University of Washington

In this talk I shall sketch some results Oliver Riordan of Oxford and I have obtained on critical probabilities in percolation. Recently, Scullard and Ziff noticed that a broad class of planar percolation models are self-dual under a simple condition...

An alternating permutation w=a1⋯an of 1,2,…,n is a permutation such that ai>ai+1 if and only if i is odd. If En (called an Euler number) denotes the number of alternating permutations of 1,2,…,n, then ∑n≥0Enxnn!=secx+tanx. We will discuss such topics...

Erdös Magic, aka The Probabilistic Method, is a powerful tool for proving the existence of a combinatorial object, such as a coloring. A probability space is created for which the probability of success is positive. Hence the desired object must...

There is a widely held belief in physics that a true astrophysical black hole, formed from the gravitational collapse of some stellar object, can be described by a certain exact solution to the Einstein equations discovered by Kerr in the 60s. This...

Abstract In this talk we will discuss issues related to the existence of a moduli space for varieties of general type. Recall that varieties of general type are the higher dimensional analog of Riemann surfaces of genus at least 2. We will explain...

Abstract: Polynomial identities can reflect deeper mathematical phenomena. In this talk, I will discuss some of the stories behind four identities (and their relatives). The stories involve algebra, analysis, number theory, combinatorics, geometry...

Summer School July 27th - 30th: The summer school will provide an opportunity for graduate students and recent PhDs to learn about several areas of active research lying at the intersection of representation theory, commutative algebra and algebraic...

Abstract: Where should one look to find bases satisfying strong uncertainty relations? Position and momentum lead the way: it's hard to do better than any orthonormal basis and its Fourier transform. The natural generalization to so-called mutually...

Although the topic of stability of solutions of partial differntial equations is important in almost any application area, the most powerful techniques one uses to examine stability are hardly ever taught in courses. This is mainly because many of...

Abstract: After reviewing ordinary finite-dimensional Morse theory, I will explain how Morse generalized Morse theory to loop spaces, and how Floer generalized it to gauge theory on a three-manifold. Then I will describe an analog of Floer cohomology...