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.

2021-06-04  09:00-10:30  Superposition principle for stochastic nonlinear Fokker-Planck-Kolmogorov equations Marco Rehmeier  129-301 
2021-06-04  16:00-17:00  Problems for the Hermite and special Hermite expansions 유재현  27-220 
2021-06-04  14:00-16:00  Introduction to derived categories 조창연  선택 
2021-06-03  10:30-12:30  Locking-free and locally-conservative enriched Galerkin methods for linear poroelasticity 이상현  129-310 
2021-06-02  16:00-18:00  Sums of free variables in symmetric spaces Éric Ricard  선택 
2021-06-01  14:00 ~ 15:00  Topics in the singularities of plurisubharmonic functions 안종봉  27-220 
2021-06-01  16:00-17:00  On the Bochner-Riesz operator in R^3 정은희  선택 
2021-05-31  16:00-17:00  Overview of some recent developments in geometric topology 백형렬  129-310 
2021-05-31  11:00-12:00  Iwasawa Theory of Elliptic Curves Debanjana Kundu  선택 
2021-05-28  09:00-11:00  Nonuniqueness in law for stochastic hypodissipative NSE Marco Rehmeier  27-220 
2021-05-28  14:00-16:00  Topological entropy 0 and conformal dimension 1 in complex dynamics 박인성  27-220 
2021-05-28  10:00-12:00  Introduction to derived categories 조창연  선택 
2021-05-27  17:00-18:00  Robustness of deep neural networks to adversarial attack: from heuristic methods to certified methods 이성윤  27-116 
2021-05-26  10:00-11:00  Characterizations of the plane and the catenoid as free boundary minimal surfaces 연응범  27-220 
2021-05-26  11:00-12:00  Uniqueness and existence results of minimal surfaces in four-dimensional Euclidean space 이재훈  27-220 
2021-05-26  15:00-16:30  Lorentzian Polynomials (우리말 강연) 허준이  129-101 
2021-05-26  16:00-17:30  Approximation numbers, entropy numbers and their applications to noncommutative tori 이기현  선택 
2021-05-25  16:00-17:00  Estimates for Spectral projectors on the torus 권예현  선택 
2021-05-24  15:00-16:00  Non-linear operators on fractal domains and homogenization for fully non-linear parabolic equations 박성하  선택