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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
2021-08-19  11:00-13:00  EXISTENCE AND REGULARITY FOR NONLINEAR PARABOLIC DOUBLE OBSTACLE PROBLEMS 유승진  27-325 
2023-09-15  15:00-17:00  Lp estimates for nonlinear double obstacle problems 유승진  27-325 
2019-09-24  16:00-18:00  Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentials file 유재현  27-116 
2022-10-04  16:00-18:00  On the maximal Bochner-Riesz conjecture for p>2 유재현  27-116 
2021-06-04  16:00-17:00  Problems for the Hermite and special Hermite expansions 유재현  27-220 
2022-10-11  17:00-18:00  On limits of sequences of operators 유재현  27-116 
2023-05-09  11:00-13:00  Singualr spherical maximal operators on a class of degenerate two-step nilpotent Lie groups 유재현  129-301 
2023-10-10  17:00-18:00  Sharp local $L^p$ estimates for the Hermite eigenfunctions 유재현  27-116 
2021-11-02  10:30-11:30  Construction of KR modules of generalized quantum group of type A 유정우  27-220 
2015-05-22  10:30-12:00  Symbolic dynamics and relatively maximal measures 유지상  129-301 
2014-06-30  15:00-16:00  Introductory Panorama of Derived Algebraic Geometry I 유필상  129-301 
2014-07-01  15:00-16:00  Introductory Panorama of Derived Algebraic Geometry II 유필상  129-301 
2014-07-02  15:00-16:00  Introductory Panorama of Derived Algebraic Geometry III 유필상  129-301 
2019-12-30  16:00-17:30  From Quantum Field Theory To Geometric Representation Theory 유필상  129-406 
2015-05-14  14:00-15:15  Synchronization of finite-state pulse-coupled oscillators 유한백  선택 
2018-05-02  16:00-18:00  Open quantum random walks as quantum Markov chains 유현재  129-301 
2022-09-13  11:00-12:30  Topological quantum error correction and knots 유형기  129-301 
2014-05-01  14:00-15:00  Rational torsion points of $J_0(pq)$ 유화종  129-310 
2014-12-05  13:30-15:30  THE STRUCTURE OF ... file 유화종  129-104 
2015-01-05  14:00-15:30  Rational torsion points of Jacobians of Shimura curves 유화종  129-406