Arithmetic Geometry

Let $X/S$ be a regular scheme over the spectrum of a discrete valuation ring. Bloch conjectured a formula relating algebraic differential forms to the total dimension of the vanishing cohomology of $X/S$. In this talk, I will explain a proof of this...

We use Teichmüller theory to construct a new geometric model for the classifying space of the mapping class group of a three-dimensional handlebody. Two consequences are obtained: (i) Chan-Galatius-Payne have shown that the homology of Kontsevich's...