신청자 김도형 특이사항
초청자 김도형 초청자 이메일 dohyeongkim@snu.ac.kr
일자 Apr 26(Mon), 2021 (15:30 ~ 17:30) 강의실 기타1
세미나 종류 정수론
기타 세미나 종류
세미나 제목 Singular moduli for real quadratic fields III
Abstract 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.
Zoom Meeting ID : 817 7139 5843
Passcode : 165930

-서울대학교 기초과학연구원 중점연구소 지원사업
강연자 Jan Vonk
소속 기관명 Leiden University
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