Critical points of holomorphic sections and string/M theory vacua

Abstract

This talk is about joint work with M. R. Douglas and B. Shiffman on statistics of supersymmetric vacua in string theory. Mathematically, it is about the number and location of critical points of holomorphic sections of a hermitian line bundle.  The average number of critical points of a random holomorphic section depends on the metric. In the case of a positive line bundle, Calabi extremal metrics are extremals for the asymptotics of the average number of critical points.