Video Lectures

We present a general framework for derandomizing random linear codes with respect to a broad class of properties, known as local properties, which encompass several standard notions such as minimum distance, list-decoding, list-recovery, and perfect...

Inflation may have occurred at energies up to 10^16 GeV, far beyond any terrestrial collider. The "cosmological collider" program aims to extract the mass spectrum and spin content of particles present during inflation from non-Gaussian correlators...

Joint project with Pavao Mardesic, Laura Ortiz-Bobadilla, and Jessie Pontigo-Herrera.

Hibert's 16th problem asks for an upper bound on the number of limit cycles of planar polynomial vector fields. For polynomial perturbations \dH+ϵω

of planar...

I will talk about a joint work with Antoine Sedillot. We study sup-norms of sections of metrized line bundles for families of arithmetic varieties. Using Riemann-Zariski spaces we obtain formulas that imply new definability results in the context of...

Numerical simulations of galaxies and the interstellar medium are now reaching resolutions where small-scale physical processes can be resolved directly. This raises a natural question: which pieces of microphysics must be modeled explicitly in...

 Constructing completions of period mappings with significant geometric and Hodge-theoretical meaning is an important topic in Hodge theory and its applications. There are rich theories for the classical case in which the period domain is Hermitian...