Contact: 郭宁 （guon314 1@mail.ustc.edu.cn） 黄可平 （kphuang@hit.edu.cn）
刘春晖 （chunhui.liu@hit.edu.cn） 田乙胜 (tysmath@mail.ustc.edu.cn)
王珺 （junwangmath@hit.edu.cn ） 赵和耳 (heerzhao@hit.edu.cn)
Upcoming talks
Past talks
October 15, 2025.14:00--15:00（Beijing time）
Speaker: 杨南君（北京雁栖湖应用3354cc金沙集团）
Title: Witt group of nondyadic curves
Abstract
Witt group of real algebraic curves has been studied since Knebusch in 1970s. But few results are known if the base field is non-Archimedean except the hyperelliptic case by works of Parimala, Arason et al.. In this talk, we compute the Witt group of smooth proper curves over nondyadic local fields with $char ≠ 2$ by reduction, with a general study of the existence of Theta characteristics.
September 13, 2025, 14:00-16:00 （Beijing time）
Speaker: Yuchen Wu（UCSD）
Title: Deformation Theory via Higher Categories
Abstract
I will introduce some basic ideas from ∞-category theory, emphasizing how they can be used in practice. As an illustration, I will explain how the deformation problem for algebras can be formulated in this framework and how this leads to a concise proof of the “fundamental theorem of deformation theory,”which identifies the obstruction to certain deformations with Ext classes of the corresponding cotangent complex.
August 14, 2025.14:00–15:00（Beijing time）
Speaker: 田志宇（北京大学）
Title: Some simple remarks about Lawson homology
Abstract
Lawson homology is defined as the homotopy group of certain space of algebraic cycles. I will explain some recent advances in understanding the fundamental group of the space of one-cycles, which leads to a proof of a very special case of some conjectures about Lawson homology.
August 13,2025.15:00-16:00 （Beijing time）
Speaker: 谢恒（中山大学）
Title: Hermitian K-theory of Lagrangian Grassmannians via reducible Gorenstein models
Abstract
We construct a family of moduli spaces, called generalized Lagrangian flag schemes, that are reducible Gorenstein (hence singular), and that admit well-behaved pushforward and pullback operations in Hermitian K-theory. These schemes arise naturally in our computations. Using them, we prove that the Hermitian K-theory of a Lagrangian Grassmannian over a regular base splits as a direct sum of copies of the base's (Hermitian) K-theory, indexed by certain shifted Young diagrams. The isomorphism is realized via pullback to each generalized Lagrangian flag scheme followed by pushforward to the Lagrangian Grassmannian. This yields an unusual example in which both the base and the target are regular schemes, while the intermediate reducible Gorenstein models remain sufficient to allow explicit computations in Hermitian K-theory of regular schemes. This is joint work with Tao Huang.
June 16, 2025.14:30-16:00 （Beijing time）
Speaker: Shang Li (YMSC, Tsinghua University)
Title: Wonderful Embedding for group schemes in Bruhat–Tits theory
Abstract
For a reductive group G over a discretely valued Henselian field k, using valuations of root datum and concave functions, the Bruhat–Tits theory defines an important class of open bounded subgroups of G(k) which are essential objects in representation theory and arithmetic geometry. Moreover, these subgroups are uniquely determined by smooth affine group schemes whose generic fibers are G over the ring of integers of k. To study these group schemes, in this talk, when G is adjoint and quasi-split, we systematically construct wonderful embedding for these group schemes which are uniquely determined by a big cell structure. The way that we construct our wonderful embedding is different from classical methods in the sense that we avoid embedding a group scheme into an ambient space and taking closure. We use an intrinsic and functorial method which is a variant of Artin–Weil method of birational group laws. Beyond the quasi-split case, our wonderful embedding is constructed by étale descent. Moreover our wonderful embedding behaves in a similar way to the classical wonderful compactification of G. Our results can serve as a bridge between the theory of wonderful compactifications and the Bruhat–Tits theory.
April 11, 2025.09:30-10:30 am （Beijing time）
Speaker: 周海港（同济大学）
Title: Explicit computation of Fourier coefficients of Siegel Eisenstein series of degree two
Abstract
In this talk, for Siegel modular forms of degree two weight two, we construct a basis of its subspace of Siegel Eisenstein series of square-free level N, and compute their Fourier coefficients explicitly. In addition, we connect the theta series from Yoshida lifting associated to Eichler orders with Siegel Eisenstein series.
