BIMSA >
BIMSA AG Seminar
BIMSA AG Seminar
Dual boundary complexes of character varieties and the geometric P=W conjecture
Dual boundary complexes of character varieties and the geometric P=W conjecture
演讲者
时间
2024年02月22日 15:00 至 16:00
地点
A6-101
线上
Zoom 638 227 8222
(BIMSA)
摘要
Aiming at a geometric interpretation of the famous P=W conjecture (now theorem) in nonabelian Hodge theory (NAH), the geometric P=W conjecture of Katzarkov-Noll-Pandit-Simpson predicts that NAH identifies the Hitchin fibration at infinity with another fibration intrinsic to the Betti moduli space M_B, up to homotopy. Its weak form states that: the dual boundary complex of M_B (of complex dimension d) is homotopy equivalent to a sphere of dimension d-1 (the Hitchin base at infinity). In this talk, I will explain a proof of the weak geometric P=W conjecture for all very generic GL_n(C)-character varieties M_B over any (punctured) Riemann surface. The proof involves two main ingredients: 1. improve A. Mellit's cell decomposition into a strong form: M_B itself is decomposed into locally closed subvarieties of the form $(\mathbb{C}^*)^{d-2b} \times A$, where $A$ is stably isomorphic to $\mathbb{C}^b$; 2. A motivic argument proving that the dual boundary complex of a stably affine space is contractible.
演讲者介绍
Tao Su obtained his Ph.D. degree from UC Berkeley in 2018. He joined BIMSA in 2024. His current research interests include interactions between algebraic analysis, algebraic geometry and symplectic geometry.