Speaker: Hao Sun（South China University of Technology）
Time: 16:00-18:00, Dec 31, 2022, Jan 4, 9, 11, 2023
Room: Tencent Meeting: 500 1723 7578, no password
Parabolic bundle was introduced by Mehta-Seshadri to study unitary representations of fundamental groups of punctured curves. In this series of four talks, at first I will discuss some basic properties about parabolic bundles, including the definition, stability conditions and the idea about the construction of the corresponding moduli spaces. Then I will give a one-to-one correspondence between parabolic (Higgs) bundles and equivariant (Higgs) bundles, which was studied by Mehta-Seshadri first in 1980. This result was generalized to bundles on root stacks by Borne in 2006. Furthermore, this correspondence gives an alternative way to construct the moduli space of parabolic (Higgs) bundles. In 1990, Simpson associated a (metrized) holomorphic bundle on noncompact curve with a parabolic bundle on the completion of the curve. This construction preserves the degree and the corresponding stability conditions. I will further discuss the relation between parabolic bundles on compact curves and holomorphic bundles on noncompact curves. This correspondence is crucial in establishing the tame nonabelian Hodge correspondence on noncompact curve. Also in 1990, Simpson established the (tame) nonabelian Hodge correspondence on noncompact curves by giving a one-to-one correspondence among filtered Higgs bundles, filtered D-modules and filtered local systems, where filtered Higgs bundles are usually called parabolic Higgs bundles. If times permits, I will review this result and share some recent results of the nonabelian Hodge theory for principal bundles on noncompact curves. The recent works are joint with P. Huang, G. Kydonakis and L. Zhao.
Video recording:
Dec 31: https://meeting.tencent.com/v2/cloud-record/share?id=08fb2815-f573-465a-a578-af183d203fb2&from=3
Jan 4: https://meeting.tencent.com/v2/cloud-record/share?id=12735044-7c9b-48a9-b5db-7c4d0f8be322&from=3
Jan 9: https://meeting.tencent.com/v2/cloud-record/share?id=3c3f2c24-62d4-4030-a6d6-ed9115538f7e&from=3
Jan 11: https://meeting.tencent.com/v2/cloud-record/share?id=6733ab14-3425-455f-a7c8-d8f369d41bc7&from=3
Password: para
