数学研究所

中国科学院华罗庚数学重点实验室

学术报告

多复变与复几何研讨班

SCV&CG Seminar

Speaker: 黄高枫 (瑞士伯尔尼大学)

Title: Large holomorphic automorphism group

Time&Venue: 2025.1.14（星期二）14:00-15:00 & 思源楼S415

Abstract: In this talk we survey a few results in the study of large holomorphic automorphism groups. First we give a short historical development of the so-called Andersen--Lempert theory, namely the study of large holomorphic automorphism groups. This field nowadays focuses on the so-called density property and a criterion for discovering more examples, many of which are smooth affine algebraic varieties.In the second part we will consider the symplectic setting, namely complex symplectic manifolds with large group of holomorphic symplectic automorphisms. An example is the even dimensional Euclidean space endowed with the standard complex symplectic form. As a new example, the Calogero--Moser space, also admits the symplectic density property, which in turn leads to a strong approximation result for symplectic automorphisms in the Carleman sense.