Video Lectures

Let $k$ be a field and $X$ a geometrically connected variety over $k$. The Tate or degeneracy locus of a $l$-adic local system on $X$ is the etale counterpart of the Hodge locus of a VHS. While in the last decade tremendous progresses have been made...

The cohomology of a family of algebraic varieties carries a number of interrelated structures, of both Hodge-theoretic and arithmetic flavors. I’ll explain joint work with Josh Lam developing analogues of some of these structures and interrelations...

In 1984 W. B. Johnson and J. Lindenstrauss showed that a random projection of an arbitrary point set S into low-dimensional space is approximately distance-preserving, as long as S is of size at most exponential in the target dimension. The...

Building on previous work of Satake and Baily, Baily and Borel proved in 1966 that arithmetic locally symmetric varieties admit canonical projective compactifications whose graded rings of functions are given by automorphic forms. Such varieties...

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...