Francois Loeser: On the homotopy type of Berkovich spaces

Abstract: To give some motivation, we shall start by reviewing some recent work of Thuillier, Berkovich and Nicaise, showing that the topology of the Berkovich analytification of an algebraic variety encodes important information about varieties and their degenerations. We shall then present recent results obtained in collaboration with Ehud Hrushovski: Berkovich analytifications of algebraic varieties retract to finite CW-complexes and are locally contractible. Our approach uses some advanced tools from Model Theory. We shall try to give at least some glimpses of what these are and what they are good for.