An invitation to higher Teichmüller theory – Anna Wienhard – ICM2018

Geometry
Invited Lecture 5.11
An invitation to higher Teichmüller theory
Anna Wienhard

Abstract: Riemann surfaces are of fundamental importance in many areas of mathematics and theoretical physics. The study of the moduli space of Riemann surfaces of a fixed topological type is intimately related to the study of the Teichmüller space of that surface, together with the action of the mapping class group. Classical Teichmüller theory has many facets and involves the interplay of various methods from geometry, analysis, dynamics and algebraic geometry. In recent years, higher Teichmüller theory emerged as a new field in mathematics. It builds as well on a combination of methods from different areas of mathematics. The goal of my talk is to invite the reader to get to know and to get involved into higher Teichmüller theory by describing some of its many facets.

ICM 2018 – International Congress of Mathematicians ©
 
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