Organizers (alphabetical order):

Baiting Xie xbt23"at"mails.tsinghua.edu.cn
Zhiwei Zheng zhengzw11"at"163.com
Jie Zhou jzhou2018"at"mail.tsinghua.edu.cn

All seminars will be held in B541, Shuangqing Complex Building on Wednesday at 10:00-12:00, unless marked in red.

Date Speaker Title Abstract Files
2026-03-11 Baiting Xie Topology and Combinatorics of Complex Hyperplane Arrangement Complements In this talk, I will introduce which topological invariants of hyperplane arrangement complements are combinatorially determined. I will briefly sketch the proof of the classical result by Orlik and Solomon on the integral cohomology, and present some conjectures and recent progress on cohomology with local coefficients.
2026-03-18 Jie Fu Smooth Hypersurface with Automorphism Group of Large Order This talk will discuss Yang-Yu-Zhu and Esser-Li’s independent work determining the smooth hypersurface with automorphism group with given dimension and degree. I will also introduce a few classical results on finite subgroups of the general linear group and the theory of regular addictive decomposition, which provides a little simplification for some steps in these works. Some further problems will be discussed ed as well.
2026-03-25 Ningzhai 217 Shihao Wang Irrationality of ζ(3) and a K3 Family In this talk, I will sketch Apéry’s proof of the irrationality of ζ(3) and explain the connection between Apéry numbers and the periods of a K3 family, discovered by Beukers and Peters. I will then present several similar phenomena that relate periods of algebraic families to special functions. Finally, I will conclude with some open problems in this topic.
2026-04-01 Zhirui Li Existence of Bridgeland Stability Condition for Complex Projective Varieties This talk outlines the recent breakthrough proving the existence of Bridgeland stability conditions on the bounded derived category $D^b(X)$ for any projective variety $X$ over $\mathbb{C}$. We will trace the core proof strategy: starting from products of elliptic curves, descending to projective spaces, and finally restrict to arbitrary projective subvarieties. This provides a complete, step-by-step solution to a major open problem in derived category.
2026-04-08 Yi Li A Monstrous Proposal In this talk, I will outline Allcock's conjecture and present the recent progress made by Allcock and Basak in 2023. The conjecture states that the orbifold fundamental group of a hyperbolic ball quotient is isomorphic to the bimonster after quotienting out the squares of certain generators. I will explain the connection between the Deligne–Mostow ball and the ball quotient arising in the conjecture. In addition, I will discuss some other results related to ball quotients.
2026-04-15 Zhirui Li Construction of Anti-symplectic Involutions by Categorical Method: from Moduli Spaces of Sheaves on K3 Surfaces to Cubic 4-Folds This talk explores explicit constructions of anti-symplectic birational involutions on moduli spaces of stable sheaves, denoted $M(v)$, on K3 surfaces and (anti)-symplectic involutions on cubic 4 folds. Traditionally, constructing these symmetries geometrically has been a challenging problem. But by using derived categories to construct, we will see how this construction not only unifies classical examples—such as the Beauville, Markman-O'Grady, and Beri-Manivel involutions —but also generates new involutions via rank-2 spherical bundles and can be extended to investigate (anti)-symplectic involutions on cubic 4 folds.
2026-04-22 Yujie Lin Symplectic Ball Packings: Rigidity, Flexibility, and Beyond An interesting question in symplectic topology concerns the existence of a full packing of N equal-sized symplectic balls in the unit symplectic ball. Surprisingly, this question is deeply connected to the Nagata conjecture on plane algebraic curves. In this talk, we will explore the resolution of the symplectic ball packing problem in dimension 4 by McDuff-Polterovich and Biran, which relies on the Lalonde-McDuff inflation technique and Taubes-Seiberg-Witten theory. The result depends on N and reflects the profound dichotomy between rigidity and flexibility in symplectic topology. Beyond that, we will also survey recent remarkable developments and highlight intriguing open problems in the broader study of symplectic embeddings.
2026-04-29 Shihao Wang Arithmeticity of Monodromy Representations of Braid Groups Venkataramana studies families of cyclic covers of the projective line branched over n+1 points. The monodromy representations of the braid group on the homology of the fiber yield the Burau and Gassner representations. By constructing enough unipotent elements in these representations, it is shown that the images are arithmetic subgroups of the corresponding unitary groups.
2026-05-20 Yizhou Li Mixed Hodge theory for unitary local systems In his work Theorie de Hodge (I, II, III), Deligne defined a mixed Hodge structure on the cohomologies of any quasi-projective smooth algebraic variety over \mathbb{C}, generalizing the Hodge structures on the cohomologies of projective smooth algebraic varieties over \mathbb{C} (which can be regarded as compact Kahler manifolds). In this talk, we consider a slight generalization of this construction, given by Timmerscheidt, by replacing cohomologies of constant sheaves to cohomologies of a unitary local system.
2026-05-27 Shuangqing Complex Building B627 ZiMing Zhao AI4Math: Landscape, Breakthroughs, and Future Directions This talk provides a high-level overview of the AI4Math landscape. We will survey several key research directions, including automated theorem proving, autoformalization, formal mathematics with proof assistants (e.g., Lean), semantic evaluation of mathematical reasoning, and math-oriented language agents. The talk aims to outline the core methodological paradigms, major benchmarks, and open challenges at the intersection of artificial intelligence and mathematics, offering a structured roadmap for researchers new to the field.
2026-06-03 Baiting Xie Torelli Problems for Hypersurfaces In this talk I will explain how the Hodge structure of a smooth hypersurface in projective space is described by its Jacobian ring. This directly leads to the infinitesimal Torelli theorem for smooth hypersurfaces. Following this line, I will sketch Donagi's proof of the generic Torelli theorem for hypersurfaces.