From
Shedule -
Séminaire "Géometrie et dynamique dans les espaces de modules"
Siegel–Veech Measures of Convex Flat Cone Spheres
IHP - Bâtiment Borel
Salle Olga Ladyjenskaïa
A classical theorem of Siegel gives the average number of lattice points in bounded subsets of $\mathbb{R}^n$. Motivated by this result, Veech introduced an analogue for translation surfaces, now known as the Siegel–Veech formula. For flat surfaces with irrational cone angles, however, no such formula is available.
A convex flat cone sphere is a Riemann sphere equipped with a flat metric with conical singularities, all with cone angles less than $2\pi$. In this talk, I will discuss recent work extending Siegel–Veech theory to this setting and outline the main ideas of the proof.