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.

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Feb 08, 2023  15:00-17:00  Infinitely wide neural networks 양홍석  선택 
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May 14, 2019  15:00-17:30  Martin boundary covers Floyd boundary Wenyuan YANG  27-220 
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Feb 02, 2018  15:00-18:00  Coalgebraic principles of quantum field theory (two lectures) Jae-suk Park  27-325 
Jun 20, 2019  15:00-18:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116 
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Oct 25, 2022  15:00-18:00  Ergodic theory of complex continued fraction maps Hitoshi Nakada  129-406 
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Mar 26, 2019  15:30-16:20  The nonlinear Brascamp-Lieb inequality Neal Bez  27-116 
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