Seminario de geometría diferencial y sistemas dinámicos, CIMAT

Fecha y hora : Lunes, 26 de Octubre de 2020, 4:30pm (en línea)

Por: Hughes Auvray, Institut de Mathématique d’Orsay, Francia

Título: Bergman kernels on punctured Riemann surfaces

Resumen: In joint works with X. Ma (Paris 7) and G. Marinescu (Cologne) we obtain refined asymptotics for Bergman kernels computed from singular data. We work on the complement of a finite number of points, seen as punctures, on a compact Riemann surface that we endow with a metric extending Poincaré’s cusp metric around the puncture points. We moreover fix a holomorphic line bundle polarizing such a metric. I’ll explain how an advanced description of the model (on the punctured unit disc) and weighted techniques In a weighted context allow to describe the Bergman kernels associated to such Riemann surfaces, up to singularities. If time permits, I’ll also mention geometric, or even arithmetic, interpretations of such results.