北京雁栖湖应用数学研究院

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.