http://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
May 15, 2015  15:00-16:30  Introduction to Number theory for topologists 박지훈  129-301 
Oct 16, 2018  15:00-16:30  UNIFORM SOBOLEV INEQUALITY ON THE d-TORUS file 정은희  27-116 
Nov 26, 2018  15:00-16:30  Generically smooth components of the Hilbert scheme of curves via ruled surfaces file Hristo Iliev  27-325 
Sep 11, 2018  15:00-16:30  The proof of the l^2 decoupling conjecture and some applications 이주영  27-116 
Sep 18, 2018  15:00-16:30  Boundedness of pseudo-differential operators of type (0,0) on Triebel-Lizorkin spaces 박배준  27-116 
Aug 24, 2022  15:00-16:30  Nonlocal problems with non-standard growth Minhyun Kim  129-301 
Jun 27, 2019  15:00-16:30  위상학적 자료 분석(Topological Data Analysis)의 통계적 추정 김지수  27-220 
Sep 21, 2023  15:00-16:30  Liouville problems in the Fluid Mechanics 채동호  27-325 
May 26, 2021  15:00-16:30  Lorentzian Polynomials (우리말 강연) 허준이  129-101 
Jul 08, 2021  15:00-16:30  Volume growth of symplectomorphisms and Floer theory 김준태  27-325 
Nov 07, 2023  15:00-16:30  Volume bounds for hyperbolic 3-polyhedra and knots Andrei Vesnin  129-309 
Mar 20, 2024  15:00-16:30  Critical norm blow-up for the energy supercritical nonlinear heat equation Hideyuki Miura  27-116 
Jun 12, 2014  15:00-17:00  Ideal triangulations, the A-polynomial and beyond Roland van der Veen  129-406 
Jul 11, 2014  15:00-17:00  ON REGULARITY OF OPTIMAL TRANSPORTATION AND THE MONGE-AMPERE EQUATION Young-Heon Kim  27-220 
Mar 19, 2015  15:00-17:00  Levi problem and the theory of Stein manifolds via L2 method Mario Chan  129-307 
Sep 02, 2015  15:00-17:00  What is Weak KAM Theory? / Regularity of solutions of Hamilton-Jacobi equation on a domain file Albert Fathi  27-220 
Oct 20, 2015  15:00-17:00  Quantum Information THeory Basics 1 지동표  129-301 
Nov 05, 2015  15:00-17:00  Free Energy of Spherical Spin Glass Model 이지운  129-301 
May 26, 2015  15:00-17:00  Regularity for elliptic and parabolic equations Lihe Wang  27-325 
May 27, 2015  15:00-17:00  Regularity for elliptic and parabolic equations Lihe Wang  27-325