Past Events

Khovanov homology is an invariant of knots in R^3. Two open problems are to extend its definition to knots in other three-manifolds, and to understand its relation to surfaces in 4-manifolds. I will discuss some partial progress in these directions. In the process I will also review some of…

Hardy’s uncertainty principle states that a function and its Fourier transform cannot have Gaussan decay simultaneously unless the function is identically zero if the rates of decay are too large. This result can be restated in terms of solutions to the Schrödinger equation with Gaussian…

Kronheimer and Mrowka recently suggested a possible approach towards a new proof of the four color theorem that does not rely on computer calculations.  One outgrowth of their approach is the definition of a combinatorial functor J^flat from the category of webs and foams to the category of…

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…