Introduction

In this course, we introduce the general notion of (G,X)-structures on manifolds. After providing the basic results on the topology of surfaces (including the topological classification theorem), we will give a general panorama of (G,X)-structures in dimension two. We will focus on two classes of geometric structures:

- metrics with constant curvature (possibly with singularities);

- geometric structures compatible with a structure of Riemann surface.

We will discuss fruitful interactions with combinatorics, dynamical systems and the general theory of moduli spaces.

Lecturer Intro

Guillaume Tahar is a BIMSA assistant research fellow. Before joining BIMSA he held a senior postdoctoral fellowship in Weizmann Institute of Science. He contributed to the study of moduli spaces of various flavours of geometric structures on surfaces: translation and dilation structures, flat metrics and cone spherical metrics. His recent research interests of include linear differential operators, isoresidual fibrations and simplicial arrangements of lines.