Previous Conferences & Workshops

Review the notion of cd-structure for a Grothendieck topology and explain how it helps check the sheaf conditions. Introduce and discuss the Nisnevich topology for schemes and analytic adic spaces; in particular, discuss their equivalent...

Video link: https://www.ias.edu/video/bombieri-and-calculus-variations

Motivated by work of Cantat-Dujardin, we study orbits by translations in K3 surfaces with two elliptic fibrations. We prove in particular that all orbits are infinite away from a proper Zariski-closed subset.

Among the tools, beyond the Pila-Wilkie...

In joint work with Jacob Tsimerman we study when the primitive of a given algebraic function can be constructed using primitives from some given finite set of algebraic functions, their inverses, algebraic functions, and composition. When the given...

We discuss a modern perspective on the winding number on $S^1$ for maps that may not be continuous. This reveals a surprising connection to Fourier analysis and motivates the question: is the winding number determined by the moduli of the Fourier...

A few years ago, Bhatt-Morrow-Scholze introduced an invariant of $p$-adic formal schemes called syntomic cohomology, which has a close relationship to (étale-localized) algebraic $K$-theory. In a recent paper, Antieau-Mathew-Morrow-Nikolaus showed...

The method of hypergraph containers is a widely-applicable technique in probabilistic combinatorics. The method enables one to gain control over the independent sets of many `interesting' hypergraphs by exploiting the fact that these sets exhibit a...