Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	刘冰萧, 科隆大学
Inviter:	谢松晏
Title:	Introduction to random zeros of holomorphic sections: number variance and central limit theorem
Language:	Chinese
Time & Venue:	2024.03.28 15:00-16:30 腾讯会议：870-915-067
Abstract:	For a compact K?hler manifold, by considering the high tensor powers of a prequantum line bundle, Shiffman and Zelditch (1999, CMP) proved the equidistribution of the zeros of random holomorphic sections in the semiclassical limit. Then several generalizations and extensions of this result have been made in different geometric or probabilistic settings. Notably, the large deviation estimates and hole probabilities for the random zeros were also established on compact Hermitian manifolds. In this series of lectures, I will give an introduction to these results and their generalization to the case of noncompact Hermitian manifolds. As the last part of the lectures, we will focus on the number variance and the asymptotic normality of random zeros. In particular, I will recall the results proved by Sodin-Tsirelson (2004, Israel J. Math.) for special models on complex plane and by Shiffman-Zelditch (2008, GAFA and 2010, Pure Appl. Math. Q.) for compact K?hler manifolds.