Date 2021-04-26
Speaker Jan Vonk
Dept. Leiden University
Room 선택
Time 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.

2022-07-04  15:00-17:00  강연1: Scale-invariant tangent-point energies for knots and fractional harmonic maps / 강연2: On Calderon-Zygmund type estimates for nonlocal PDE Armin Schikkora  27-220 
2022-07-04  15:00-17:00  Free Random Variables followed by the Semicircular Law Il Woo Cho  129-406 
2022-07-05  15:00-17:00  Overview of DeGiorgi-Nash-Moser theory Karthik Adimurthi  27-325 
2017-12-11  15:00-17:30  딥러닝에 있어서의 체인룰의 역할 김영록  129-301 
2019-07-02  15:00-17:30  Exact Lagrangian fillings of Legendrian torus knots. Lec 1,2 배영진  129-310 
2019-05-14  15:00-17:30  Martin boundary covers Floyd boundary Wenyuan YANG  27-220 
2016-06-21  15:00-18:00  Linear recurrence relations in Q-systems Chul-hee Lee  129-406 
2018-02-02  15:00-18:00  Coalgebraic principles of quantum field theory (two lectures) Jae-suk Park  27-325 
2019-06-20  15:00-18:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116 
2021-12-07  15:00-18:00  The canonical commutation relations and the local geometry of symplectic spaces 김현문  27-325 
2019-10-18  15:10-16:10  Introduction to Dwork's theory 박지훈  129-104 
2019-03-26  15:30-16:20  The nonlinear Brascamp-Lieb inequality Neal Bez  27-116 
2014-04-24  15:30-16:30  Recent progress on the Boltzmann equation without angular cutoff Tong Yang  27-220 
2016-01-29  15:30-16:30  삼성 생산기술연구소 소개 및 수학의 필요성 박상봉  27-220 
2021-02-09  15:30-16:30  Data-Driven Methods for Artist-Directed Fluid Simulations Byungsoo Kim  선택 
2021-04-02  15:30-16:30  CM congruence and the derivatives of p-adic L-functions for imaginary quadratic fields Ming-Lun Hsieh  선택 
2021-04-12  15:30-16:30  Singular moduli for real quadratic fields I Jan Vonk  선택 
2021-04-19  15:30-16:30  Singular moduli for real quadratic fields II Jan Vonk  선택 
2021-04-26  15:30-16:30  Singular moduli for real quadratic fields III Jan Vonk  선택 
2021-04-16  15:30-16:30  Hecke system of harmonic Maass functions and applications to modular curves of higher genera 김창헌  선택