Speaker：Kefeng Liu (Chongqing University of Technology)

Time：2025-4-10, 16:30

Location：Conference Room C503 at Administration Building at Haiyun Campus 

Abstract:

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.