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
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Jun 17, 2021  16:00-17:00  Pairs Trading of two Assets with uncertainty in co-integration's level of mean reversion 이상민  27-325
Jun 11, 2021  14:30-15:30  The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma 주장원  27-116
Jun 07, 2021  11:00-12:00  Iwasawa Theory of Elliptic Curves Debanjana Kundu  선택
Jun 04, 2021  09:00-10:30  Superposition principle for stochastic nonlinear Fokker-Planck-Kolmogorov equations Marco Rehmeier  129-301
Jun 04, 2021  16:00-17:00  Problems for the Hermite and special Hermite expansions 유재현  27-220
Jun 04, 2021  14:00-16:00  Introduction to derived categories 조창연  선택
Jun 03, 2021  10:30-12:30  Locking-free and locally-conservative enriched Galerkin methods for linear poroelasticity 이상현  129-310
Jun 02, 2021  16:00-18:00  Sums of free variables in symmetric spaces Éric Ricard  선택
Jun 01, 2021  14:00 ~ 15:00  Topics in the singularities of plurisubharmonic functions 안종봉  27-220
Jun 01, 2021  16:00-17:00  On the Bochner-Riesz operator in R^3 정은희  선택
May 31, 2021  16:00-17:00  Overview of some recent developments in geometric topology 백형렬  129-310
May 31, 2021  11:00-12:00  Iwasawa Theory of Elliptic Curves Debanjana Kundu  선택
May 28, 2021  09:00-11:00  Nonuniqueness in law for stochastic hypodissipative NSE Marco Rehmeier  27-220
May 28, 2021  14:00-16:00  Topological entropy 0 and conformal dimension 1 in complex dynamics 박인성  27-220
May 28, 2021  15:30-16:30  RAMANUJAN CONTINUED FRACTIONS OF ORDER SIXTEEN 박윤경  선택
May 28, 2021  10:00-12:00  Introduction to derived categories 조창연  선택
May 27, 2021  17:00-18:00  Robustness of deep neural networks to adversarial attack: from heuristic methods to certified methods 이성윤  27-116
May 26, 2021  10:00-11:00  Characterizations of the plane and the catenoid as free boundary minimal surfaces 연응범  27-220
May 26, 2021  11:00-12:00  Uniqueness and existence results of minimal surfaces in four-dimensional Euclidean space 이재훈  27-220