seminars

$$heading_1$$ Singular moduli for real quadratic fields III

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