October 26th, 10:00-12:00 am （Beijing time）
Speaker: 李烨暄 (中北大学)
Title: The relative Auslander-Reiten theory over an infinite-dimensional coalgebra
Abstract
In this talk, we will cover several aspects: Firstly, we will delve into the higher-dimensional Auslander-Reiten theory over an infinite-dimensional coalgebra; the finite-dimensional case by duality reduces to that of finite-dimensional algebra. We will introduce the n-transpose of a finitely n-copresented comodule and n-Auslander-Reiten translations, and then prove the n-Auslander-Reiten formula on n-cluster-tilting subcategories of comodule categories. Secondly, we will introduce the Gorenstein transpose via a minimal Gorenstein injective copresentation of a quasi-finite comodule, and explore the relations between the Gorenstein transpose of comodules and the transpose of the same comodule. As an application, we will construct the almost split sequences in terms of Gorenstein transpose. Finally, we will generalize the notion of the Auslander transpose of comodules to that of the transpose with respect to a semidualizing bicomodule T and showcase some nice homological properties of T-transpose. Additionally, we will provide a Foxby equivalence of comodule categories and investigate a characterization of T-reflexive comodules. This work is joint with Prof. Hailou Yao.
October 24th, 21:00-22:00 pm （Beijing time）
Speaker: Oussama Hamza（Western University）
Title: Special quotients of Absolute Galois Groups with applications in Number Theory and Pythagorean fields
Abstract
This talk aims to present the results obtained by Oussama Hamza, during his PhD studies, and his collaborators: Christian Maire, Jan Minac and Nguyen Duy Tan.
Their work precisely focuses on realisation of pro-p Galois groups over some fields with specific properties for a fixed prime p: especially filtrations and cohomology. Hamza was particularly interested on Number and Pythagorean fields.
This talk will mostly deal with the latest results obtained by Hamza and his collaborators on Formally real Pythagorean fields of finite type (RPF). For this purpose, they introduced a class of pro-2 groups, which is called $\Delta$-RAAGs, and studied some of their filtrations. Using previous work of Minac and Spira, Hamza and his collaborators showed that every pro-2 Absolute Galois group of a RPF is $\Delta$-RAAG. Conversely if a group is $\Delta$-RAAG and a pro-2 Absolute Galois group, then the underlying field is necessarily RPF. This gives us a new criterion to detect Absolute Galois groups.
Finally, the work of Hamza and his collaborators also proved that pro-2 Absolute Galois groups of RPF satisfy the Kernel unipotent conjecture; jointly introduced by Minac and Tan with the Massey vanishing conjecture, which attracted a lot of interest.
October 9th, 14:30-16:00 pm （Beijing time）
Speaker: 阳煜 (京都大学数理解析研究所)
Title: Fundamental groups of curves and local moduli
Abstract
In 1996, A. Tamagawa discovered a surprising phenomenon: anabelian geometry also exists for curves over algebraically closed fields of characteristic p>0 (i.e., curves in positive characteristic can possibly be determined by their geometric fundamental groups without relying on Galois actions). However, after 28 years, only a few results have emerged in this field. In this talk, I want to explain the following insight of the speaker about fundamental groups of curves in positive characteristic:
The (admissible or geometric log etale) fundamental groups of pointed stable curves over algebraically closed fields of characteristic p can be regarded as an analogue of local moduli spaces of the curves.
This observation led to the speaker discovering some new kinds of anabelian phenomena of curves in characteristic p and to formulated numerious new conjectures. For example, the following highly non-trivial anbelian results of the speaker provide strong evidence supporting this insight:
• The homeomorphism conjecture holds for 1-dimensional moduli spaces (roughly speaking, this conjecture means that the moduli spaces of curves can be reconstructed group-theoretically as topological spaces).
• A new proof of Mochizuki’s famous result concerning (Isom-version) Grothendieck’s anabelian conjecture for curves over sub-p-adic fields without using Faltings’ p-adic Hodge theory.
• The group-theoretical specialization conjecture holds (roughly speaking, this conjecture means that the topological and group-theoretical degeneration of curves can be completely determined by open continuous homomorphisms of dmissible fundamental groups).
October 10th, 10:30-12:00 am （Beijing time）
Speaker: 陈升 (长春理工大学)
Title: Arithmetic purity of strong approximation for complete toric varieties
Abstract
In this talk, I will discuss arithmetic purity of strong approximation: motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.
September 12th, 14:30-16:30 pm （Beijing time）
Speaker: 张旭成(清华大学丘成桐数学中心)
Title: A stacky approach to identifying the stability condition
Abstract
For any reductive group we find a stacky interpretation of the stability condition for principal bundles over a curve: it is the unique maximal open locus that admits a schematic moduli space. Some applications and further progress will be discussed. This is a joint work with Dario Weissmann and Andres Fernandez Herrero.
August 7th, 16:45-17:45 pm （Beijing time）
Speaker: 吕昌(中国科学院)
Title: Brauer-Manin obstruction of finite product of some algebraic stacks
Abstract
I shall start from a classical result on Brauer-Manin obstruction of a product of two varieties, by introducing Yang Cao's formulas of Kunneth type. Then we will generalize it to a class of algebraic stacks.
