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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
Feb 02, 2018  15:00-18:00  Coalgebraic principles of quantum field theory (two lectures) Jae-suk Park  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 
Dec 15, 2015  14:00-17:00  Recursiveness and Propagation for 2-variable Weighted Shifts Jasang Yoon  129-406 
Jun 16, 2017  13:00-15:00  Square Root Problems for bounded operators Jasang Yoon  27-116 
May 23, 2019  15:00-17:00  Generalized Aluthge transforms, spherically log and p-hyponormal operators, and their powers I Jasang Yoon  27-116 
May 24, 2019  15:00-17:00  Generalized Aluthge transforms, spherically log and p-hyponormal operators, and their powers II Jasang Yoon  27-116 
Dec 17, 2019  16:00-18:00  Common hyperinvariant subspaces through the generalized spherical Aluthge transforms for commuting pairs of operators Jasang Yoon  129-406 
Nov 04, 2014  17:00-18:00  Mapping class groups Jason Behrstock  129-104 
Jul 28, 2017  16:00-17:00  Recent developments on complex Tauberian theorems for Laplace Jason Vindas  27-116 
Oct 30, 2018  15:00-16:00  The linear and nonlinear wave equations with critical Lorentz regularity file Javier Ramos  27-116 
Mar 26, 2019  16:30-17:20  Inhomogeneous Strichartz estimates for certain critical cases Jayson Cunanan  27-116 
Mar 17, 2014  17:00-18:00  Topological Invariants in Disordered Systems Jean V. Bellissard  129-301 
Mar 18, 2014  14:00-15:00  Topological Invariants in Disordered Systems Jean V. Bellissard  129-301 
Mar 19, 2014  17:00-18:00  Topological Invariants in Disordered Systems Jean V. Bellissard  129-301 
Mar 21, 2014  10:30-12:00  Topological Invariants in Disordered Systems jean V. Bellissard  129-301