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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
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2023-12-26  14:00-17:00  Quantum Connections and Mirror Symmetry 김용환  129-309 
2023-12-27  11:00-12:30  Pressure–Poisson Equation in Numerical Simulation of Cerebral Arterial Circulation and Its Effect on the Electrical Conductivity of the Brain Maryam Samavaki  129-309 
2024-01-03  11:00-13:00  Fluid Equations and Dynamic Blood Flow Maryam Samavaki  129-309 
2024-03-29  10:00-12:00  Littlewood-Paley-Stein inequality to the Burkholder-Gundy inequality Zhendong Xu  129-309 
2024-04-05  10:00-12:00  First Example of a Maximal Amenable Subalgebra in Quantum Group Context Xumin Wang  129-309 
2024-05-31  10:00-12:00  Representing topological full groups in Steinberg algebras and C*-algebras 강은지  129-309 
2024-06-05  17:00-18:15  Introduction to spectral network Eugen Rogozinnikov  129-309 
2024-07-22  14:00-15:30  Acylindrical hyperbolicity of outer automorphism groups of right-angled Artin groups 김준석  129-309 
2024-08-28  15:00-16:00  Construction of Markov processes by the martingale problem with a special focus on non-local generators: part 1 Walter Hoh  129-309 
2024-11-05  16:00-17:00  On the distribution of primitive lattice points in large dimensions 한지영  129-309 
2024-11-15  14:00-16:30  Lagrangian knot problems in symplectic four-manifolds 김준태  129-309 
2024-11-18  14:00-16:30  Lagrangian knot problems in symplectic four-manifolds 김준태  129-309 
2024-12-27  11:00-12:00  Area measures and branched polymers in supercritical Liouville quantum gravity Jinwoo Sung  129-309 
2025-01-02  16:00-17:00  On-Diagonal Upper Heat Kernel Estimates for Symmetric Dirichlet Forms on Doubling Spaces Soobin Cho  129-309 
2025-01-03  11:00-12:00  Slim and fat triangles in random graphs Joon-Hyeok Yim  129-309 
2025-01-03  14:00-15:30  Non-commutative nodal curves and their homological mirror symmetry Kyungmin Rho  129-309 
2014-03-17  10:30-12:00  Probabilistic Topic Models: Models and Applications 김성현  129-310 
2014-03-24  10:30-12:00  Tutorial for Topological Data Analysis Talks Cho, Eungchun  129-310 
2014-05-01  14:00-15:00  Rational torsion points of $J_0(pq)$ 유화종  129-310