Video Lectures

I will talk about ongoing work with S. Venugopalan on computing disk potentials (which are counts of holomorphic disks with boundary on a Lagrangian) via multi-directional neck stretching. The focus will be on examples.

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...

The upper critical dimension of the O(N) vector model is well-known to be 4. In dimension 4-epsilon it is described by the Wilson-Fisher IR fixed point of the O(N) invariant scalar field theory with a small positive quartic coupling. Above 4...

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...

Finding low-scatter relationships in properties of complex systems (e.g., stars, supernovae, galaxies) is important to gain physical insights into them and/or to estimate their distances/masses. As the size of simulation/observational datasets grow...

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...