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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
2016-05-17  16:00-18:00  Oscillatory Integrals over Global Domains file 김준일  27-116 
2016-05-18  16:00-17:30  Schrodinger Operators and Spectral Theory 허인조  129-301 
2016-05-18  14:00-17:00  Regualarity Theory for Elliptic and Parabolic Equations Lihe Wang  129-406 
2016-05-19  16:00-18:00  AMOEBAS AND COAMOEBAS Mounir Nisse  25-103 
2016-05-20  11:00-12:00  CONGRUENCES OF HARDER TYPE AND AN EXAMPLE IN HILBERT MODULAR FORMS file 이동건  25-103 
2016-05-20  16:00-18:00  ON COAMOEBAS OF ALGEBRAIC HYPERSURFACES Mounir Nisse  25-103 
2016-05-20  11:00-12:00  Fluctuation-Dissipation Theorem and Detailed Balance in Langevin Systems 이현근  27-116 
2016-05-20  14:00-16:00  Non-commutative quantum field theory and Chen’s iterated path integrals 박재석  25-103 
2016-05-24  16:00-18:00  Decay estimates for Fourier transform of measures on fractal sets 함세헌  27-116 
2016-05-25  09:00-10:00  On quantum hydrodynamics Paolo Antonelli  129-406 
2016-05-25  17:00-18:00  Quantum Heisenberg manifolds as twisted groupoid C^*-algebras file 강수란  129-301 
2016-05-25  16:00-17:00  Sofic mean length Hanfeng Li  129-301 
2016-05-25  17:00-19:00  Random flight processes in external fields Douglas Rizzolo  129-104 
2016-05-30  15:00-16:00  Refined error estimates and decay properties for a damped semi linear wave equation Debora Amadori  129-406 
2016-05-31  16:00-18:00  Unique continuation for the Schrodinger equation with gradient terms 서이혁  27-116 
2016-06-02  17:00-18:00  Multiple sections of ruled surfaces 최인송  129-406 
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 
2016-06-09  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