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.

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2017-12-06  17:00-18:30  Computational Algebraic Geometry and Computer Vision II Joe Kileel  129-406 
2017-12-08  17:00-18:30  Computational Algebraic Geometry and Computer Vision III Joe Kileel  129-104 
2019-04-16  16:00-17:00  On the inverse Galois problem with ramification conditions Joachim König  27-325 
2015-10-08  09:30-14:30  Post-quantum cryptography:Multivariate Public Key Cryptography Jintai Ding  129-301 
2022-06-04  10:20-10:50  C 1,α-regularity for nonlinear equations Jihoon Ok  27-325 
2018-12-26  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 
2017-02-06  10:00-11:30  Lecture 1. Vertex Algebras and the Free Boson Jethro van Ekeren  129-406 
2017-02-06  14:00-15:30  Lecture 2. The Free Fermion and the Boson-Fermion Correspondence Jethro van Ekeren  129-406 
2017-02-08  10:00-12:00  Lecture 3. The Virasoro Algebra Jethro van Ekeren  129-406 
2021-10-12  09:30-11:00  Vertex algebras and chiral homology I Jethro van Ekeren  선택 
2021-10-14  09:30-11:30  Vertex algebras and chiral homology II Jethro van Ekeren  선택 
2018-04-19  16:00-18:30  Decompositions of 3-manifolds and hyperbolic geometry Jessica Purcell  27-116 
2018-04-20  16:00-17:30  Decompositions of 3-manifolds and hyperbolic geometry (second talk) Jessica Purcell  129-104 
2017-06-22  14:00-15:00  Higher order multipoint flux mixed finite element methods Jeonghun Lee  선택 
2015-05-21  16:00-17:00  RECENT TRENDS: DYNAMIC CONTACT PROBLEMS Jeongho Ahn  129-104 
2016-05-16  16:00-17:00  DYNAMIC CONTACT OF NONLINEAR BEAMS Jeongho Ahn  27-325 
2017-06-06  16:00-17:00  Mathematical and numerical approaches to dynamic contact of nonlinear springs Jeongho Ahn  27-325 
2019-12-23  14:00-15:00  A frictional thermoviscoelastic nonlinear beam problem Jeongho Ahn  27-116 
2022-05-18  17:00-18:00  A dynamic contact problem with Signorini’s condition and the normal compliance file Jeongho Ahn  27-325