http://www.math.snu.ac.kr/board/files/attach/images/698/d7f811aae9dfd8ef6b3d16c547a28844.png
seminars
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.

제목
2021-03-24  16:00-18:00  Type semigroups of ample groupoids, and a purely-infinite/stably-finite dichotomy Aidan Sims  129-406 
2021-03-31  16:00-18:00  Concavity of certain trace functionals and applications to data processing inequalities Haonan Zhang  129-406 
2021-04-02  10:30-12:00  Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types. 오세진  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 
2021-04-06  16:00-17:00  Hamiltonian structure, Stability, and Variational methods 석진명  선택 
2021-04-06  16:00-16:30  Generalization of Synchronization models 박한솔  129-101 
2021-04-06  16:40-17:10  The Regularity Theory for the Double Obstacle Problem 박진완  129-101 
2021-04-07  16:00-18:00  Furstenberg boundary for discrete quantum groups Roland Vergnioux  129-406 
2021-04-09  14:00-16:00  Bound entangled states that allow players to distill one-way genuine secret-sharing state 최민진  선택 
2021-04-12  15:30-16:30  Singular moduli for real quadratic fields I Jan Vonk  선택 
2021-04-14  16:00-18:00  Boundary and rigidity of nonsingular Bernoulli actions Yusuke Isono  129-406 
2021-04-16  15:30-16:30  Hecke system of harmonic Maass functions and applications to modular curves of higher genera 김창헌  선택 
2021-04-19  15:30-16:30  Singular moduli for real quadratic fields II Jan Vonk  선택 
2021-04-20  16:00-16:30  Simplicial networks for higher-order Interactions 이강주  129-101 
2021-04-20  16:40-17:10  Data-driven chance-constrained optimization under Wasserstein ambiguity 이다빈  129-101 
2021-04-21  16:00-18:00  Polytope structures for Greenberger-Horne-Zeilinger diagonal states 계승혁  129-406 
2021-04-26  15:30-16:30  Singular moduli for real quadratic fields III Jan Vonk  선택 
2021-05-03  15:30-16:30  Local Shimura varieties and their cohomology I, II, III David Hansen  선택 
2021-05-04  16:40-17:10  Deformation of period integrals and its application 김예슬  129-101 
2021-05-04  16:00-16:30  Demazure modules and $0$-Hecke modules of type $A$ 최승일  129-101