KIAS Number Theory Seminar

Upcoming seminars

May 13 (Thu), 2021, 15:30--16:30, online

Title: Congruences for weakly holomorphic modular forms of half-integral weight

Speaker: Subong Lim (Sungkyunkwan University)

Abstract: In this talk, we discuss congruences involving U_l operator for weakly holomorphic modular forms of half-integral weight. By using this, we obtain the distribution of the Fourier coefficients of weakly holomorphic modular forms in congruence classes. This applies to the congruence properties for traces of singuli moduli.

June 17 (Thu), 2021, 16:00--17:00, online

Title: TBA

Speaker: Hae-Sang Sun (UNIST)

Abstract: TBA

Past seminars

April 15 (Thu), 2021, 10:00--11:00, online

Title: Robba-valued cohomology

Speaker: Koji Shimizu (UC Berkeley)

Abstract: Rigid cohomology is a good p-adic cohomology theory for algebraic varieties in characteristic p. In this talk, I will explain a relevant idea by Monsky and Washnitzer and then discuss my ongoing attempt to define a p-adic cohomology theory for rigid analytic varieties over a local field of characteristic p.

April 01 (Thu), 2021, 17:00--18:00, online

Title: On Euler systems for adjoint modular Galois representations

Speaker: Eric Urban (Columbia University)

Abstract: The purpose of this talk is to illustrate a new method to construct Euler systems based on the study of congruences between modular forms of arbitrary weights and level and their corresponding deformations of Galois representations. We will focus on the case of adjoint modular Galois representations attached to an ordinary eigenform and connect our construction to a conjecture for the Fitting ideal of the equivariant congruence module attached to the abelian base changes of that moduar form.

March 05 (Fri), 2021, 10:30--11:30, online

Title: Some analytic quantities having arithmetic information on elliptic curves

Speaker: Masato Kurihara (Keio University)

Abstract: I will discuss some analytic quantities constructed from modular symbols for a rational elliptic curve, which have some interesting arithmetic information on the Mordell-Weil group and related subjects.

February 04 (Thu), 2021, 10:00--11:00, online

Title: Slopes of modular forms and the ghost conjecture

Speaker: Robert Pollack (Boston University)

Abstract: Modular forms are mathematical objects born in complex analysis but in fact have become central objects in number theory. In particular, special modular forms, called eigenforms, have Fourier coefficients which are algebraic integers and these integers contain loads of number theoretic data. In this talk, we will focus on one slice of this data, namely, the highest power of p dividing the pth Fourier coefficient (called the slope of the form). Through many numerical examples, we will discuss the properties of these slopes and ultimately state the so-called "ghost conjecture" which predicts them in a combinatorial way.

Please send one of the organizers an email if you are interested in giving a talk. If you want to receive regular email announcement, please send an email with your name/affiliation, in title of "subscribe", to the organizer.

The first number theory seminar started March 10th, 2005 and it became a regular seminar since then. For more information on the early history of the number theory seminar, see the article (by Soon-Yi Kang in KIAS News Letter, Fall 2005) and the following archive files.

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Number Theory Group at KIAS

Choi, Youn-Seo
Choi, Junhwa (
Kim, Chan-Ho
Lee, Chulhee
Lee, Jungin
Yu, Myungjun