We will hold a half-day workshop on number theory in Chuo University. 

Date: August 23 (Friday, afternoon), 2024.

Venue: Chuo University, Korauken Campus, Building 6, 11th floor, Room 61125B. (Access guide, Campus map)

Speakers :

• Keisuke Arai (Tokyo Denki University)

• Jia-Wei Guo (Soochow University)

• Yifan Yang (National Taiwan University)

Program: 

   August 23 (Friday) 

• 13:40 Opening

• 13:45--14:45 Jia-Wei Guo: Modular forms and class number relations

• 15:00--16:00 Keisuke Arai: Drinfeld-Stuhler curves and an infinite family of Hasse principle violations

• 16:30--17:30 Yifan Yang: Conformal metrics on the Riemann sphere and modular differential equations

• 17:35  Closing

Abstract:

• Keisuke Arai:  Drinfeld-Stuhler curves and an infinite family of Hasse principle violations

Jordan gave a sufficient condition for non-existence of quadratic points on a Shimura curve. The speaker extended this result to that on rational points over number fields of any degree. As an application, he obtained an explicit infinite family of Hasse principle violations when we fix a Shimura curve and vary number fields. In this talk we give its function field analogue, that is, an explicit infinite family of Hasse principle violations on a Drinfeld-Stuhler curve when we fix the curve and vary function fields. Note that such a family of Hasse principle violations is given over quadratic fields and quartic fields (resp. quadratic fields) in the case of number fields (resp. function fields). This talk is based on a joint work with Shin Hattori, Satoshi Kondo, and Mihran Papikian.

• Jia-Wei Guo:  Modular forms and class number relations

Many identities are known to hold between Hurwitz class numbers. In this talk, we will investigate extensions of  Eichler's famous relation between Hurwitz class numbers to certain sum of generalized Hurwitz class numbers, where the unary quadratic form is replaced with a binary quadratic form, by using (mock) modular forms.

• Yifan Yang:  Conformal metrics on the Riemann sphere and modular differential equations

Abstract: In this talk we consider the problem of existence of conformal metrics of constant curvature on the Riemann sphere with conic singularities of given angles at given points. In some cases we will see that this problem can be solved using modular forms. This talk is based on the joint works with Zhijie Chen, Jia-Wei Guo, and Chang-Shou Lin.

This workshop is supported by JSPS Kakenhi grant (21K03153).

Organizer : Takao Yamazaki (Chuo University)