Michele Ancona: Metric aspects of random plane curves

Speaker
Michele Ancona, Université Côte d’Azur

Abstract
A (complex) plane curve is the zero locus in CP^2 of a homogeneous complex polynomial in three variables. Any plane curve is endowed with a Riemannian metric induced by the ambient Fubini-Study metricof the complex projective plane. We give probabilistic lower bounds on some metric quantities (such as the systole, the curvature, or the spectral gap) of the plane curves when these are chosen randomly in the Fubini-Study ensemble. This is a joint work with Damien Gayet.