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
May 10, 2017  16:00-18:00  Rigidity of group actions Nhan-Phu Chung  129-301 
Dec 14, 2016  16:00-17:00  SOBOLEV CAPACITIES IN NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS Nguyen Cong Phuc  27-325 
Mar 17, 2015  16:00-17:00  Some applications of the Funk-Hecke theorem to smoothing Neal Bez  129-406 
Apr 29, 2016  16:00-18:00  Strichartz estimates for kinetic and Schrödinger equations Neal Bez  129-406 
Oct 19, 2016  17:30-18:30  Estimates for the kinetic transport equation in hyperbolic Sobolev spaces Neal Bez  27-116 
Mar 26, 2019  15:30-16:20  The nonlinear Brascamp-Lieb inequality Neal Bez  27-116 
May 30, 2023  16:00-18:00  A pointwise convergence problem for orthonormal systems Neal Bez  27-116 
Nov 16, 2018  16:00-18:00  The Laplacian on some round Sierpin´ski carpets and Weyl’s asymptotics for its eigenvalues file Naotaka Kajino  27-325 
Dec 19, 2018  11:00-13:00  Wakimoto representations and Parabolic inductions for W-algebras Naoki Genra  27-325 
Nov 15, 2016  11:00-13:00  Introduction to moduli space of flat connections over a Riemann surface 1 Nankuo Ho  129-406 
Nov 17, 2016  11:00-13:00  Introduction to moduli space of flat connections over a Riemann surface 2 Nankuo Ho  129-406 
May 26, 2015  16:00-17:00  학부 고년차 학생들을 위한 기하강연 1 Naichung Conan Leung  129-301 
May 26, 2015  17:10-18:10  학부 고년차 학생들을 위한 기하강연 2 Naichung Conan Leung  129-301 
May 27, 2015  11:00-12:00  학부 고년차 학생들을 위한 기하강연 3 Naichung Conan Leung  129-406 
Jul 18, 2016  11:00-12:00  Modeling biology with simple geometric objects: Application to therapeutic effect on cancer cell mechanics Myles Kim  27-220 
Oct 27, 2017  15:00-17:00  Metrical theory for the set Dirichlet non-improvable numbers Mumtaz Hussain  129-104 
May 19, 2016  16:00-18:00  AMOEBAS AND COAMOEBAS Mounir Nisse  25-103 
May 20, 2016  16:00-18:00  ON COAMOEBAS OF ALGEBRAIC HYPERSURFACES Mounir Nisse  25-103 
Apr 19, 2022  16:00-16:30  Quasi-stationarity of the underdamped Langevin dynamics Mouad Ramil  129-101 
Nov 28, 2018  16:00-18:00  Quantum information and random matrices Motohisa Fukuda  129-301