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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
2021-04-19  15:30-16:30  Singular moduli for real quadratic fields II Jan Vonk  선택 
2021-04-26  15:30-16:30  Singular moduli for real quadratic fields III Jan Vonk  선택 
2021-04-16  15:30-16:30  Hecke system of harmonic Maass functions and applications to modular curves of higher genera 김창헌  선택 
2021-05-12  16:00-18:00  Functional analytical techniques in the analysis of infinitely wide neural networks 류경석  선택 
2021-05-14  15:30-16:30  On some results about non-holomorphic Jacobi forms 진석호  선택 
2021-05-03  15:30-16:30  Local Shimura varieties and their cohomology I, II, III David Hansen  선택 
2021-05-10  15:30-16:30  Local Shimura varieties and their cohomology I, II, III David Hansen  선택 
2021-05-17  15:30-16:30  Local Shimura varieties and their cohomology I, II, III David Hansen  선택 
2021-02-03  15:00-15:45  Geometric analysis on linear groups over a local field of positive characteristic 권상훈  선택 
2021-02-01  15:00-15:45  Intrinsic Diophantine Approximation of circles and spheres 김동한  선택 
2021-02-01  14:00-14:45  Dynamical approach to distribution of modular inverses 선해상  선택 
2021-05-18  16:00-17:00  What is abstract harmonic analysis? 이훈희  선택 
2021-05-24  15:00-16:00  Non-linear operators on fractal domains and homogenization for fully non-linear parabolic equations 박성하  선택 
2021-05-24  11:00-12:00  Iwasawa Theory of Elliptic Curves Debanjana Kundu  선택 
2021-05-31  11:00-12:00  Iwasawa Theory of Elliptic Curves Debanjana Kundu  선택 
2021-06-07  11:00-12:00  Iwasawa Theory of Elliptic Curves Debanjana Kundu  선택 
2021-05-25  16:00-17:00  Estimates for Spectral projectors on the torus 권예현  선택 
2021-05-28  15:30-16:30  RAMANUJAN CONTINUED FRACTIONS OF ORDER SIXTEEN 박윤경  선택 
2021-05-26  16:00-17:30  Approximation numbers, entropy numbers and their applications to noncommutative tori 이기현  선택 
2021-05-14  15:00-17:00  Introduction to derived categories 조창연  선택