Beijing Institute of Mathematical Sciences and Applications Beijing Institute of Mathematical Sciences and Applications

  • About
    • President
    • Governance
    • Partner Institutions
    • Visit
  • People
    • Management
    • Faculty
    • Postdocs
    • Visiting Scholars
    • Staff
  • Research
    • Research Groups
    • Courses
    • Seminars
  • Join Us
    • Faculty
    • Postdocs
    • Students
  • Events
    • Conferences
    • Workshops
    • Forum
  • Life @ BIMSA
    • Accommodation
    • Transportation
    • Facilities
    • Tour
  • News
    • News
    • Announcement
    • Downloads
About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > GRASP seminar The spectral base of Hitchin maps
The spectral base of Hitchin maps
Organizers
Pengfei Huang , Tao Su , Hao Sun
Speaker
Jie Liu
Time
Wednesday, March 20, 2024 10:00 AM - 11:00 AM
Venue
A3-2-303
Online
Zoom 518 868 7656 (BIMSA)
Abstract
Let $X$ be a projective manifold. The Hitchin morphism is a map from the moduli stack of Higgs bundles over $X$ to the Hitchin base, which sends a Higgs bundle to its characteristic polynomial. If $X$ is a curve, it is well-known that the Hitchin morphism is surjective and it plays an important role in the study of the moduli space of Higgs bundles. However, if $X$ has dimension at least two, the Hitchin morphism in general is not surjective. Thus a closed subset of the Hitchin base, called the spectral base, is introduced by Tsao-Hsien Chen and Bao Chau Ngo and it is conjectured that the Hitchin morphism is onto the spectral base. This conjecture is confirmed when $X$ is a surface by the works of Tsao-Hsien Chen and Bao Chau Ngo and Lei Song and Hao Sun. In this talk, I will present our solution to this conjecture for rank two Higgs bundles and also show the vanishing of the spectral base for Hermitian locally symmetric spaces with higher rank. This is joint work with Siqi He and Ngaiming Mok.
Beijing Institute of Mathematical Sciences and Applications
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

Copyright © Beijing Institute of Mathematical Sciences and Applications

京ICP备2022029550号-1

京公网安备11011602001060 京公网安备11011602001060