Past Events
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…
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…