Video Lectures

The theory of higher Reidemeister torsion yields characteristic classes of (stable) fiber bundles of smooth manifolds. We use this theory to define a new family of invariants for Legendrians in 1-jet spaces which we collectively call Legendrian...

The goal of this talk is to discuss a new local-global phenomenon in the Langlands program on automorphic forms and Galois representations. Spaces of modular forms are parametrized by weights, and those same weights parametrize local deformation...

Let n greater than 2. Weigold conjectured that if G is a finite simple group then the product replacement graph on n-generating tuples is connected (which also implies that it is an expander for n greater than 3). This conjecture is still (wide)...

Optimal bubble cluster problems concern the study of partitions of ℝn

into a fnite collection of chambers, some with finite volume and some with infinite volume. One looks for local minimizers of interfacial area subject to volume constraints on the...

Tensor decomposition is the task of writing an n x n x n input tensor T as \sum_{i = 1}^r a_i \otimes b_i \otimes c_i for the smallest possible r (called the rank of T). This problem is NP-hard in general. Jennrich's algorithm succeeds if a_is, b_is...

Locally Decodable Codes (LDCs) are a special type of error correcting codes which are constructed from finite point sets that support many small linear dependencies (e.g. many collinear triples). Despite their importance, there are still huge gaps...

The conformal bootstrap has proven very powerful for analyzing reflection-positive conformal models. In my talk, I will review this method and suggest a way to generalize it beyond the reflection-positive case, drawing inspiration from the spectral...