seminars

$$heading_1$$ Singular moduli for real quadratic fields III

Date Apr 26, 2021 Jan Vonk Leiden University 선택 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
Mar 24, 2021  16:00-18:00  Type semigroups of ample groupoids, and a purely-infinite/stably-finite dichotomy Aidan Sims  129-406
Mar 31, 2021  16:00-18:00  Concavity of certain trace functionals and applications to data processing inequalities Haonan Zhang  129-406
Apr 02, 2021  10:30-12:00  Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types. 오세진  선택
Apr 02, 2021  15:30-16:30  CM congruence and the derivatives of p-adic L-functions for imaginary quadratic fields Ming-Lun Hsieh  선택
Apr 06, 2021  16:00-17:00  Hamiltonian structure, Stability, and Variational methods 석진명  선택
Apr 06, 2021  16:00-16:30  Generalization of Synchronization models 박한솔  129-101
Apr 06, 2021  16:40-17:10  The Regularity Theory for the Double Obstacle Problem 박진완  129-101
Apr 07, 2021  16:00-18:00  Furstenberg boundary for discrete quantum groups Roland Vergnioux  129-406
Apr 09, 2021  14:00-16:00  Bound entangled states that allow players to distill one-way genuine secret-sharing state 최민진  선택
Apr 12, 2021  15:30-16:30  Singular moduli for real quadratic fields I Jan Vonk  선택
Apr 14, 2021  16:00-18:00  Boundary and rigidity of nonsingular Bernoulli actions Yusuke Isono  129-406
Apr 16, 2021  15:30-16:30  Hecke system of harmonic Maass functions and applications to modular curves of higher genera 김창헌  선택
Apr 19, 2021  15:30-16:30  Singular moduli for real quadratic fields II Jan Vonk  선택
Apr 20, 2021  16:00-16:30  Simplicial networks for higher-order Interactions 이강주  129-101
Apr 20, 2021  16:40-17:10  Data-driven chance-constrained optimization under Wasserstein ambiguity 이다빈  129-101
Apr 21, 2021  16:00-18:00  Polytope structures for Greenberger-Horne-Zeilinger diagonal states 계승혁  129-406
Apr 26, 2021  15:30-16:30  Singular moduli for real quadratic fields III Jan Vonk  선택
May 03, 2021  15:30-16:30  Local Shimura varieties and their cohomology I, II, III David Hansen  선택
May 04, 2021  16:40-17:10  Deformation of period integrals and its application 김예슬  129-101
May 04, 2021  16:00-16:30  Demazure modules and $$extract_itex$$0$$/extract_itex$$-Hecke modules of type $$extract_itex$$A$$/extract_itex$$ 최승일  129-101