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.

2021-11-02  16:00-16:30  Multilinear Harmonic Analysis and Applications file 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 file 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 $L^2$ estimates for solutions of the wave equation file 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