Previous Conferences & Workshops

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...

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...

A natural problem in the study of local systems on complex varieties is to characterize those that arise in a family of varieties. We refer to such local systems as motivic. Simpson conjectured that for a reductive group G, rigid G-local systems...

Consider a point mass traveling in a polygon. It travels in a straight line, with constant speed, until it hits a side, at which point it obeys the rules of elastic collision. What can we say about this? When all the angles of the polygon are...