Past Events

Abstract

It is known that the asymptotics of the ECH capacities of a star-shaped domain in R^4 recover its volume. We conjecture that generically the next term in the asymptotics is determined by the "Ruelle invariant" which, roughly speaking, measures the average rotation speed of the Reeb flow on the…

Abstract

Abstract: Let G be a reductive group. Following Gross, and generalizing Serre's classical notion in the two-dimensional case, I will define what it means for a G-valued representation of the Galois group of a (totally real) number field to be odd. This notion provides a natural setting for…

I'll give an introduction to rational homotopy theory. The plan is to describe the basic ideas of the theory, and hopefully to comment on some connections to differential and symplectic geometry.

Let X be a Hirzebruch surface.  Moduli spaces of semistable sheaves on X with fixed numerical invariants are always irreducible by a theorem of Walter.  On the other hand, many other basic properties of sheaves on Hirzebruch surfaces are unknown.  I will discuss two different…

The Gagliardo-Nirenberg inequality allows an interpolation of L^p-based Sobolev spaces by combining L^p estimates of higher-order derivatives for p small and L^p estimates of lower-order derivatives for p large to give an L^p estimate of intermediate derivatives for p intermediate. Such…