Heegaard Floer homology and Khovanov...

The theory of quantum homology, which originally arose from physics, is currently generating a great deal of interest, due in part to its striking predictions regarding enumerative algebraic geometry. In this talk we will introduce the quantum...

I'll discuss connections between the distribution of zeros and values of $L$-functions, such as the Riemann zeta function, and of characteristic polynomials of matrices from the classical compact groups. Very little background will be assumed and...