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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
2017-11-09  16:00-17:00  Infinitely Many Solutions to the Black-Scholes Partial Differential Equation for a European Option: Mathematics Point of View 최병선  129-301 
2017-11-08  16:00-17:00  The non-commutative Khintchine inequality and its implication on Fourier multipliers from L^p into l^1 윤상균  129-301 
2019-01-23  16:00-17:00  Regularity for elliptic equations in heterogeneous media Li-Ming Yeh  129-301 
2017-11-29  16:00-17:00  Additive energy estimates and their application to extension problems for paraboloids in finite fields 고두원  129-301 
2017-12-06  16:00-17:00  The Beurling-Lax-Halmos Theorem 이우영  129-301 
2019-04-26  16:00-17:00  Categorical similarities among the finite dimensional module categories over quantum affine algebras 오세진  27-116 
2019-05-03  16:00-17:00  Infinite rank of abelian varieties over certain infinite extensions Bo-Hae Im  27-325 
2019-05-31  16:00-17:00  Combinatorial proofs between some classes of partition functions 손재범  27-325 
2019-07-03  16:00-17:00  Exact Lagrangian fillings of Legendrian torus knots.Lec 3 배영진  선택 
2019-08-14  16:00-17:00  How to train generative adversarial networks with stochastic gradients Ernest Ryu  129-104 
2019-10-22  16:00-17:00  Well-posedness issues of some dispersive equations under the periodic boundary condition file 곽철광  27-116 
2019-11-01  16:00-17:00  STRUCTURE OF THE MORDELL-WEIL GROUP OVER $\mathbb{Z}_p$ - EXTENSIONS 이재훈  27-325 
2019-11-26  16:00-17:00  A sharp square function estimate for the cone in R^3 고혜림  27-116 
2019-11-27  16:00-17:00  Quantum group and canonical basis 권재훈  129-406 
2018-05-30  16:00-17:00  Quantizing Convolutional Neural Networks for Low-Power High-Throughput Inference Engines Sean O. Settle  129-307 
2021-05-31  16:00-17:00  Overview of some recent developments in geometric topology 백형렬  129-310 
2018-11-13  16:00-17:00  Green's functions and Well-posedness of Compressible Navier-Stokes equation Shih-Hsien Yu  27-220 
2019-03-15  16:00-17:00  A quantitative analysis of the level lowering congruences 김찬호  27-325 
2022-05-11  16:00-17:00  Schatten properties of quantum derivatives on quantum tori file Xiao Xiong  선택 
2019-03-19  16:00-17:00  Transference of Bilinear Restriction Estimates to Quadratic Variation Norms 홍석창  27-116