Video Lectures

Morrey’s conjecture arose from a rather innocent looking question in 1952: is there a local condition characterizing "ellipticity” in the calculus of variations? Morrey was not able to answer the question, and indeed, it took 40 years until first...

This talk will serve as an introduction to the random algebraic method. This method has its origins in the following problem: suppose the binomial random graph comes "close" to having some property of interest P, but fails to do so because of the...

In this talk I will discuss a joint project with Yuanpu Liang in which we establish several properties of the sequence of symplectic capacities defined by Gutt and Hutchings for star-shaped domains using S1-equivariant symplectic homology. Among the...

I will present joint work with V. Paškūnas and G. Böckle concerning deformation rings for mod p Galois representations of p-adic local fields. After giving a short introduction to the subject, I will explain our main result which says that framed...

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...

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...