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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
Dec 21, 2021  14:30-15:30  Kinetic description of stable white dwarfs 석진명  선택 
Nov 14, 2023  14:30-15:30  Refinements of Strichartz inequalities via decoupling and applications to nonlinear equations Robert Schippa  27-116 
Dec 23, 2020  14:30-15:30, 15:45-16:45  Zeta함수와 L함수에 대한 역사적 고찰ⅴ 신석우  선택 
Oct 02, 2014  14:30-15:45  Quantum groups and free Araki-Woods factors Michael Brannan  129-301 
May 16, 2017  14:30-16:00  Extreme Value Theory in Dynamical Systems Maxim Kirsebom  129-406 
Aug 17, 2023  14:30-16:00  Symplectic Torelli classes of positive entropy 김준태  129-104 
Jul 11, 2022  14:30-16:30  <QSMS-BK21 Toric Seminar> Lefschetz Bifibrations and Matching Cycles 김용환  129-309 
Jun 05, 2023  14:30-16:30  Surgery along nullhomologous tori and Lagrangian tori 윤기헌  129-104 
Dec 10, 2020  14:30-16:45  Zeta함수와 L함수에 대한 역사적 고찰ⅲ 신석우  선택 
Dec 17, 2020  14:30-16:45  Zeta함수와 L함수에 대한 역사적 고찰ⅳ 신석우  선택 
Jan 07, 2021  14:30-16:45  Zeta함수와 L함수에 대한 역사적 고찰ⅶ 신석우  선택 
Mar 03, 2021  14:30-16:45  Zeta함수와 L함수에 대한 역사적 고찰 Ⅹ 신석우  선택 
Dec 29, 2020  14:30-17:00  Zeta함수와 L함수에 대한 역사적 고찰ⅵ 신석우  선택 
Feb 25, 2021  14:30-17:00  Zeta함수와 L함수에 대한 역사적 고찰Ⅸ 신석우  선택 
Jun 24, 2022  14:40-16:40  Quantum amplitude amplification operators 배준우  선택 
May 18, 2017  14:45-15:45  Inhomogeneous Diophantine approximation with a fixed irrational number 김동한  129-406 
Feb 03, 2021  15:00-15:45  Geometric analysis on linear groups over a local field of positive characteristic 권상훈  선택 
Feb 01, 2021  15:00-15:45  Intrinsic Diophantine Approximation of circles and spheres 김동한  선택 
Jun 24, 2014  15:00-16:00  Introduction to Hecke operators 이철희  27-325 
Jun 30, 2014  15:00-16:00  Introductory Panorama of Derived Algebraic Geometry I 유필상  129-301