https://www.math.snu.ac.kr/board/files/attach/images/698/d7f811aae9dfd8ef6b3d16c547a28844.png
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
Feb 04, 2021  14:00-15:30  Auslander-Reiten transformation and tau-tilting theory Sota Asai  선택 
Feb 05, 2021  14:00-15:30  Auslander-Reiten transformation and tau-tilting theory Sota Asai  선택 
Feb 09, 2021  11:00-12:00  Note on Solving FBSDE using BSDE 남기훈  선택 
Feb 25, 2021  14:30-17:00  Zeta함수와 L함수에 대한 역사적 고찰Ⅸ 신석우  선택 
Mar 03, 2021  14:30-16:45  Zeta함수와 L함수에 대한 역사적 고찰 Ⅹ 신석우  선택 
Mar 08, 2021  16:30-17:30  On class groups of random number fields Alex Bartel  선택 
Mar 15, 2021  16:30-17:30  On class groups of random number fields Alex Bartel  선택 
Mar 22, 2021  16:30-17:30  On class groups of random number fields Alex Bartel  선택 
Mar 16, 2021  11:00-12:00  Transfer operators and limit laws for typical cocycles Kiho Park  선택 
Mar 19, 2021  14:00-16:00  QKD 기반의 보안네트워크 구축 손일권  선택 
Apr 12, 2021  15:30-16:30  Singular moduli for real quadratic fields I Jan Vonk  선택 
Apr 19, 2021  15:30-16:30  Singular moduli for real quadratic fields II Jan Vonk  선택 
Apr 26, 2021  15:30-16:30  Singular moduli for real quadratic fields III Jan Vonk  선택 
Apr 09, 2021  14:00-16:00  Bound entangled states that allow players to distill one-way genuine secret-sharing state 최민진  선택 
May 12, 2021  16:00-18:00  Functional analytical techniques in the analysis of infinitely wide neural networks 류경석  선택 
May 14, 2021  15:30-16:30  On some results about non-holomorphic Jacobi forms 진석호  선택 
May 03, 2021  15:30-16:30  Local Shimura varieties and their cohomology I, II, III David Hansen  선택 
May 10, 2021  15:30-16:30  Local Shimura varieties and their cohomology I, II, III David Hansen  선택 
May 17, 2021  15:30-16:30  Local Shimura varieties and their cohomology I, II, III David Hansen  선택 
Feb 01, 2021  17:00-17:45  Dynamics of Ostrowski skew-product: Limit laws and Hausdorff dimensions 이정원  선택