AG Seminar Spring 2017
Student No.:50
Time:Thursday 15:00-16:00, 2017-3-2~2017-7-16
Instructor:Eduard Looijenga, Dun Liang, Quan Xu  
Place:Lecture Hall, Floor 3, Jin Chun Yuan West Building
Starting Date:2017-3-2
Ending Date:2017-7-16



Date: 2017-06-01



Time: Thursday, 15:00-16:00



Place: Lecture Hall, Floor 3, JingChunYuan West Building



Speaker: Weizhe Zheng (Morningside Center of Mathematics, CAS)



Title:Nearby cycles over general bases



Astract: Nearby cycles and vanishing cycles in étale cohomology were introduced by Grothendieck in the cohomological study of singular families. Deligne extended these notions to bases of higher dimension. I will review this theory and discuss some recent results.





Time: Thursday, 15:00-16:00


Place: Lecture Hall, Floor 3,JinChunYuan West Buildin


Speaker: Jilong Tong, Capital Normal University & University of Bordeaux 1

Title: A glimpse of anabelian geometry

Abstract: After a quick review of the definition of algebraic fundamental groups, we shall survey certain aspects of the anabelian geometry introduced by Grothendieck, including some important progress made by Tamagawa and Mochizuki. If time allows, we will explain a new (but still vague) idea in my joint project with Mao SHENG aiming at a better understanding of anabelian geometry in positive characteristic.











Time: Thursday, 15:00-16:00


Place: Lecture Hall, Floor 3, JinChunYuan West Building


Speaker: Minxian Zhu, YMSC, Tsinghua University


Title: Periods and hypergeometric equations


Abstract: We will investigate the periods of Calabi-Yau hypersurfaces in toric varieties. It turns out that they satisfy a system of differential equations, known as the Gelfand-Kapranov-Zelevinsky (GKZ) hypergeometric equations. We will review some basic properties about these equations and discuss a conjecture by Hosono-Lian-Yau (HLY) describing the precise relation between periods and solutions to the GKZ system. This talk is intended as a survey of HLY's work in the mid 90s.




Time: Thursday, 15:00-16:00

Place: Lecture Hall, Floor 3, JinChunYuan West Building

Speaker:Jin Cao, YMSC, Tsinghua University

Title: Construct Elliptic Motives by Cycle Algebras

Abstract: In this talk, we recall the theory of cdgas over a reductive group. As one application, we show that how to use this theory to reconstruct motives of an elliptic curve without CM in the sense of Voevodsky.



Time: Thursday, 15:00-16:00

Place:Conference room 4, Floor 2,JinChunYuan West Building

Speaker: Eduard Looijenga (YMSC)

Title: Some Algebraic Geometry related to the mapping class group

Abstract: Since this talk is aimed at algebraic geometers, we begin with reviewing some basic constructions of Teichmueller theory. We then explain how Hodge theory helps us to understand certain representations of the mapping class group. But this talk is more about open problems than about definitive results.


Date: 2017-03-16

Time: Thursday, 15:00-16:00

Place: Conference Room 4, 2nd Floor, JinChunYuan West Building

Speaker: Chao Zhang, YMSC Tsinghua University

Title: Truncated displays with additional structure and reductions of Shimura varieties

Abstract: The theory of displays, invented by D.Mumford and later developped by P.Norman, T.Zink, and E.Lau, is a Dieudonne theory dealing with p-divisible groups. Truncated displays are introduced by Lau recently to study truncated p-divisible groups, i.e. BT-ms. In this talk, I will explain what are truncated displays, and how to put additional structure on them. Then I will show how to use them to define and study level m tratifications on reductions of Shimura varieties.

Date: 2017-03-09

Time: Thursday, 15:00-16:00

Place: Conference Room 4, 2nd Floor, JinChunYuan West Building

Speaker: Prof. Dasheng Wei, AMSS CAS

Title: Strong approximation for certain norm varieties.
Abstract: In this talk, we will introduce some norm varieties which satisfy weak approximation or strong approximation.These norm varieties are a generalization of universal torsors of Chatelet surfaces. Some applications were also given for rational points and integral points by the descent theory.


Date: 2017-03-02

Time: Thursday, 15:00-16:00

Place: Conference Room 4, 2nd Floor, JinChunYuan West Building

Speaker: Thomas Koberda, University of Virginia US

Title: Quotients of surface groups via TQFT

Abstract: I will show how to construct linear quotients of surface groups which are infinite, and where each simple loop has finite order. As an application, I will construct finite covers of surfaces where the pullbacks of simple loops fail to generate the integral homology. We thus answer questions due to Looijenga. This represents joint work with R. Santharoubane.

Ps: The talk is also very relate to the toplogy, so you are welcome if you are interesting in topology.\