seminars

$$heading_1$$ Singular moduli for real quadratic fields III

Date Apr 26, 2021 Jan Vonk Leiden University 선택 15:30-16:30

※ Zoom Meeting ID : 817 7139 5843
Passcode : 165930

Singular moduli are special values of the j-function at imaginary quadratic arguments. They play a central role in CM theory and have close connections with the class field theory of imaginary quadratic fields. With the advent of the work of Gross and Zagier, investigations of the prime factorisation of differences of singular moduli have led to a renaissance of the subject, and paved the way for their celebrated work on Heegner points on elliptic curves.

In this series of talks, we will explore what happens when we replace the imaginary quadratic fields in CM theory with real quadratic fields, and propose a framework for a conjectural 'RM theory', based on the notion of rigid meromorphic cocycles, introduced in joint work with Henri Darmon. We will start with a discussion of classical CM theory and the work of Gross and Zagier, particularly the analytic arguments based on the diagonal restrictions of a family of Eisenstein series studied by Hecke in the early 20th century. We will then discuss the theory of RM singular moduli, as well as the extent to which arguments based on analytic families of modular forms can be fruitful. In particular, I will discuss recent progress obtained in various joint works with Henri Darmon and Alice Pozzi.

Subject
Feb 02, 2021  14:00-15:30  Auslander-Reiten transformation and tau-tilting theory Sota Asai  선택
Feb 03, 2021  14:00-15:30  Auslander-Reiten transformation and tau-tilting theory Sota Asai  선택
Feb 04, 2021  14:00-15:30  Auslander-Reiten transformation and tau-tilting theory Sota Asai  선택
Feb 05, 2021  14:00-15:30  Auslander-Reiten transformation and tau-tilting theory Sota Asai  선택
Feb 09, 2021  15:30-16:30  Data-Driven Methods for Artist-Directed Fluid Simulations Byungsoo Kim  선택
Feb 09, 2021  11:00-12:00  Note on Solving FBSDE using BSDE 남기훈  선택
Feb 25, 2021  14:30-17:00  Zeta함수와 L함수에 대한 역사적 고찰Ⅸ 신석우  선택
Mar 03, 2021  14:30-16:45  Zeta함수와 L함수에 대한 역사적 고찰 Ⅹ 신석우  선택
Mar 08, 2021  16:30-17:30  On class groups of random number fields Alex Bartel  선택
Mar 15, 2021  16:30-17:30  On class groups of random number fields Alex Bartel  선택
Mar 22, 2021  16:30-17:30  On class groups of random number fields Alex Bartel  선택
Mar 16, 2021  11:00-12:00  Transfer operators and limit laws for typical cocycles Kiho Park  선택
Apr 02, 2021  10:30-12:00  Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types. 오세진  선택
Apr 02, 2021  15:30-16:30  CM congruence and the derivatives of p-adic L-functions for imaginary quadratic fields Ming-Lun Hsieh  선택
Apr 06, 2021  16:00-17:00  Hamiltonian structure, Stability, and Variational methods 석진명  선택
Apr 12, 2021  15:30-16:30  Singular moduli for real quadratic fields I Jan Vonk  선택
Apr 19, 2021  15:30-16:30  Singular moduli for real quadratic fields II Jan Vonk  선택
Apr 26, 2021  15:30-16:30  Singular moduli for real quadratic fields III Jan Vonk  선택
Apr 16, 2021  15:30-16:30  Hecke system of harmonic Maass functions and applications to modular curves of higher genera 김창헌  선택
May 12, 2021  16:00-18:00  Functional analytical techniques in the analysis of infinitely wide neural networks 류경석  선택