主持人：刘钢 教授

报告人简介：
刘克峰，美国加州大学洛杉矶分校教授、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》主编，《Pure and Appl. Math. Quarterly》创刊主编，《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180余篇学术论文，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、全球华人数学家大会银奖、斯隆(Sloan)奖、特曼(Terman)奖等。

报告摘要：
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.