https://www.math.snu.ac.kr/board/files/attach/images/698/d7f811aae9dfd8ef6b3d16c547a28844.png
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
2023-09-01  15:00-16:00  Pattern avoidance and smoothness of Hessenberg Schubert varieties 허지선  129-301 
2024-02-26  15:00-16:00  Heterogeneous diffusion: uniqueness, non-uniqueness, and selection Ilya Pavlyukevich  129-301 
2021-05-24  15:00-16:00  Non-linear operators on fractal domains and homogenization for fully non-linear parabolic equations 박성하  선택 
2022-06-03  15:00-16:00  Calderon-Zygmund estimates for elliptic equations with nonstandard growth 이호식  27-220 
2022-06-08  15:00-16:00  Convergence and Complexity of Stochastic Block Majorization-Minimization 류한백  27-220 
2022-09-20  15:00-16:00  Relation numbers and generalized Farey graphs 김경로  129-309 
2022-09-27  15:00-16:00  Categories of Whittaker Modules over Lie superalgebras and Categorification of Fock Spaces Shun-Jen Cheng  선택 
2022-11-01  15:00-16:00  Fredholm Property of the Linearized Boltzmann Operator for a Mixture of Polyatomic Gases Marwa Shahine  27-325 
2022-11-11  15:00-16:00  Fredholm Property of the Linearized Boltzmann Operator for a Mixture of Polyatomic Gases Marwa Shahine  27-325 
2022-12-02  15:00-16:00  Regularity theory for local and nonlocal measure data problems 송경  27-220 
2022-11-25  15:00-16:00  Metastability of Langevin dynamics 이중경  27-220 
2023-01-18  15:00-16:00  Comparison estimates below L^1 spaces for parabolic problems 신필수  27-325 
2023-03-24  15:00-16:00  Mixed local and nonlocal equations with measure data 송경  27-116 
2023-04-14  15:00-16:00  From De Giorgi's minimizing movements to gradient flows 권도현  27-325 
2023-05-25  15:00-16:00  Recent topics for the regularity of local and nonlocal elliptic equations 이호식  27-325 
2023-08-17  15:00-16:00  Calderon-Zygmund estimates for the fractional p-Laplacian Lars Diening  27-325 
2023-10-05  15:00-16:00  Sup-norm Estimates for Cauchy-Riemann Operator and Corona Problem Song-Ying Li  27-325 
2023-11-14  15:00-16:00  Extreme value theorem of continued fractions and geodesic flows 이슬비  129-104 
2024-03-29  15:00-16:00  Quantum Grothendieck rings of Hernandez-Leclerc Categories 박의용  129-104 
2014-12-17  15:00-16:00, 16:00-17:00  Coding Theory from the Viewpoint of Lattices 김종락  129-104