https://www.math.snu.ac.kr/board/files/attach/images/698/d7f811aae9dfd8ef6b3d16c547a28844.png
seminars
Date Apr 26, 2021
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.

Subject
Jun 09, 2015  14:00-16:00  Statistical Modeling for Real Data Analysis Inyoung Kim  129-301 
Jun 08, 2016  10:00-12:00, 13:30-14:30  The flexible Bayesian hierarchical modeling’s and their application in the Analysis of Financial Data Inyoung Kim  129-406 
Feb 22, 2016  16:00-18:00  Using Random Matrices in Quantum Information Theory Ion Nechita  129-301 
Feb 23, 2016  16:00-18:00  Using Random Matrices in Quantum Information Theory Ion Nechita  129-301 
Feb 24, 2016  16:00-18:00  Using Random Matrices in Quantum Information Theory Ion Nechita  129-301 
Oct 12, 2022  11:00-12:00  Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction file Jacky Chong  선택 
Apr 27, 2016  17:00-18:00  Quantitative topology and Cheeger-Gromov universal bounds Jae Choon Cha  129-104 
Nov 13, 2015  15:00-16:00  Spectral methods for solving PDEs with singular defect terms Jae-Hun Jung  선택 
Nov 30, 2015  15:00-16:00  Spectral methods for convection-diffusion problems Jae-Hun Jung  선택 
Dec 01, 2015  15:00-16:00  Pseudospectral methods for hyperbolic equations Jae-Hun Jung  선택 
Feb 02, 2018  15:00-18:00  Coalgebraic principles of quantum field theory (two lectures) Jae-suk Park  27-325 
Aug 14, 2023  15:00-18:00  KAM theory in active scalar equations I Jaemin Park  129-104 
Aug 16, 2023  15:00-18:00  KAM theory in active scalar equations, II Jaemin Park  129-104 
Apr 14, 2023  16:00-17:00  Homological interpretation of Hecke L--values over real quadratic fields Jaesung Kwon  27-325 
Aug 14, 2018  11:00-11:50  On high-order methods for moment-closure approximations of kinetic Boltzmann equations James Rossmanith  27-220 
Apr 05, 2017  16:00-17:30  Exotic examples related to unbounded subnormality via theory of moments Jan Stochel  129-301 
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 
Dec 14, 2015  14:00-17:00  The flatness and Schur product of mono-weakly hyponormal two variable weighted shifts Jasang Yoon  129-301