Past Events

In positive characteristic, there are two different notions of rational connectedness: a variety can be rationally connected or separably rationally connected (SRC). SRC varieties share many of the nice properties that rationally connected varieties have in…

The Geometrization Theorem of Thurston and Perelman provides a roadmap to understanding topology in dimension 3 via geometric means.  Specifically, it states that every closed 3-manifold has a decomposition into geometric pieces, and each piece is realizable as a finite volume quotient…

Abstract: Given a curve $\Gamma$, what is the surface $T$ that has least area among all surfaces spanning $\Gamma$? This classical problem and its generalizations are called Plateau's problem. In this talk we consider area minimizers among the class of integral currents, or…

Toeplitz asked in 1911 whether every Jordan curve in the Euclidean plane contains the vertices of a square. The problem remains open, but it has given rise to many interesting variations and partial results. I will describe some of these and the proof of a result which is best possible when the…

We will talk about classification of ancient solutions in geometric flows. In particular, we will show the only closed ancient noncollapsed Ricci flow solutions are the shrinking spheres and Perelman's solution. We will talk about the higher dimensional analogue of this result under…

Macdonald polynomials are a remarkable family of functions. They are a common generalization of many different families of special functions arising in the representation theory of reductive groups, including spherical functions and Whittaker functions.

In turn, Macdonald polynomials can…

This paper studies the consumption-saving decisions of "present-biased" consumers who face self-control problems when making these choices. I show that continuous-time methods allow for present bias to be tractably incorporated into rich consumption-saving models featuring stochastic income…

Two knots in homology 3-spheres are homology concordant if they are smoothly concordant in a homology cobordism. I will explain how to construct integer-valued homomorphisms from this group of knots up to homology concordance. This construction generalizes concordance homomorphisms from knot…