Past Events

The cosmic censorship conjectures, proposed by Roger Penrose, attempt to describe singularities in general relativity. I will describe the conjectures and explain some recent mathematical progress.

Homology cobordisms are a special type of manifold which are relevant to a variety of areas in geometric topology, including knot theory and triangulability. We study the behavior of a variety of invariants under a particular family of four-dimensional homology cobordisms, including Floer…

In past weeks, we've seen two theories which solve certain problems in classical physics: general relativity and quantum field theory. Unfortunately, they don't play well together. String theory tries to reconcile these two sets of ideas to produce a "theory of everything." I will attempt to…

It is natural to ask which properties of a smooth projective variety are recovered by its derived category. In this talk, I will consider the question: is the existence of a rational point preserved under derived equivalence? In recent joint work with Nicolas Addington, Ben Antieau, and Katrina…

In 1966 Lennart Carleson proved that the Fourier series of an L^2 function converges pointwise almost everywhere, resolving a question of Fourier himself.  Since then, the proof has been simplified by Fefferman, and then Lacey and Thiele.  I will go over some of the ideas in these…

The Chow group of zero-cycles on a surface is a notoriously difficult object to study, but a set of far-reaching conjectures due to Bloch and Beilinson aim to describe the structure of this group. Focusing our attention on products of two elliptic curves, we will specifically consider the…

A 4-manifold is constructed with some curious metric properties; or maybe it is many 4-manifolds masquerading as one, which would explain why it looks curious.  Anyway, knots in the 3-sphere with complete finite volume hyperbolic metrics on their complements play a role in this…