Number Theory Seminar at MCM----Morningside Center of Mathematics Chinese Academy of Sciences

Number Theory Seminar at MCM

2023-10-11 10:30-11:30am

This is a weekly seminar focus on the research on number theory and arithmetic algebraic geometry. It usually takes place 10:30-11:30am each Tuesday or Wednesday at MCM 110.

If you have any questions, please contact with Prof. Yichao Tian (yichaot@math.ac.cn).

Speaker: Prof. Bin Xu (Tsinghua University)

Time: 10:30-11:30am, October 11, 2023 (Wednesday)

Place: MCM110

Title: TBA

Abstract: TBA

Speaker: Prof. Thomas J. Haines (University of Maryland)

Time: 10:30-11:30am, October 17, 2023 (Tuesday)

Place: MCM110

Title: TBA

Abstract: TBA

Speaker: Prof. Huayi Chen (Westlake University)

Time: 10:30-11:30am, October 18, 2023 (Wednesday)

Place: MCM110

Title: TBA

Abstract: TBA

Speaker: Prof. Haining Wang (Fudan University)

Time: 10:30-11:30am, October 25, 2023 (Wednesday)

Place: MCM110

Title: TBA

Abstract: TBA

Speaker: Prof. Chia-Fu Yu (Institute of Mathematics, Academia Sinica of Taiwan)

Time: 10:30-11:30am, November 1, 2023 (Wednesday)

Place: MCM110

Title: On the supersingular locus of Shimura varieties for quaternionic unitary groups

Abstract: We study a Shimura variety attached to a unitary similitude group of a skew-Hermitian form over a totally indefinite quaternion algebra over a totally real number field. We give a necessary and sufficient condition for the existence of skew-Hermitian self-dual lattices, and show that the superspecial locus in the fiber at p of the associated Shimura variety is non-empty. We also give an explicit formula for the number of irreducible components of the supersingular locus when p is odd and unramified in the quaternion algebra. This talk is the joint work with Yasuhiro Terakado and Jiangwei Xue.

Speaker: Prof. Mao Sheng (University of Science and Technology of China)

Time: 10:30-11:30am, November 8, 2023 (Wednesday)

Place: MCM110

Title: TBA

Abstract: TBA

Speaker: Prof. Enlin Yang (Peking University)

Time: 10:30-11:30am, November 15, 2023 (Wednesday)

Place: MCM110

Title: TBA

Abstract: TBA

Speaker: Prof. Yongqi Liang (University of Science and Technology of China)

Time: 10:30-11:30am, September 20, 2023 (Wednesday)

Place: MCM110

Title: 奇亏格超椭圆曲线的局部整体原则

Abstract: Scharaschkin和Skorobogatov等人猜测Brauer-Manin障碍是定义在数域上的射影光滑曲线上的有理点不满足局部整体原则的唯一障碍。对于任意数域和任意给定奇自然数g，我们具体构造出无穷条亏格为g的由Brauer-Manin障碍解释的局部整体原则失效的曲线。我们的结论为上述猜想给出了具体的例证。这是我指导的博士生黄凯最近的工作。

Speaker: Prof. Meng Fai Lim (Central China Normal University)

Time: 10:30-11:30am, September 26, 2023 (Tuesday)

Place: MCM110

Title: On fine Selmer groups

Abstract: The fine Selmer group has been a much studied object in Iwasawa theory. One of its original roles was to provide a means of formulating (and proving) the main conjecture. On the other hand, the work of Coates and Sujatha initated a systematic study on this group on its own right. My talk will focus on this latter aspect. I shall begin with giving a brief survey on the work of Coates-Sujatha. After that, I will then report some of my work on the following two themes.

(1) A torsioness conjecture on the fine Selmer group over an arbitrary Zp-extension.

(2) A question of Greenberg concerning an explicit description of the structure of the fine Selmer group over the cyclotomic Zp-extension of Q and formulation of its variants.