Summary: Conference on Theories and Computations in Mathematical Physics and Topology
The Kunming Tianyuan Conference on Theories and Computations in Mathematical Physics and Topology took place at the Tianyuan Mathematics Research Center in Kunming from September 14 to September 20, 2025. Organized by Professors Yi Liu, Yongbin Ruan, and Zhouli Xu, the meeting brought together leading mathematicians from institutions such as Peking University, Tsinghua University, Fudan University, University of Science and Technology of China, Nankai University, Zhejiang University, Southern University of Science and Technology, Westlake University, Ningbo Eastern Institute of Technology, the University of Washington Seattle, and the Chinese Academy of Sciences.
The first day of the conference, September 15, was chaired by Professor Zhouli Xu (UCLA). In his opening remarks, he stressed the importance of bridging topology, geometry, and mathematical physics with computational approaches. The organizers also emphasized that a central aim of the meeting was to create new opportunities for collaboration across diverse areas of mathematics and to highlight the value of theoretical advances in addressing problems inspired by physics.
On the morning of September 15, Professor Yi Liu (Peking University) delivered a talk on Hempel pairs and Turaev–Viro invariants, examining whether quantum invariants can distinguish periodic surface bundles with profinitely isomorphic fundamental groups. Professor Honghao Gao (Tsinghua University) followed with Legendrian knots, Poisson variety and quantization, introducing a Poisson structure on the noncommutative dg algebra associated to Legendrian knots and explaining how it leads to a quantization framework. The session concluded with Professor Weiwei Wu (Zhejiang University), C^0-closedness of Symp₀(X), outlining a proof of the closedness of the identity component of the symplectomorphism group for log Calabi–Yau surfaces using J-holomorphic foliations and inflation techniques. The afternoon was devoted to group discussions.
On the morning of September 16, Professor Shicheng Wang (Peking University) spoke on Chirality of commensurability classes of geometric 3-manifolds, highlighting how commensurability and geometry shape orientation-reversing symmetries and their links to algebra and number theory. Professor Longting Wu (Southern University of Science and Technology) presented Poincaré polynomials of moduli spaces of 1-dimensional sheaves on the projective plane, featuring new Betti number computations via refined sheaves/Gromov–Witten correspondences and consequences for divisibility properties and leading terms. Professor Tianyu Yuan (Eastern Institute of Technology, Ningbo) then discussed Morse theory, Floer homology, and Hecke algebra, developing a Morse-type A∞ algebra on based loop spaces and relating it to wrapped Heegaard Floer structures. The afternoon featured group discussions.
On the morning of September 17, Professor Qiongling Li (Nankai University) presented Higgs bundles over non-compact surfaces, establishing existence and uniqueness results for harmonic metrics that extend the non-abelian Hodge correspondence beyond the compact case. Professor Xiaolei Wu (Fudan University) followed with Embedding groups into acyclic groups, describing constructions that embed groups of type Fₙ into acyclic groups of the same finiteness type and produce examples that are Fₙ but not Fₙ₊₁. The session finished with Professor Zhongzi Wang (Peking University), Cobordism between 3-manifolds with constraints on H₁, including obstructions to H₁-injective null-cobordism for certain lens spaces and positive results for low-rank first homology. The afternoon was reserved for group discussions.
On the morning of September 18, Professor Xiaolin Danny Shi (University of Washington, Seattle) delivered Periodicities of higher real K-theories, proving periodicity theorems at the prime 2 and explaining implications for equivariant computations and RO(G)-graded homotopy of Lubin–Tate theories. Professor Ruizhi Huang (Chinese Academy of Sciences) spoke on Algebraic topology of 24-dimensional string manifolds, surveying structural results and connections to index theory. Professor Jingbang Guo (Fudan University) concluded the morning with On the q-de Rham operators, outlining their role via prismatic cohomology and their links to topological cyclic homology and algebraic K-theory, with explicit complexes available in polynomial cases. The afternoon was devoted to group discussions.
On the morning of September 19, Professor Zhe Sun (University of Science and Technology of China) presented Exponential volumes of moduli spaces of hyperbolic surfaces, introducing a finite “exponential” volume form for moduli spaces with crown ends and deriving recursion relations that generalize Mirzakhani’s formulas. Professor Shuo Zhang (Chinese Academy of Sciences) followed with Composed Dehn twist exact sequence through A∞ n-modules, establishing long exact sequences relating Lagrangian Floer cohomology and fixed-point Floer cohomology via quilted Floer methods. The final talk was given by Professor Cheng Shu (Westlake University), The tame Deligne–Simpson problem, resolving the existence question for irreducible tuples with prescribed conjugacy classes by combining non-abelian Hodge theory with variations of stability conditions. The afternoon was dedicated to group discussions and closing remarks.
Over the course of the week, participants shared significant new advances, took part in lively discussions, and exchanged forward-looking ideas at the interface of mathematical physics and topology. The conference concluded with closing remarks from Professor Weiwei Wu (Zhejiang University), who warmly thanked all the speakers and attendees for their active participation and contributions. He noted that the interactions and insights developed during the meeting will provide a strong impetus for future research directions. Professor Wu also expressed his sincere gratitude to the Tianyuan Mathematics Research Center for its generous support in making the event possible.