Video Lectures

In the first part of this talk, we take the ideas of the second talk and focus on the case of (arithmetic) lattices in PSL(2,R) and PSL(2,C). The required representation rigidity is achieved by what we call Galois rigidity. In particular if Γ1 is a...

An immersion from a smooth n-dimensional manifold M into Rq is called totally nonparallel if, for every pair of distinct points x and y in M, the tangent spaces at f(x) and f(y) contain no parallel lines. The simplest example is the map R→R2 sending...

 I will report on my recent work with Natalie Paquette, where we derive expressions for form factors and scattering amplitudes of gauge theory as correlators of a chiral algebra.  The chiral algebra is closely related to algebras appearing in the...

In this talk we will discuss connections between the geometric and analytic/PDE properties of sets. The emphasis is on quantifiable, global results which yield true equivalence between the geometric and PDE notions in very rough scenarios, including...

Pulsar radio emission may be generated in pair discharges which fill the pulsar magnetosphere with plasma as an accelerating electric field is screened by freshly created pairs. In this talk we present a simplified analytic theory for the screening...

A surprising property of the cohomology of locally symmetric spaces is that Hecke operators can act on multiple cohomological degrees with the same eigenvalues. We will discuss this phenomenon for the coherent cohomology of line bundles on modular...

Taking up the terminology established in the first lecture, in 1970 Grothendieck showed that when two groups (G,H) form a Grothendieck pair, there is an equivalence of their linear representations. For recent work showing that certain groups are...