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seminars
Date 2021-04-26
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.

제목
2016-07-05  16:30-17:30  Non-commutative mirror functor Siu-Cheong Lau  129-301 
2016-07-05  15:00-16:00  Noncommutative Mirror Functors 홍한솔  129-301 
2016-06-29  16:00-17:00  A Mathematical Model of the Pathogenesis, Prevention, Reversal of Type 2 Diabetes, and Clinical Implications file Ha, Joon  129-301 
2016-06-28  16:00-17:00  Numerical Simulation of Bouncing Jets and Hydraulic Fracture Propagation Sanghyun Lee  선택 
2016-06-21  15:00-18:00  Linear recurrence relations in Q-systems Chul-hee Lee  129-406 
2016-06-21  16:00-17:00  An inductive formula of the Gross-Keating invariant of a quadratic form 조성문  27-325 
2016-06-18  10:00-13:00  Existence and regularity results of very weak solutions to nonlinear elliptic equations file 유승진  27-325 
2016-06-17  15:00-16:00  Asymptotic issues in infinite ctlinders file Michel Chipot  129-301 
2016-06-17  16:00-17:00  Projective multiresolution structures for Hilbert modules over unital C*-algebras Judith Packer  129-301 
2016-06-16  16:00-17:30  Fractals and fractal wavelets Judith Packer  129-301 
2016-06-15  17:00-18:00  Okounkov bodies associated to pseudoeffective divisors 최성락  129-310 
2016-06-15  16:00-17:00  Variational Mean Field Games Filippo Santambrogio  27-220 
2016-06-09  14:00-15:00  Weighted estimates in Orlicz spaces for fully nonlinear elliptic equations 이미경  129-307 
2016-06-09  15:00-16:00  Existence of multiple positive solutions for a singular p(x)-Laplacian equation file 고은경  129-307 
2016-06-08  17:00-18:00  Tropical Grassmannian and Dressian 신재호  129-310 
2016-06-08  10:00-12:00, 13:30-14:30  The flexible Bayesian hierarchical modeling’s and their application in the Analysis of Financial Data Inyoung Kim  129-406 
2016-06-02  17:00-18:00  Multiple sections of ruled surfaces 최인송  129-406 
2016-05-31  16:00-18:00  Unique continuation for the Schrodinger equation with gradient terms 서이혁  27-116 
2016-05-30  15:00-16:00  Refined error estimates and decay properties for a damped semi linear wave equation Debora Amadori  129-406 
2016-05-25  09:00-10:00  On quantum hydrodynamics Paolo Antonelli  129-406