Report Title：Local Index Theory: From the Index to Analytic Torsion and Eta Invariants
Reporter：Xiaonan Ma
Affiliation: Chern Institute of Mathematics, Nankai University
Report Time: September 14, 2026, 16:00–17:00
Report Location: Room 209, Zhengxin Building
Abstract:
For an elliptic operator, one can define its index and determinant. If the operator is self-adjoint, its eta invariant is an infinite-dimensional analogue of the signature of a self-adjoint matrix. These quantities are all defined in terms of the operator’s eigenvalues. We will introduce their applications in geometry, topology, and number theory. Heat kernel methods play a central role, providing, in particular, a bridge between local and global phenomena.
Bio:
Xiaonan Ma is a Chair Professor at Nankai University and Director of the Chern Institute of Mathematics. He has been an invited speaker at the International Congress of Mathematicians (ICM) and is the principal investigator of an Innovative Research Group project funded by the National Natural Science Foundation of China. His research focuses on differential geometry, complex geometry, and topology, with particular emphasis on index theory and global analysis on manifolds.
Using ideas and techniques from analytic localization, Ma and Weiping Zhang proved the geometric quantization conjecture for noncompact spaces proposed by Vergne, a member of the French Academy of Sciences, in her plenary address at the 2006 ICM. His international honors include Spain’s Ferran Sunyer i Balaguer Prize (2006), the French Academy of Sciences’ Sophie Germain Grand Prize (2017), and Germany’s Gay-Lussac–Humboldt Award (2022).
He also serves as Secretary-General of the Education Committees for the Sino-French Mathematics Programs at the University of Science and Technology of China and Wuhan University, overseeing all matters involving the French partners.
