Piotr Achinger

Title: Homotopy types of varieties and rigid analytic spaces over C((t))

Abstract:
I will give an introduction to logarithmic geometry of Fontaine--Illusie and Kato 
and show how it can be used in the study of the topology of singularities of families 
of algebraic varieties. I will then give an overview of recent work joint with Mattia Talpo
(https://arxiv.org/abs/1909.02903) aiming to construct well-behaved homotopy types 
of varieties defined by formal Laurent series over C, as well as their non-archimedean 
counterparts, which come endowed with a monodromy action of the fundamental group 
of the circle.