Program

Resolution of Singularities
Dan Abramovich

Local Systems in Arithmetic Geometry
Hélène Esnault

Non abelian Hodge Theory and Applications to the Shafarevich Conjecture
Philippe Eyssidieux

We will give an introduction to Corlette-Simpson’s non abelian Hodge theory and some if its applications.

Birational complexity of algebraic varieties
Robert Lazarsfeld

I will talk about a circle of ideas loosely centered around the theme of studying ”how complicated” a given variety is from a birational viewpoint. For example, given a projective variety X whose irrationality is known, how can one quantify and control “how irrational” it is? Given two varieties of the same dimension, how far are they from being birationally isomorphic? The work in this direction is still at an experimental stage, so I will emphasize examples and especially open questions. They involve a lot of concrete down-to-earth geometry.