https://www.math.snu.ac.kr/board/files/attach/images/698/d7f811aae9dfd8ef6b3d16c547a28844.png
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
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2018-10-19  09:00-11:00  An introduction to intrinsic scaling Lecutre III Jose Miguel Urbano  27-325 
2018-10-22  09:00-11:00  An introduction to intrinsic scaling Lecutre IV Jose Miguel Urbano  27-325 
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2017-12-18  11:00-13:00  Universal sums of generalized polygonal numbers Ben Kane  27-325 
2019-05-03  16:00-17:00  Infinite rank of abelian varieties over certain infinite extensions Bo-Hae Im  27-325 
2019-05-24  17:00-18:00  p-adic analogue of Riemann-Hilbert correspondence Yong Suk Moon  27-325 
2017-12-29  13:00-17:00  A Series of Invited Talks 김유찬외 3인  27-325