Abstract:
For a complete Kähler manifold endowed with a positive line bundle, we use the theory of abstract Wiener spaces to construct a probabilistic model for Berezin-Toeplitz quantization. We associate to a function with compact support (a classical observable) a sequence of square-integrable Gaussian holomorphic sections. Our focus then is on the asymptotic distributions of their zeros in the semi-classical limit, in particular, we prove equidistribution results, large deviation estimates, central limit theorem of the random zeros on the support of the given function. This talk is based on the joint work with Alexander Drewitz and George Marinescu.
Biography:
Bingxiao Liu is a postdoctoral research assistant at University of Cologne. He received his PhD from Université Paris-Saclay (Orsay) in 2018. Before moving to Cologne, he was a postdoctoral fellow at Max Planck Institute for Mathematics in Bonn. His research is focused on Selberg's trace formula and real analytic torsions for locally symmetric spaces, Bergman kernel on complex manifolds, random holomorphic sections and their connections to mathematical physics.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.