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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
Jun 16, 2016  16:00-17:30  Fractals and fractal wavelets Judith Packer  129-301 
Jun 17, 2016  16:00-17:00  Projective multiresolution structures for Hilbert modules over unital C*-algebras Judith Packer  129-301 
Oct 16, 2018  09:00-11:00  An introduction to intrinsic scaling Lecuture 1 Jose Miguel Urbano  27-325 
Oct 19, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre III Jose Miguel Urbano  27-325 
Oct 22, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre IV Jose Miguel Urbano  27-325 
Oct 23, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre V Jose Miguel Urbano  27-325 
Oct 17, 2018  09:00-11:00  An introduction to intrinsic scaling Lecture II Jose Miguel Urbano  27-325 
Jul 14, 2022  16:00-18:00  Renormalization of Dynamical Systems Jonguk Yang  27-317 
Dec 05, 2017  17:00-18:30  Computational Algebraic Geometry and Computer Vision I Joe Kileel  129-301 
Dec 06, 2017  17:00-18:30  Computational Algebraic Geometry and Computer Vision II Joe Kileel  129-406 
Dec 08, 2017  17:00-18:30  Computational Algebraic Geometry and Computer Vision III Joe Kileel  129-104 
Apr 16, 2019  16:00-17:00  On the inverse Galois problem with ramification conditions Joachim König  27-325 
Oct 08, 2015  09:30-14:30  Post-quantum cryptography:Multivariate Public Key Cryptography Jintai Ding  129-301 
Jun 04, 2022  10:20-10:50  C 1,α-regularity for nonlinear equations Jihoon Ok  27-325 
Dec 26, 2018  11:00-12:00  Families of periodic orbits in the restricted three-body problem and the Cieliebak-Frauenfelder-van Koert invariants Jeungeun Park  27-116 
Feb 06, 2017  10:00-11:30  Lecture 1. Vertex Algebras and the Free Boson Jethro van Ekeren  129-406 
Feb 06, 2017  14:00-15:30  Lecture 2. The Free Fermion and the Boson-Fermion Correspondence Jethro van Ekeren  129-406 
Feb 08, 2017  10:00-12:00  Lecture 3. The Virasoro Algebra Jethro van Ekeren  129-406 
Oct 12, 2021  09:30-11:00  Vertex algebras and chiral homology I Jethro van Ekeren  선택 
Oct 14, 2021  09:30-11:30  Vertex algebras and chiral homology II Jethro van Ekeren  선택