seminars

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

Date 2021-04-26 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.

제목
2022-08-10  15:30-18:00  Hyperkahler manifolds in mathematics and physics Arnav Tripathy  129-104
2020-11-20  15:30-17:45  Zeta함수와 L함수에 대한 역사적 고찰 신석우  129-101
2015-03-09  15:30-17:30  G-structures associated to Hermitian symmetric spaces 김신영  27-325
2015-07-24  15:30-17:30  Spectral Analysis of Graphs using Quantum Probability Nobuaki Obata  129-104
2017-04-24  15:30-17:30  THE ROKHLIN PROPERTY FOR ACTIONS OF DISCRETE GROUPS ON C*-ALGEBRAS AND RELATED TOPICS Hiroyuki Osaka  129-301
2017-04-25  15:30-17:30  THE ROKHLIN PROPERTY FOR ACTIONS OF DISCRETE GROUPS ON C*-ALGEBRAS AND RELATED TOPICS Hiroyuki Osaka  129-301
2014-10-20  15:30-17:00  Lectures on Algebraic Quantum Field theory 박재석  129-406
2014-10-22  15:30-17:00  Lectures on Algebraic Quantum Field theory 박재석  129-406
2014-10-24  15:30-17:00  Lectures on Algebraic Quantum Field theory 박재석  129-406
2018-02-21  15:30-17:00  Inversion of Toeplitz-plus-Hankel Bezoutians Torsten Ehrhardt  129-301
2014-04-24  15:30-16:30  Recent progress on the Boltzmann equation without angular cutoff Tong Yang  27-220
2016-01-29  15:30-16:30  삼성 생산기술연구소 소개 및 수학의 필요성 박상봉  27-220
2021-02-09  15:30-16:30  Data-Driven Methods for Artist-Directed Fluid Simulations Byungsoo Kim  선택
2021-04-02  15:30-16:30  CM congruence and the derivatives of p-adic L-functions for imaginary quadratic fields Ming-Lun Hsieh  선택
2021-04-12  15:30-16:30  Singular moduli for real quadratic fields I Jan Vonk  선택
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
2021-05-14  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