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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Jul 12, 2018  15:00-17:00  Isolated points in the spectrum of linear pencil of operators Slavisa V. Djordjevic  129-406
Jul 27, 2018  15:00-17:00  Regularity for multi-phase variational problems 오제한  27-325
Aug 08, 2018  15:00-17:00  Taylor spectra of a spherically quasinormal pair of operators 윤자상  129-307
Sep 12, 2017  15:00-17:00  Three-distance theorem and some constructions for the higher-dimensional 김동한  129-301
Sep 20, 2017  15:00-17:00  Structure of Entropy solutions in one space dimension for convex flux and its applications Adimurthi  27-116
Oct 27, 2017  15:00-17:00  Metrical theory for the set Dirichlet non-improvable numbers Mumtaz Hussain  129-104
Dec 07, 2018  15:00-17:00  Discrete radial absorbing boundary condition for wave equations 전영목  129-310
May 23, 2019  15:00-17:00  Generalized Aluthge transforms, spherically log and p-hyponormal operators, and their powers I Jasang Yoon  27-116
May 24, 2019  15:00-17:00  Generalized Aluthge transforms, spherically log and p-hyponormal operators, and their powers II Jasang Yoon  27-116
Oct 12, 2019  15:00-17:00  Regularity for generalized double phase functionals 오제한  27-325
Apr 11, 2018  15:00-17:00  Analysis of pseudoholomorphic curves and Hofer's displacement energy 오용근  129-406
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Jul 03, 2018  15:00-17:00  The topological Fukaya category and mirror symmetry for 3d toric LG models Nicolo Sibilla  129-406
Jul 04, 2018  15:00-17:00  Log schemes, root stacks and parabolic bundles Nicolo Sibilla  129-406
Feb 24, 2020  15:00-17:00  Codimension two cycles in Iwasawa theory Bharathwaj Palvannan  27-116
Jun 14, 2019  15:00-17:00  Abundance of irreducible tensor product of linear operators Caixing Gu  27-116
Jul 23, 2019  15:00-17:00  Financial crises, regime dependence and, BSDEs in filtrations without martingale representation theorem Stephan Sturm  129-307
Jul 25, 2019  15:00-17:00  Comparing large-scale graphs based on quantum probability theory 최하영  129-301
Feb 04, 2020  15:00-17:00  Developing Nonlinear Procedures for PDEs: Regularized Long-Wave equation 장택수  129-104