Past Events

A basic question in algebraic geometry is whether there can be any non-constant maps between (smooth, projective) varieties of different types. I will explain some basic and some more sophisticated obstructions to the existence of such maps, mostly...

The moduli space \M_g of genus g curves (or Riemann surfaces) is a central object of study in algebraic geometry. Its cohomology is important in many fields. For example, the cohomology of M_g is the same as the cohomology of the mapping class group...

The problem of counting the number of eigenvalues of a differential operator is exactly as old as quantum theory and was inspired by various physical questions. In the century since Weyl’s first asymptotic result on the topic, the question has...

The Vlasov-Landau-Maxwell equation is often regarded as the first-principle physics model for plasmas, which collectively accounts for particle transport, electromagnetic field effects, and particle collisions. We introduce a novel particle method...

A useful way of producing samples from a given measure ν on a state space Ω is by providing a Markov chain whose stationary measure in ν. In order to be able to sample efficiently, one needs to show that the chain "mixes" quickly in terms of the rate...

A Kakeya set is a compact subset of R^n that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that such sets must have dimension n. This conjecture is closely related to several open problems in harmonic...

The past twenty-five years have heralded an unparalleled increase in understanding of cancer. At the same time, mathematical modelling has emerged as a natural tool for unravelling the complex processes that contribute to the initiation and...

Poincaré-Einstein spaces are a generalization of the Poincaré model of hyperbolic space. They were introduced to study holographically the conformal geometry of the boundary at infinity. This geometric correspondence underlies the AdS/CFT...

Vertex operator algebras (VOAs) are a mathematical approach to quantum field theories which won their creator a Fields medal. But they are highly complicated structures -- if you haven't already learned what they are, it is surely best if you never...