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seminars
Date Apr 26, 2021
Speaker Jan Vonk
Dept. Leiden University
Room 선택
Time 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
Nov 01, 2022  15:00-16:00  Fredholm Property of the Linearized Boltzmann Operator for a Mixture of Polyatomic Gases Marwa Shahine  27-325 
Nov 01, 2022  16:00-18:00  A stationary set method for estimating oscillators integrals 오세욱  27-116 
Nov 01, 2022  16:00-17:00  Approaches to the alleviation of the burden of learning for Weakly Supervised Object Localization 구본경  129-301 
Oct 26, 2022  16:00-18:00  Free Probability, Regularity, and Free Stein Dimension Ian Charlesworth  129-406 
Oct 25, 2022  10:00-11:00  Rational liftings and gRSK Travis Scrimshaw  선택 
Oct 25, 2022  11:00-12:00  Crystal Invariant Theory Travis Scrimshaw  선택 
Oct 25, 2022  15:00-18:00  Ergodic theory of complex continued fraction maps Hitoshi Nakada  129-406 
Oct 21, 2022  14:00-15:00  Regularity properties of Brjuno functions associated with classical continued fractions 이슬비  선택 
Oct 19, 2022  15:30-16:20  일본에서의 ODE 발전에 대해서 신정선  27-325 
Oct 18, 2022  16:00-16:30  Genera of manifolds 김승원  129-101 
Oct 18, 2022  16:40-17:10  Counting surfaces on Calabi-Yau 4-folds 박현준  129-101 
Oct 18, 2022  10:00-12:00  Remarks on the long-time dynamics of 2D Euler Theodore Drivas  선택 
Oct 17, 2022  13:00-14:30  The rank of new regular quadratic forms 김민규  27-325 
Oct 12, 2022  11:00-12:00  Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction file Jacky Chong  선택 
Oct 12, 2022  16:00-18:00  Haagerup inequalities on non-Kac free orthogonal quantum groups 윤상균  129-406 
Oct 11, 2022  17:00-18:00  On limits of sequences of operators 유재현  27-116 
Oct 05, 2022  16:00-18:00  A universal framework for entanglement detection of invariant quantum states 박상준  선택 
Oct 04, 2022  16:00-17:00  On an extreme value law for the unipotent flow on $\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$. Keivan Mallahi Karai  선택 
Oct 04, 2022  16:00-18:00  On the maximal Bochner-Riesz conjecture for p>2 유재현  27-116 
Oct 04, 2022  16:00-16:30  Universality Classes in Probability Theory 변성수  129-101