Past Events
This talk is about travelling fronts going through an array of obstacles for reaction-diffusion equations. I will consider the setting of bistable type equations and periodic obstacles. One can also think of a wave going through a perforated wall. We show in general that the wave is either…
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…