seminars

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

Date 2021-04-26 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.

제목
2019-12-10  16:30-18:00  Spectral independence of compact groups Keivan Mallahi-Karai  129-406
2022-10-04  16:00-17:00  On an extreme value law for the unipotent flow on $$extract_itex$$\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$$/extract_itex$$. Keivan Mallahi Karai  선택
2014-06-11  16:00-17:00  Mirror symmetry and K3 surfaces Kazushi Ueda  129-301
2016-05-02  17:00-18:00  Stability of heat kernel estimates under Feynman-Kac perturbations for symmetric Markov processes Kazuhiro Kuwae  27-116
2018-03-19  11:00-12:10  Twisted Donaldson Invariant (3/19-3/22"room 24-112.25-103) KATO Tsuyoshi  25-103
2018-11-28  14:00-15:30  Geometric structures from dynamical rigidity Kathryn Mann  129-301
2016-07-12  16:00-18:00  The Teichmüller diameter of the thick part of moduli space Kasra Rafi  129-301
2016-07-19  16:00-17:00  Global a priori estimates below the natural exponent for quasilinear equations in non-smooth domains Karthik Adimurthi  129-406
2019-12-23  15:00-16:00  Uniform L^{infty}, Lipschitz and C^{1,alpha} estimates for quasilinear parabolic equations Karthik Adimurthi  27-116
2022-07-05  15:00-17:00  Overview of DeGiorgi-Nash-Moser theory Karthik Adimurthi  27-325
2021-09-29  16:00-18:00  Minimal dynamical systems, C*-algebras, and the classification program Karen Strung  선택
2022-07-18  11:00-12:00  New multiplicity results for critical p-Laplacian problems (joint work with Carlo Mercuri) Kanishka Perera  27-220
2022-12-06  17:00-18:00  Trilinear smoothing inequality and its applications Kalachand Shuin  27-220
2021-12-23  16:00-17:00  Weighted estimates for maximal product of spherical averages Kalachand Shuin  선택
2021-12-24  16:00-17:00  Weighted estimates for bilinear Bochner-Riesz means at the critical index Kalachand Shuin  선택
2021-12-24  17:00-18:00  Bilinear Bochner-Riesz means and square function Kalachand Shuin  선택
2022-05-17  16:00-16:30  Bilinear Bochner-Riesz means and square function Kalachand shuin  129-101
2019-04-05  16:00-18:00  Dynamics of continued fractions and conjecture of Mazur-Rubin Jungwon Lee  27-325
2018-12-14  11:00-12:00  Ergodicity and nodal counting of eigenfunctions on 3-manifolds Junehyuk Jung  27-220
2022-12-02  10:00-11:00  Torsion points and concurrent exceptional curves on del Pezzo surfaces of degree one Julie Desjardins  선택