*主持人：刘博 教授

*讲座内容简介：

For a compact Kaehler manifold equipped with a prequantum line bundle, by considering the high tensor powers of the line bundle, Shiffman and Zelditch (1999) proved the equidistribution of the zeros of random holomorphic sections under the semiclassical limit. There are already many generalizations and extensions of this result in different geometric or probabilistic settings, in particular, the large deviation estimate and hole probability were also proved for compact Kaehler manifolds. In this talk, I would like to present a generalization of these results to the case of noncompact complex manifolds. More precisely, we construct the Gaussian-like random holomorphic sections of Hermitian holomorphic line bundles on a noncompact Hermitian complex manifold. In particular, we are interested in the case where the space of L2-holomorphic sections is infinite dimensional. Then we study their random zeros in the context of semiclassical limit, including the equiditribution, the large deviation estimate and the hole probability. This talk is based on the joint work with Alexander Drewitz and George Marinescu.

*主讲人简介：

刘冰萧，博士毕业于法国巴黎十一大（Orsay），曾在马普所（波恩）访问两年，目前在德国科隆大学数学所从事博士后研究，主要研究方向是亚椭圆Laplace算子，解析挠率，复流形上的Bergman核和全纯线丛截面。