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seminars
Date 2021-04-26
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.

제목
2023-05-25  15:00-16:00  Recent topics for the regularity of local and nonlocal elliptic equations 이호식  27-325 
2023-05-25  16:00-17:00  Global maximal regularity for equations with variable exponents and degenerate weights in nonsmooth domains Rui Yang  27-325 
2023-05-25  16:00-17:00  Entropy, large deviations, and applications 김태형  선택 
2023-05-17  16:00-18:00  Affinizations, R-matrices and reflection functors 박의용  129-309 
2023-05-16  16:40-17:10  The river of regular quadratic polynomials 김민규  129-101 
2023-05-16  16:00-16:30  Theta series and representation by integral quadratic forms 김대준  129-101 
2023-05-12  15:00-16:00  Shrinking targets on translation surfaces Josh Southerland  129-104 
2023-05-12  16:00-17:00  Computation of the Kontsevich--Zorich cocycle over the Teichmueller flow Dami Lee  129-104 
2023-05-12  16:30-19:00  Regular ternary pentagonal forms 김민규  27-116 
2023-05-09  11:00-13:00  Singualr spherical maximal operators on a class of degenerate two-step nilpotent Lie groups 유재현  129-301 
2023-05-03  16:00-17:30  Super duality for quantum affine superalgebras of type A 이신명  129-406 
2023-05-02  16:40-17:10  Homological Mirror Symmetry of Degenerate Cusps and Their Representations 노경민  129-101 
2023-05-02  16:00-16:30  Why is the Fukaya category important in Symplectic topology? 이상진  129-101 
2023-04-28  13:00-18:00  PGL(2,Q_p)-ORBIT CLOSURES ON A p-ADIC HOMOGENEOUS SPACE OF INFINITE VOLUME 정진호, 김성호  27-325 
2023-04-25  16:00-17:00  Regularity criterion for Navier-Stokes equations in the Fourier space 김남권  27-116 
2023-04-25  17:00-18:30  A proof of Fuglede’s conjecture for convex domains 이진봉  27-116 
2023-04-21  18:00-20:00  Lifting problem for universal quadratic forms over totally real cubic number fields 김대준  27-325 
2023-04-21  10:30-12:00  Non-freeness of certain two-parabolic groups 김상현  129-309 
2023-04-21  15:30-16:30  Joint normality of representations of numbers 손영환  27-116 
2023-04-21  14:00-15:00  Selberg's central limit theorem of L -functions near the critical line 이윤복  27-317