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
2022-09-06  16:40-17:10  Maximal averages over curves 오세욱  129-101 
2022-09-06  16:00-16:30  Maximal functions and their applications 함세헌  129-101 
2022-09-20  16:40-17:10  An invitation to quantum groups 이신명  129-101 
2022-09-20  16:00-16:30  Introduction to representation theory 허태혁  129-101 
2022-10-04  16:00-16:30  Universality Classes in Probability Theory 변성수  129-101 
2022-10-04  16:40-17:10  Mathematical study of metastability 이중경  129-101 
2022-10-18  16:00-16:30  Genera of manifolds 김승원  129-101 
2022-10-18  16:40-17:10  Counting surfaces on Calabi-Yau 4-folds 박현준  129-101 
2022-11-01  16:00-16:30  Stable diffeomorphism of exotic 4-manifolds 강성경  129-101 
2022-11-01  16:40-17:10  Surgery techniques in 4-manifolds 최학호  129-101 
2023-04-04  16:00-16:30  Teichmuller space and its generalizations 정홍택  129-101 
2023-04-18  16:00-16:30  Schubert polynomials and the inhomogeneous TASEP on a ring 김동현  129-101 
2023-04-18  16:40-17:10  Combinatorics of coinvariants 오재성  129-101 
2023-05-02  16:40-17:10  Homological Mirror Symmetry of Degenerate Cusps and Their Representations 노경민  129-101 
2023-05-02  16:00-16:30  Why is the Fukaya category important in Symplectic topology? 이상진  129-101 
2023-05-16  16:00-16:30  Theta series and representation by integral quadratic forms 김대준  129-101 
2023-10-12  16:00-16:30  Mathematical understanding of first-order optimization algorithms 박지선  129-101 
2023-10-12  16:40-17:10  What are Generative Models? 최재웅  129-101 
2023-11-09  16:00-16:30  Some special solutions of incompressible Euler equations 임덕우  129-101 
2023-11-09  16:40-17:10  On wellposedness of $\alpha$-SQG equations 김준하  129-101