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
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.
Past talks
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.