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seminars
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.

제목
2015-10-13  12:30-13:30  Graded ring methods in the construction of varieties Miles Reid  129-406 
2024-01-12  12:20-13:00  Global well-posedness of the kinetic Cucker-Smale equation with a singular communication 정진욱  27-220 
2023-03-10  12:00-17:00  (QSMS-BK21 Symplectic Seminar) Mirror Symmetry for Log Calabi-Yau Surfaces 김현빈  129-309 
2021-12-15  12:00-16:00  Toric actions on symplectic manifolds 노경민  129-309 
2018-11-30  12:00-13:00  Optimal investment and consumption with liquid and illiquid assets 최진혁  129-301 
2021-02-02  12:00-13:00  Measure changes for jump processes and derivative pricing 안신미  27-317 
2022-06-04  11:40-12:40  Regularity estimates for nonlinear elliptic equations with Schrödinger type lower order terms Mikyoung Lee  27-325 
2022-01-26  11:30-1300  Computing Husimi functions using COMSOL Multiphysics file 김주만  선택 
2017-01-10  11:30-12:30  Multiscale Methods for Filtering Turbulent Systems 이윤상  129-310 
2021-08-03  11:20-12:20  Geometric approaches to the local Langlands correspondence I-IV 홍세린  27-220 
2021-08-05  11:20-12:20  Geometric approaches to the local Langlands correspondence I-IV 홍세린  27-220 
2015-05-15  11:10-12:10  Positive maps; non-linear and liner Tsuyoshi Ando  129-301 
2023-07-28  11:00-18:00  Associative Yang-Baxter equations and Fukaya categories 노경민  선택 
2019-07-18  11:00-16:00  Generalized quantum Schur-Weyl duality using quiver Hecke algebras 박의용  129-301 
2021-07-14  11:00-15:00  Transverse foliations for three-dimensional Reeb flows 김성찬  27-220 
2019-07-17  11:00-14:30  Finite-dimensional representations of quantum affine algebras 1, 2 이철희  129-301 
2014-09-05  11:00-13:00  Stable pair invariants and surfaces with holomorphic 2-form Martijn Kool  129-307 
2016-11-15  11:00-13:00  Introduction to moduli space of flat connections over a Riemann surface 1 Nankuo Ho  129-406 
2016-11-17  11:00-13:00  Introduction to moduli space of flat connections over a Riemann surface 2 Nankuo Ho  129-406 
2016-08-08  11:00-13:00  The Unlikely Intersection Theory and the Cosmetic Surgery Conjecture BoGwang Jeon  129-301