Seminar on Arithmetic Geometry and Algebraic Groups
This seminar is focusing on various research topics in arithmetic geometry with special regard to algebraic groups, homogeneous spaces and related structures or problems.
Normally, one or two online talks are expected to be scheduled per month. The date and time of each talk will be flexibly arranged according to the speaker’s convenience.
The online talks are usually run via Zoom Meeting or sometimes Voov Meeting (or equivalently, Tencent meeting in China mainland). Please read the instructions on downloading and using Voov here.
If you want to receive annoucements of the seminar talks, please email one of the organizers.
Organizers
CAO Yang (Shandong Univ., Jinan); yang###1988@email.sdu.edu.cn ###=Yang’s family name
HU Yong (Southern Univ. Sci. Tech., Shenzhen) ; ###@sustech.edu.cn ###=first 3 letters of “huyong”
HUANG Zhizhong (Chinese Acad. Sci., Beijing) ; zhizhong.#####@yahoo.com #####=Zhizhong’s family name
LEE Ting-Yu (Taiwan Univ., Taiwan); tingyu###@ntu.edu.tw ###=Tingyu’s family name
TIAN Yisheng (Harbin Institute Tech., Harbin); tys####@mail.ustc.edu.cn ####=first 4 letters of “mathematics”
XU Fei (Capital Normal Univ., Beijing); xuf##@math.ac.cn ##=last 2 letters of “fei”
Past sessions: 2022 Session 2023 Session 2024 Session
2025 Spring Session
The next talk on Monday, June 9, 2025, 16:00--17:00 (Beijing Time).
Date: 20.06.2025 (dd.mm.yyyy) Time:
or
Date: 20.06.2024 (dd.mm.yyyy) Time:
Zoom Meeting ID: available upon request
Speaker: Lois Faisant
Title: TBA
Abstract: TBA
Ref:
Date: 13.06.2025 (dd.mm.yyyy) Time: 16:00–17:00 (Beijing Time)
or
Date: 13.06.2024 (dd.mm.yyyy) Time: 10:00–11:00 (Central European Summer Time)
Zoom Meeting ID: available upon request
Speaker: Ratko Darda (Sabanci University)
Title: Around Manin’s conjecture for stacks
Abstract: A fundamental question in Diophantine geometry is to understand the distribution of solutions to polynomial equations over the rational numbers. A prominent example of such a question is Manin’s conjecture, which predicts the number of rational points of bounded height on certain algebraic varieties. Specifically, the number of rational points of height at most B is expected to be asymptotic to CB^a log(B)^b, for certain constants C,a,b. Very similar formulas arise in other counting problems, such as in counting of elliptic curves of bounded naive height or in Malle’s conjecture, which concerns the number of Galois extensions of Q with bounded discriminant.
In this talk, we discuss a generalization of Manin’s conjecture to stacks, which unifies and extends the Manin’s and Malle’s conjecture. We will also address the wild case—when the orders of automorphism groups of points of stacks are divisible by the characteristics of the global field over which the stack is defined. This talk is based on joint works with Takehiko Yasuda.
Ref:
R. Darda and T. Yasuda, The Batyrev-Manin conjecture for DM stacks II
R. Darda and T. Yasuda, The Manin conjecture for toric stacks
R. Darda and T. Yasuda, The Batyrev-Manin conjecture for DM stacks
Date: 09.06.2025 (dd.mm.yyyy) Time: 16:00–17:00 (Beijing Time)
or
Date: 09.06.2024 (dd.mm.yyyy) Time: 10:00–11:00 (Central European Summer Time) ; 11:00–12:00 (Israel Time)
Zoom Meeting ID: available upon request
Speaker: Boris Kunyavskii (Bar-Ilan University)
Title: Birational properties of word varieties
Abstract: We prove that the subvariety of SL(2)xSL(2) given by the matrix equation w(X,Y)=g, where w is a word in two letters, is closely related to an explicit smooth conic bundle over the associated `trace surface’ in the 3-dimensional affine space. When w is the commutator word, we show that this variety can be irrational if the ground field k is not algebraically closed, answering a question of Rapinchuk, Benyash-Krivetz, and Chernousov. When k is a number field, it satisfies weak approximation with the Brauer–Manin obstruction.
The talk is based on our joint work with Tatiana Bandman and Alexei Skorobogatov.
Ref:
T. Bandman, B. Kunyavskii and A. Skorobogatov, Birational properties of word varieties
Date: 28.04.2025 (dd.mm.yyyy) Time: 16:30–17:30 (Beijing Time)
or
Date: 28.04.2024 (dd.mm.yyyy) Time: 10:30–11:30 (Central European Summer Time)
Zoom Meeting ID: available upon request
Speaker: Tim Santens (University of Cambridge)
Title: Leading constant in Malle’s conjecture
Abstract: *Let G be a finite permutation group, Malle has put forward a conjecture on the number of G-extensions of a number field of bounded discriminant. In this talk I will discuss recent efforts to interpret Malle’s conjecture as a form of Manin’s conjecture on rational points of bounded height for the stack BG. Based on this analogy me and Loughran have given a conjectural interpretation of the leading constant in Malle’s conjecture. *
Ref:
D. Loughran and T. Santens, Malle’s conjecture and Brauer groups of stacks