温州大学数理学院2025年第3期数理大讲堂

题目: Automorphic cohomology, Penrose transformation, and geometry of non-classical flag domains.

报告人: 刘克峰教授 (加州大学洛杉矶分校、重庆理工大学)

邀请人：丁青教授

时间：5月10日（星期六）下午2：00-3：00，

地点：岩松堂展示厅

摘要: I will present my recent joint works with Yang Shen on the geometry and representation theory aspects of non-classical flag domains.

We prove several conjectures of Griffiths about the the structures of automorphic cohomology on compact quotients of non-classical flag domains.

We construct new complex structures on non-classical flag domains $D=G_\R/V$ with $G_\R$ of Hermitian type and their compact quotients. As applications, we give new examples of compact smooth manifolds on which there are two complex structures with very different geometric properties.

Building on these works, we construct Penrose transformations of the cohomology groups of homogeneous line bundles on flag domains $D = G_\R / T$ and identify conditions under which the Penrose transformation of the automorphic cohomology groups on compact quotients of flag domains is an isomorphism. As applications we prove that the higher automorphic cohomology groups of certain homogeneous line bundles are isomorphic to the groups of automorphic forms on the Hermitian symmetric domain.

报告人简介：刘克峰，美国加州大学洛杉矶分校数学系教授，浙江大学数学中心执行主任，重庆理工大学数学中心主任。现任国际著名数学杂志Communications in Analysis and Geometry、Pure and App. Math Quarterly主编, Pacific J. Math.、Asian J. Math.编委。刘教授在微分几何、拓扑、数学物理等研究方向取得了大量国际一流的原始创新成就，先后在PNAS、J. Amer, Math, Soc.、Invent. Math.、J. Differential Geom.、Duke Math. J.、Topology等杂志发表130多篇学术论文，并在2002年国际数学家大会上被邀请作45分钟报告。他曾荣获全球华人数学最高奖晨兴数学金奖和2004年国家教育部十大科技进展，以及国际上著名的谷庚海默奖、斯隆(Sloan)奖、特曼(Terman)奖等。