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 24, 2022  16:00-19:00  Lifting problem for universal quadratic forms 김대준  27-116 
Dec 28, 2023  16:00-19:00  Generalized polynomial functors Jonathan Axtell  129-301 
Sep 16, 2014  16:00-18:30  Universality for random matrices 이지운  129-301 
Mar 03, 2015  16:00-18:30  Introduction to Cluster Algebras coming from surfaces I, II 이경용  129-301 
Jul 19, 2016  16:00-18:30  Computation in Weyl groups Chul-Hee Lee  129-301 
Oct 24, 2016  16:00-18:30  Bounded Euler number of actions of 2-orbifold groups on the circle Yoshifumi Matsuda  27-325 
Oct 20, 2017  16:00-18:30  Dynamics on the surfaces 백형렬  27-325 
Apr 19, 2018  16:00-18:30  Decompositions of 3-manifolds and hyperbolic geometry Jessica Purcell  27-116 
May 27, 2014  16:00-18:00  On the least prime primitive root and the polynomial equation X+Y=Z 하준수  129-307 
Jul 24, 2014  16:00-18:00  Arithmetically Cohen - Macaulay vector bundles on hypersurfaces in P4 Carlo Madonna  129-310 
Mar 17, 2015  16:00-18:00  Weak KAM theory on the Wasserstein torus Wilfrid Gangbo  129-301 
Mar 19, 2015  16:00-18:00  Weak KAM theory on the Wasserstein torus Wilfrid Gangbo  129-301 
Sep 18, 2015  16:00-18:00  Prosimity in Banach Spaces: Conjectures and Recent Results P. L. Combettes  27-220 
Mar 31, 2015  16:00-18:00  Group actions and Frobenius manifolds 이병호  27-220 
Apr 01, 2015  16:00-18:00  Group actions and Frobenius manifolds 이병호  129-301 
Apr 02, 2015  16:00-18:00  Group actions and Frobenius manifolds 이병호  129-301 
Dec 17, 2015  16:00-18:00  Quantum Information Theory Basics 지동표  129-301 
Dec 22, 2015  16:00-18:00  Global well-posedness of the NLS system for infinitely many fermions 홍영훈  27-116 
Jan 07, 2016  16:00-18:00  Exotic quotients of surface groups Thomas Koberda  129-301 
Jan 05, 2016  16:00-18:00  Quantum Information in continuous variable regime 김호준  129-301