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
Dec 05, 2023  16:00-16:30  Free boundary minimal surfaces in a ball and eigenvalue problems 서동휘  129-101 
Mar 28, 2024  16:00-16:30  <Rookies Pitch> About deformation rigidity of some quasi-homogeneous varieties with Picard number one 김신영  129-101 
Mar 28, 2024  16:40-17:10  <Rookies Pitch> Finite path integral and a second monoidal cohomology class of cobordism category 김민규  129-101 
May 30, 2014  09:00-12:00  Well-posedness in anisotropic conductivity reconstruction 이민기  129-104 
Oct 07, 2014  17:00-18:00  Geodesics in nilpotent groups Moon Duchin  129-104 
Jun 10, 2014  16:30-17:30  Introduction to Arithmetic Dynamics 이종규  129-104 
Nov 04, 2014  17:00-18:00  Mapping class groups Jason Behrstock  129-104 
Nov 27, 2014  15:00-16:00  The very-ampleness part of Fujita's conjecture Mario Chan  129-104 
Dec 05, 2014  13:30-15:30  THE STRUCTURE OF ... file 유화종  129-104 
Dec 29, 2014  13:30-16:00  Introduction to quarternionic modular forms 김찬호  129-104 
Mar 13, 2015  16:00-17:00  On a conservativeness criteria for symmetric jump processes Toshihiro Uemura  129-104 
Apr 02, 2015  11:00-12:30  Construction of unramified extensions with a prescribed solvable Galois group 김광섭  129-104 
Oct 14, 2014  17:00-18:00  Concordance group and stable commutator length in braid groups Michael Brandenbursky  129-104 
Nov 13, 2014  14:00-15:00  Random groups surface subgroups Alden Walker  129-104 
Jul 23, 2015  11:00-12:30  On some orders generated by units and their unit groups 이준호  129-104 
Nov 28, 2014  11:00-11:50  Stochastic modeling of biochemical networks Hye-Won Kang  129-104 
Dec 17, 2014  15:00-16:00, 16:00-17:00  Coding Theory from the Viewpoint of Lattices 김종락  129-104 
Oct 20, 2015  17:00-18:00  Additivity conjecture of entropies in quantum information 정갑균  129-104 
Dec 15, 2015  16:00-17:00  Coordinate systems of higher Teichmuller spaces Hyunkyu Kim  129-104 
Apr 27, 2015  16:00-17:30  INTERVENTION STRATEGIES ON EBOLA AND 2009 A/H1N1 INFLUENZA EPIDEMICS 정은옥  129-104