Geometry of Large Genus Flat Surfaces

par Elise Goujard (Université de Nantes)

lundi 12 janv. 2026, 14:00 → 15:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Gluing the opposite sides of a square gives a flat torus: a torus endowed with a flat metric induced by the Euclidean metric on the square. Similarly, one can produce higher genus surfaces by gluing parallel sides of several squares. These "square-tiled surfaces" inherit from the squares a flat metric with conical singularities. In this talk we will present several recent results and conjectures on the large genus asymptotics of these surfaces, and more generally of some families of flat surfaces (joint work with V. Delecroix, P. Zograf and A. Zorich). We will also see how these results can be interpreted in the language of closed curves on surfaces. We will finish with some recent results joint with E. Duryev and I. Yakovlev that should allow to generalize these results to a larger family of flat surfaces.