Video Lectures

Let K be the function field of a smooth projective curve B over the complex numbers and let g be a positive integer. The uniform boundedness conjecture predicts that there exists a constant N, depending only on g and K, such that for any g...

Globally valued fields form a generalisation of global fields that fits into the context of first order (continuous) logic. I will describe these structures, and outline how they are connected to various parts of arithmetic geometry: Arakelov...

Massive black holes (MBHs) exist at the centers of many dense star systems, particularly in galactic nuclei.  Steady accretion onto MBHs powers active galactic nuclei, but dynamical processes near MBHs can generate various forms of transient...

I'll introduce o-minimality from a user's perspective assuming zero background. I'll talk about some of the main examples of o-minimal structures: as a user of o-minimality your first goal is to find out whether your favorite set lives in one of...

I will present a program of extracting cosmological information by combining effective field theory (EFT) techniques with data from spectroscopic galaxy surveys. I will highlight previous successes of this program and share recent results, including...

Given a one-parameter degenerating family of rational maps on the projective line, it is possible to construct a non-archimedean limit which captures how this family degenerates.  Recently, Luo used ultrafilters to construct limits for an arbitrary...

The mathematical core of deep learning is function approximation by neural networks trained on data using stochastic gradient descent. I will present a collection of sharp results on training dynamics for the deep linear network (DLN), a...

Higher-dimensional Heegaard Floer homology (HDHF) is defined by extending Lipshitz's cylindrical reformulation of Heegaard Floer homology from surfaces to arbitrary Liouville domains. The HDHF also serves as a model for Lagrangian Floer homology of...

In this talk, we will discuss new algorithms for solving instances of random and semirandom planted constraint satisfaction problems (CSPs). Random CSP are generated by first choosing a solution x and then sampling constraints so that x satisfies...

I will discuss the path integral of pure 3D gravity on a finite region of spacetime, with boundary conditions that fix dihedral angles or geodesic lengths. This amplitude calculates corrections to the Gaussian statistics of OPE coefficients in the...