Video Lectures

Fix a metric (Riemannian or Finsler) on a compact manifold M. The critical points of the length function on the free loop space LM of M are the closed geodesics on M. Filtration by the length function gives a link between the geometry of closed...

A few years ago Ichino-Ikeda formulated a quantitative version of the Gross-Prasad conjecture, modeled after the classical work of Waldspurger. This is a powerful local-to-global principle which is very suitable for analytic and arithmetic...

Incidence geometry is a part of combinatorics that studies the intersection patterns of geometric objects. For example, suppose that we have a set of L lines in the plane. A point is called r-rich if it lies in r different lines from the set. For a...

olynomials are a special class of functions. They are useful in many branches of mathematics, often in problems which don't mention polynomials. We discuss two examples: polynomials in error-correcting codes and polynomials in geometric inequalities...

In 2007, Zeev Dvir shocked experts by giving a one-page proof of the finite field Kakeya problem. The new idea in the proof was to introduce high degree polynomials into a problem about points and lines. This idea has led to progress on several...

There are two important measures of the complexity of a boolean function: the sensitivity and block sensitivity. Whether or not they are polynomial related remains a major open question. In this talk I will survey some known results on this...