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.

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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 
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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 
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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 
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