What is... the skeleton of a curve?

Vortrag von Michaël Maex

Datum: 21.10.25  Zeit: 16.30 - 18.30  Raum:

Skeleta of Berkovich spaces link together the worlds of combinatorics, arithmetic geometry, analytic geometry, tropical geometry and resolution of singularities. Rather than getting lost into tedious details, this talk aims to give an overview of historic and recent developments of non-archimedean geometry in the sense of Tate and Berkovich in a way that is understandable by any graduate student in mathematics.
We will introduce non-archimedean fields and how they historically led to a new type of analytic space. Then we discuss analogies between geometry of Berkovich spaces and complex spaces, which is captured by skeleta. Finally we discuss different different ways of obtaining skeleta and canonical forms can play a key role in this, and further reduce the dependence on tools from algebraic geometry.