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
2021-11-02  16:00-16:30  Multilinear Harmonic Analysis and Applications 이진봉  129-101
2021-11-16  16:00-16:30  Crystal base and unipotent quantum coordinate ring 장일승  129-101
2022-03-08  16:00-16:30  Parametrizing rings of low rank 이석형  129-101
2022-03-22  16:00-16:30  Introduction to Secure Computation 이기우  129-101
2022-04-05  16:00-16:30  On the space of anti-symplectic involutions of rational symplectic 4-manifolds 문지연  129-101
2022-04-19  16:00-16:30  Quasi-stationarity of the underdamped Langevin dynamics Mouad Ramil  129-101
2022-05-03  16:00-16:30  Fukaya categories of singularities 좌동욱  129-101
2022-05-17  16:00-16:30  Bilinear Bochner-Riesz means and square function Kalachand shuin  129-101
2018-11-21  16:00 -18:00  Four independences in non-commutative probability Takahiro Hasebe  129-301
2015-05-26  16:00 - 17:00  Green functions for elliptic systems 최종근  27-220
2014-02-05  16:00  On weighted $$extract_itex$$L^2$$/extract_itex$$ estimates for solutions of the wave equation 고영우  27-220
2017-12-13  15:30-19:30  LWE over the integers and improved side-channel attacks against BLISS Mehdi Tibouchi  129-104
2022-05-17  15:30-18:30  Lectures on Financial Mathematics Constantinos Kardaras  129-104
2022-05-19  15:30-18:30  A production equilibrium model for capacity expansion (WIP) Constantinos Kardaras  129-104
2018-05-29  15:30-18:00  Sign coherence of unit vectors in certain lattices 이규환  129-307
2021-12-01  15:30-18:00  Asymptotic behavior at singularities of mean curvature flow 최경수  선택
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