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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
Dec 05, 2024  19:00~21:00  Maximal estimates for various averaging operators and their generalizations Shuijiang Zhao  27-325 
Nov 22, 2024  17:00-18:30  Bases of Norm Generators and Applications 2 윤종흔  27-116 
Nov 21, 2024  19:00~21:00  Maximal estimates for various averaging operators and their generalizations Shuijiang Zhao  27-325 
Nov 18, 2024  11:00-13:00  Local superconformal algebras Surya Raghavendran  129-406 
Nov 18, 2024  14:00-16:30  Lagrangian knot problems in symplectic four-manifolds 김준태  129-309 
Nov 15, 2024  17:00-19:00  Sharp Lp-Lq estimates for the spherical harmonic projection 권예현  27-116 
Nov 15, 2024  10:00-12:00  First-order differential calculi and Laplacians on $q$-deformations of compact semisimple Lie groups 이헌  129-301 
Nov 15, 2024  16:00-17:00  Modified scattering for Dirac equations of scattering-critical nonlinearity 양창훈  129-301 
Nov 15, 2024  14:00-16:30  Lagrangian knot problems in symplectic four-manifolds 김준태  129-309 
Nov 14, 2024  16:00-16:30  What a colorful world: a biased personal introduction to discrete geometry 이승훈  129-101 
Nov 14, 2024  16:40-17:10  Signed Graph Theory: Extensions and Applications 허철원  129-101 
Nov 12, 2024  17:00-18:00  Recent advances on the weight part of Serre's conjecture Heejong Lee  선택 
Nov 07, 2024  19:00~21:00  Maximal estimates for various averaging operators and their generalizations Shuijiang Zhao  27-325 
Nov 06, 2024  15:00-16:00  3D mirror symmetry Naichung Conan Leung  129-406 
Nov 06, 2024  16:00-17:00  3d mirror symmetry is mirror symmetry Naichung Conan Leung  129-406 
Nov 05, 2024  16:00-17:00  On the concentration phenomenon for the Sobolev flow Masashi Misawa  27-325 
Nov 05, 2024  10:00-11:00  On the concentration phenomenon for the Sobolev flow Masashi Misawa  27-116 
Nov 05, 2024  16:00-17:00  On the distribution of primitive lattice points in large dimensions 한지영  129-309 
Nov 04, 2024  17:00-18:00  A unified approach to Rohrlich-type divisor sums Toshiki Matsusaka  27-325 
Nov 01, 2024  17:00-18:30  Bases of Norm Generators and Applications 윤종흔  27-116