Previous Conferences & Workshops

Abstract: 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...

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...

Abstract: 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...

Sponsored by Dr. John P. Hempel 

Organizer: Jacob Tsimerman

The goal of the workshop was to investigate recent progress on special cycles from various perspectives, and the connection between geometric and arithmetic methods. 

Speakers:
Yves Andre...

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...

An open book is a topological concept aptly named by Elmar Winkelnkemper.

The binding of the book is a fibred knot (of any dimension), and open books and fibred knots are essentially synonymous. Currently the standard reference for the existence and...

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...

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...