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
Jan 15, 2021  15:00-17:00  Voronoi summation formulas and the first moments of L-functions Min Lee  선택
May 14, 2021  15:00-17:00  Introduction to derived categories 조창연  선택
Jul 04, 2022  15:00-17:00  강연1: Scale-invariant tangent-point energies for knots and fractional harmonic maps / 강연2: On Calderon-Zygmund type estimates for nonlocal PDE Armin Schikkora  27-220
Jul 04, 2022  15:00-17:00  Free Random Variables followed by the Semicircular Law Il Woo Cho  129-406
Jul 05, 2022  15:00-17:00  Overview of DeGiorgi-Nash-Moser theory Karthik Adimurthi  27-325
Dec 02, 2022  15:00-17:00  N=2 supersymmetric W algebras from Hamiltonian reduction Eric Ragoucy  27-116
Jan 13, 2023  15:00-17:00  Nonclassicality and Entanglement beyond Gaussian Regime 나현철  선택
Feb 03, 2023  15:00-17:00  Infinitely wide neural networks 양홍석  선택
Feb 08, 2023  15:00-17:00  Infinitely wide neural networks 양홍석  선택
Feb 10, 2023  15:00-17:00  Infinitely wide neural networks 양홍석  선택
Dec 11, 2017  15:00-17:30  딥러닝에 있어서의 체인룰의 역할 김영록  129-301
Jul 02, 2019  15:00-17:30  Exact Lagrangian fillings of Legendrian torus knots. Lec 1,2 배영진  129-310
May 14, 2019  15:00-17:30  Martin boundary covers Floyd boundary Wenyuan YANG  27-220
Jun 21, 2016  15:00-18:00  Linear recurrence relations in Q-systems Chul-hee Lee  129-406
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
Dec 07, 2021  15:00-18:00  The canonical commutation relations and the local geometry of symplectic spaces 김현문  27-325
Oct 25, 2022  15:00-18:00  Ergodic theory of complex continued fraction maps Hitoshi Nakada  129-406
Oct 18, 2019  15:10-16:10  Introduction to Dwork's theory 박지훈  129-104
Mar 26, 2019  15:30-16:20  The nonlinear Brascamp-Lieb inequality Neal Bez  27-116