Previous Conferences & Workshops

I will describe a problem of unlikely intersections in a product of modular curves, tracing the problem itself and the tools for some results through the work of Enrico.

Most effective results for integral points on affine curves use the works of Baker or Bombieri on Diophantine approximation by S-units. Still, no completely general result is known already in genus 2. I will briefly present some recent work with...

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...