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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
2018-03-21  16:00-18:00  Fourier analysis arising from type III representations of the noncommutative 2-torus Francesco Fidaleo  129-301 
2019-08-12  14:00-16:00  Maximally graded matrix factorizations for an invertible polynomial of chain type Atsushi Takahashi  129-301 
2018-03-28  16:00-18:00  On Heisenberg modules over noncommutative tori Franz Luef  129-301 
2018-04-04  16:00-18:00  Separability of multi-qubit states in terms of diagonal and anti-diagonal entries 계승혁  129-301 
2019-08-16  15:00-16:00  Autocorrelation functions of characteristic polynomial of Sato-Tate groups 이규환  129-301 
2019-09-18  16:00-17:30  Indecomposable exposed positive multi-linear maps and applications to quantum information theory 계승혁  129-301 
2019-09-25  16:00-18:00  Twisted crossed product algebras arose from physical systems 이기현  129-301 
2018-04-06  13:30-15:30  양자알고리즘 및 양자머신러닝 방정호  129-301 
2018-04-11  16:00-18:00  Resource theory of quantum coherence 권혁준  129-301 
2018-04-13  11:00-13:00  Activation of quantum capacity of Gaussian channels 임영롱  129-301 
2019-10-02  16:00-18:00  Twisted Fourier(-Stieljes) space, multipliers and amenability 이훈희  129-301 
2018-04-20  16:00-18:00  Lecture Hall Tableaux 김장수  129-301 
2018-04-25  16:00-18:00  정보이론, 양자정보 그리고 함수해석 이훈희  129-301 
2018-05-02  16:00-18:00  Open quantum random walks as quantum Markov chains 유현재  129-301 
2018-05-16  16:00-18:00  Canonical Systems on Spectral Theory 허인조  129-301 
2019-10-16  17:00~18:00  On the applications of representable and continuous functionals on Banach Quasi *-algebras to their tensor products file Maria Stella Adamo  129-301 
2018-05-23  16:00-18:00  Resolution of wavefront sets using wavelets Mahya Ghandehari  129-301 
2019-11-06  16:00-17:30  The Beurling-Lax-Halmos Theorem for infinite multiplicity (I) file 이우영  129-301 
2019-11-27  16:00-17:30  UCT for discrete quantum groups Yuki Arano  129-301 
2019-12-04  16:00-18:00  The Beurling-Lax-Halmos Theorem for infinite multiplicity (II) file 이우영  129-301