时间：2026年3月1日
地点：西湖大学云谷校区E14-222
10:00-10:50
Title: A study of local systems in nonabelian Hodge theory
Speaker：Pengfei Huang, Nanjing University
Abstract：
In his seminal work on tame nonabelian Hodge correspondence, Simpson identified the appropriate objects on the Betti side as local systems with parabolic structures, known as filtered local systems. In this talk, we will first review these objects and then demonstrate a construction of their moduli spaces, along with some examples. As an application, we establish a nonabelian Hodge correspondence at the level of moduli spaces. This approach is applicable to general reductive groups. Based on joint work with Hao Sun.
13:30-14:20
Title: Fundamental groups of compact Kahler varieties with nef anti canonical bundle
Speaker：Xin Fu, Westlake University
Abstract：
It is proved by M. Paun that the fundamental group of a compact Kahler manifold X is almost Abelian if the anti-canonical bundle -KX is nef. In this paper, we apply the recent geometric analytic theory of Kahler spaces developed by Guo-Phong-Song-Sturm to study fundamental groups of mildly singular compact Kahler varieties. This is joint work with Bin Guo, Jian Song, Juanyong Wang.
14:35-15:25
Title: Equivariant min-max theory and the spherical Bernstein problem in $\mathbb S^4$
Speaker：Tongrui Wang, Shanghai Jiao Tong University
Abstract：
In this talk, I will introduce a new resolution of Chern's spherical Bernstein problem in S^4 by constructing an embedded non-equatorial minimal S^3. The construction is based on our equivariant min-max theory for G-invariant minimal hypersurfaces with reduced genus bound, where G is a compact Lie group acting by isometries on a closed Riemannian manifold M with 3-dimensional orbit space M/G. Our approach also shows the existence of two distinct minimal hyperspheres and a minimal hypertorus in a certain class of Riemannian S^4 with symmetries. This talk is based on the joint work with Zhichao Wang and Xin Zhou.
15:55-16:45
Title: Stable degenerations of Fano fibration germs
Speaker：Linsheng Wang, Fudan University
Abstract：
In this talk, I would like to introduce the stable degeneration conjecture of Fano fibration germs (relative version), which can be viewed as a unification of the algebraic Hamilton-Tian conjecture of Fano varieties (global version) and the stable degeneration conjecture of klt singularities (local version). This is a joint work with Jiyuan Han, Minghao Miao, Lu Qi and Tong Zhang.
