Previous Conferences & Workshops

The field of unlikely Intersections presents a robust paradigm for problems in which several subjects intermingle: arithmetic, o-minimality, and hodge theory. The goal of this talk will be to introduce some of those connections. My aim is to...

Abstract: A linear extension of $P$ is a linear ordering compatible with the poset relations. Let $p(x< y), p(y < x))$ and $\delta(P)$ be the maximum value of $\delta(x, y)$ over all $x, y$ in $P$. The following two conjectures about $\delta(P)$ are both well-known:

1. (The "1/3-2/3 Conjecture") $\delta(P) \geq \frac{1}{3}$ whenever $P$ is not a chain.
2. (The "Kahn-Saks Conjecture") $\delta(P) \to \frac{1}{2}$ as $w(P) \to \infty$ (where $w(P)$ is the maximum size of an antichain in $P$).

While still far from either of these, we prove a number of conditions for $\delta(P) \to \frac{1}{2}$ and $\delta(P) \geq \frac{1}{e} - o(1)$, using a mix of geometric and probabilistic techniques. Joint with Jeff Kahn.

Borel proved that every holomorphic map from a product of punctured unit discs to a complex Shimura variety extends to a map from a product of discs to its Bailey-Borel compactification. In joint work with Oswal, Zhu, and Patel, we proved a p-adic...

Given a bounded sequence of zero mean, we study the problem of its orthogonality to all continuous  observables in topological dynamical systems whose all invariant measures yield measure-theoretic systems belonging to a fixed characteristic class...

In the past decade, $p$-adic Hodge theory has been transformed by the discovery of perfectoid spaces and the Fargues–Fontaine curve. One area, however, that has remained almost untouched by these breakthroughs is the theory of $p$-adic differential...

I will describe a recent extension of the classical PAC (Probably Approximately Correct) learning framework [Vapnik and Chervonenkis, 1970s; Valiant, 1980s]. This extension makes it possible to model a wide range of common and practical data...

The Gysin map, or the wrong-way map, is a classical construction that has been available for various cohomology theories and in 𝐀¹-homotopy theory. In this talk, I will give a construction of it based on 𝐏¹-homotopy theory, so that it specializes to...

The $r$-colour Ramsey number $R_r(k)$ is the minimum $n \in \mathbb{N}$ such that every $r$-colouring of the edges of the complete graph $K_n$ on $n$ vertices contains a monochromatic copy of $K_k$. We prove, for each fixed $r \ge 2$, that 

$$R_r(k)...