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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
Apr 11, 2017  16:00-19:00  Crystal interpretation of a formula on the branching rule of C_n-type Toya Hiroshima  129-301 
Jun 19, 2017  16:00-17:00  To B(infty) and beyond Travis Scrimshaw  129-301 
Jun 16, 2017  14:00-16:30  An Introduction to algebra and representation theory in Sage Travis Scrimshaw  27-325 
Apr 03, 2018  17:00-19:00  Multiline queues with spectral parameters Travis Scrimshaw  129-301 
Oct 25, 2022  10:00-11:00  Rational liftings and gRSK Travis Scrimshaw  선택 
Oct 25, 2022  11:00-12:00  Crystal Invariant Theory Travis Scrimshaw  선택 
May 15, 2015  11:10-12:10  Positive maps; non-linear and liner Tsuyoshi Ando  129-301 
Feb 17, 2022  19:00-20:00  The little sibling of Rabinowitz action functional Urs Frauenfelder  선택 
Aug 11, 2023  16:00-18:00  Spectral numbers in Tate Rabinowitz Floer Homology 1 Urs Frauenfelder  129-104 
Aug 17, 2023  16:00-18:00  Spectral numbers in Tate Rabinowitz Floer Homology 2 Urs Frauenfelder  129-104 
Aug 28, 2023  15:00-17:00  From Babylonian lunar observations to global surfaces of section Urs Frauenfelder  129-406 
Dec 03, 2015  14:00-15:00  Hypercontractivity of heat semigroups on free quantum groups Uwe Franz  129-301 
Jun 27, 2017  16:30-17:30  Towers of regular self-covers and linear endomorphisms of tori Van Limbeek  129-301 
Apr 01, 2022  10:30-11:30  Randomness and structure for sums of cubes Victor Wang  선택 
Dec 07, 2015  16:00-17:00  e lectures on Geometric Invariant Theory (1) Victoria Hoskins  129-301 
Dec 08, 2015  16:00-17:00  Five lectures on Geometric Invariant Theory (2) Victoria Hoskins  129-301 
Dec 09, 2015  16:00-17:00  Five lectures on Geometric Invariant Theory (3) Victoria Hoskins  129-301 
Dec 10, 2015  16:00-17:00  Five lectures on Geometric Invariant Theory (4) Victoria Hoskins  129-301 
Dec 11, 2015  16:00-17:00  Five lectures on Geometric Invariant Theory (5) Victoria Hoskins  129-301 
Aug 11, 2017  16:00-17:00  Numerical Solutions of Stochastic Partial Differential Equations and Uncertainty Quantification Viet Ha Hoang  129-310