Video Lectures

Link spectral invariants and their homogenizations have been defined by Cristofaro-Gardiner et.al. In joint work with Ibrahim Trifa, we define a linear combination of such quasimorphism and show that it vanishes on the stabilizer of the equator in...

In this talk, I will discuss some effective computations for variations of integral Hodge structures.

Several years ago, with Ren and Javanpeykar-Kühne, I conjectured (in the Shimura setting) that a variation has only finitely many "non-factor"...

Cold Neptunes appear to be among the most abundant planets in the Galaxy, yet their role in shaping planetary systems remains poorly understood. We study the dynamical evolution of cold Neptune systems born in resonant chains through disk-driven...

A Hodge structure is a certain linear algebraic datum.  Importantly, the cohomology groups of any smooth projective algebraic variety come equipped with Hodge structures which encode the integrals of algebraic differential forms over topological...

The theory of rigidity for lattices in higher rank semisimple Lie groups is a powerful and exciting subject, combining methods from algebra, number theory, geometry and dynamics. One of the most celebrated results is Margulis' normal subgroup...

Cosmological data has opened up new vistas on fundamental physics yet it is limited in its scope. While it has given us tantalizing hints at how the Universe might be expanding, it is unclear whether it can ever be used to find the microphysical...

Around 1992, Aldous made the following bold conjecture. Let A be any set of transpositions in the symmetric group Sym(N). Then the spectral gap of the Cayley graph Cay(Sym(N),A) is identical to that of a relatively tiny N-vertex graph defined by A...

In a spacetime with asymptotically anti-de-Sitter boundaries, localized bulk events produce characteristic signals at boundary locations that are lightlike from the event. I will describe (thought) experiments that use boundary wavepackets to...

I'll give a brief introduction to o-minimality and how it can be used to prove asymptotic estimates for the number of rational points in definable sets. I'll then show how problems from various areas of mathematics can be reformulated as questions...

In this talk, I will describe our construction of the first explicit lossless vertex expanders. These are graphs where every small subset of vertices has about as many neighbors as their sparsity allows. Previously, the strongest known explicit...