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Séminaire de Géométrie

Siegel–Veech Measures of Convex Flat Cone Spheres

Kai Fu

( IMB )

Salle 2

le 27 juin 2025 à 10:45

A convex flat cone sphere is a Riemann sphere equipped with a conformal flat metric with conical singularities, all of whose cone angles are less than 2pi. In this talk, I introduce recent work on extending the Siegel–Veech formula for translation surfaces to this setting. We define the Siegel–Veech measures on the positive real line associated to the moduli space of convex flat cone spheres. This measure can be viewed as a generalization of the classical Siegel–Veech formula. We show that it is absolutely continuous and piecewise real analytic, and compute its asymptotic at zero.