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