【7月7日-7月20日】Geometry&Topology Seminar系列讲座-Higgs bundles, higher Teichmüller theory and minimal surfaces(I, II, III, IV)

发布者:王欣发布时间:2022-07-01浏览次数:190

报告人:聂鑫(东南大学)

时间:2022年7月7日、8日、19日、20日的上午9:00-10:30

地点:五教5106

报告摘要: 

提纲:

1. Holomorphic vector bundles and Higgs bundles

      • Symplectic reduction and its Kähler/hyperkähler versions

      • Relation with G.I.T. (Kempf-Ness theorem)

      • Holomorphic vector bundles, Atiyah-Bott's reduction and Narasimhan-Seshadri theorem

      • Higgs bundles, Hitchin's reduction and Hitchin-Kobayashi correspondence

 

2. G-Higgs bundles and surface group representations

      • SL(2,R)-Hitchin component and Teichmüller theory

      • SL(n,R)-Hitchin component, cyclic Higgs bundles

      • Theory of semsimple Lie algebras and principal 3d subalgebras

      • G-Higgs bundles for a general Lie group G

      • SO(p,q)-Higgs bundles

 

3. Harmonic maps associated to G-Higgs bundles and Labourie's conjecture

      • harmonic maps, minimal surfaces and Riemannian symmetric spaces

      • harmonic maps given by G-Higgs bundles

      • Energy functional and Labourie's conjecture

      • Strategy via Infinitesimal rigidity and the SL(3,R)-case (affine spheres)

      • Cyclic surfaces (Labourie Ann.Math.2017)

 

4. Minimal surfaces in pseudo-hyperbolic spaces

      • pseudo-hyperbolic spaces

      • second variation formula and maximal surfaces

      • Relation with Teichmüller theory (Bonsante-Schlenker Invent.Math.2010)

      • Labourie's conjecture for SO(2,n) (Collier-Tholozan-Toulisse Duke.Math.J. 2019)

      • A-surfaces and their infinitesimal rigidity (speaker arXiv:2206.13357)




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