Topology of abelian fibrations

报告人

Speaker

Qizheng Yin 訚琪峥

Beijing International Center for Mathematical Research

时间

Time

15:00-16:30, Thursday & Friday

April 9 /10 / 23, 2026

地点

Venue

B541, Shuangqing Complex Building A

Abstract

Topology of abelian fibrations

We present in this lecture series some recent progress in understanding the topology of abelian fibrations. We first introduce the “perverse filtration” which encodes key cohomological information of the fibrations. Then we explain how various structures (such as Fourier-Mukai transforms, intersection theory, BBDG decomposition theorem, and Ngô support theorem) can be combined to give a new characterization of the perverse filtration for certain abelian fibrations. Applications include the P=W conjecture, the motivic decomposition conjecture for the Hitchin fibration, and the construction of an intrinsic cohomology ring of the universal compactified Jacobian. Finally we specialize to Lagrangian fibrations and survey a few known results and open questions in this direction. Based on joint work with Davesh Maulik, Junliang Shen, and others.

About the Speaker

訚琪峥，北京国际数学研究中心副教授，主要研究领域为代数几何。他于2013年博士毕业于法国巴黎第六大学和荷兰奈梅亨大学数学系，后在瑞士苏黎世联邦理工学院从事博士后研究。2017年，他获得由Compositio Mathematica基金会颁发的首届“代数几何奖”（Algebraic Geometry Prize）。2025年，他与合作者撰写的论文“Perverse filtrations and Fourier transforms”发表于国际顶尖数学期刊《Acta Mathematica》。