Professor at Department of Mathematics, Capital Normal University (首都师范大学数学系).
105 Xisanhuan Beilu, Haidian District, Beijing 100048, P. R. China.（北京市海淀区西三环北路105号，100048）
E-mail: sunsz AT cnu.edu.cn
I graduated from Chern Institute of Mathematics, Nankai University, Tianjin and got my PhD degree in 2001.
I spent two years from 2001 to 2003 at School of Mathematical Sciences, Peking University as postdoc.
Then I joined Capital Normal University in 2003 as a faculty member of Department of Mathematics.
Here is my CV (to be added).
My research interests lie at the crossroads of mathematics and physics, and I work on such topics as N-body problem in celestial mechanics, Fukaya category in symplectic topology, semiclassical trace formula and resurgence theory.
More precisely, I am interested in
Symplectic Geometry and Symplectic Topology: symplectic reduction; Floer homologies and Fukaya categories; quiver varieties; cluster varieties; singularities from symplectic perspective
Hamiltonian Systems and Celestial Mechanics: Maslov index; N-body problem (stability; central configurations; periodic orbits); Gutzwiller’s semiclassical trace formula; (algebraic) completely integrable Hamiltonian systems (ACIS) and their interactions with geometry and physics
Mathematical Physics: higher structures (homotopical algebras, higher categories,…) behind quantum mechanics and quantum field theory; quantization (semiclassical, deformation quantization, BV, brane quantization…); modularity; gauge theory; Feynman diagrams
Resurgence Theory and Mould Calculus à la Écalle with applications in mathematics (BCH, MZV, modularity…) and quantum physics (wall-crossing, Écalle-Voros exact WKB analysis, complex Chern-Simons theory, topological string theory…)
Spring 2025
Calculus IV (Gamma, differential forms and Stokes theorem, Fourier)
Topics on Riemann Surfaces (modular)
Working seminar: Resurgence theory applied to gauge theory and topological string theory
Reading seminar: Les fonctions resurgentes, Ecalle (Tome I)
天体力学数学理论研讨会（系列，2019年始）
科普报告（2017年始）
讨论班报告
题目：Automorphisms of the Boutet de Monvel algebra
摘要：In a remarkable work, Duistermaat and Singer in 1976 studied the algebras of all classical pseudodifferential operators on smooth (boundaryless) manifolds. They gave a description of order preserving algebra isomorphism between the algebras of classical pseudodifferential operators of two manifolds. The subject of this talk is the generalisation of their results to manifolds with boundary. The role of the algebra of pseudodifferential operators that we are interested in is the Boutet de Monvel algebra. The main fact of life about manifold with boundary is that vector fields do not define global flows and the “boundary conditions” are a way of dealing with this problem. The Boutet de Monvel algebra corresponds to the choice of local boundary conditions and is, effectively, a non-commutative completion of the manifold. One can think of it as a parametrised version of the classical Toeplitz algebra as a completion of the half-space. What appears in the study of automorphisms are Fourier integraloperators and we will try to explain their appearance - both in boundaryless and boundary case. as it turns out, the non-trivial boundary case introduces both some complications but also some simplifications of the analysis involved, Once this is done, the analysis that we need reduces to a high degree to relatively classical results about automorphisms and homology of the Toeplitz algebra and some basic facts from K-theory. This is a joint work in progress with Elmar Schrohe.
报告人：Ryszard NEST教授（哥本哈根大学）
时地：2024年12月13日（周五）上午10:00-11:00，首都师范大学本部新教二楼608教室