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seminars
Date Apr 26, 2021
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.

Subject
Nov 16, 2021  16:00-16:30  Crystal base and unipotent quantum coordinate ring 장일승  129-101 
Mar 08, 2022  16:00-16:30  Parametrizing rings of low rank 이석형  129-101 
Mar 22, 2022  16:00-16:30  Introduction to Secure Computation 이기우  129-101 
Apr 05, 2022  16:00-16:30  On the space of anti-symplectic involutions of rational symplectic 4-manifolds 문지연  129-101 
Apr 19, 2022  16:00-16:30  Quasi-stationarity of the underdamped Langevin dynamics Mouad Ramil  129-101 
May 03, 2022  16:00-16:30  Fukaya categories of singularities 좌동욱  129-101 
May 17, 2022  16:00-16:30  Bilinear Bochner-Riesz means and square function file Kalachand shuin  129-101 
Sep 06, 2022  16:00-16:30  Maximal functions and their applications 함세헌  129-101 
Sep 20, 2022  16:00-16:30  Introduction to representation theory 허태혁  129-101 
Oct 04, 2022  16:00-16:30  Universality Classes in Probability Theory 변성수  129-101 
Nov 21, 2018  16:00 -18:00  Four independences in non-commutative probability Takahiro Hasebe  129-301 
May 26, 2015  16:00 - 17:00  Green functions for elliptic systems 최종근  27-220 
Feb 05, 2014  16:00  On weighted $L^2$ estimates for solutions of the wave equation file 고영우  27-220 
Dec 13, 2017  15:30-19:30  LWE over the integers and improved side-channel attacks against BLISS Mehdi Tibouchi  129-104 
May 17, 2022  15:30-18:30  Lectures on Financial Mathematics Constantinos Kardaras  129-104 
May 19, 2022  15:30-18:30  A production equilibrium model for capacity expansion (WIP) Constantinos Kardaras  129-104 
May 29, 2018  15:30-18:00  Sign coherence of unit vectors in certain lattices 이규환  129-307 
Sep 28, 2022  15:30-18:00  On the long-time behavior of scale-invariant solutions to the 2d Euler equation Ayman R. Said  129-301 
Dec 01, 2021  15:30-18:00  Asymptotic behavior at singularities of mean curvature flow 최경수  선택 
Aug 10, 2022  15:30-18:00  Hyperkahler manifolds in mathematics and physics Arnav Tripathy  129-104