A lecture by Ming-Lun Hsieh (National Taiwan University) will be held as follows:

Date & Time: Thursday, March 12, 2026, 14:00–15:30
Venue: Room 127, Science Building No. 3, Graduate School of Science, Kyoto University

Title：「Modular forms and Selmer groups」

Abstract：
The classical class number formula for imaginary quadratic fields reveals a mysterious and profound connection between the special values of L-functions and the size of ideal class groups.
In 1990, Spencer Bloch and Kazuya Katoformulated the so-called Bloch–Kato conjecture, a far-reaching generalization of the class number formula.
This conjecture predicts a deep relationship between the special values of motivic L-functions at integers and the sizes of Selmer groups, which are defined in terms of certain Galois cohomology groups.
Currently, there are two major approaches to studying this conjecture. One is the theory of Euler systems, which is used to bound the size of Selmer groups in terms of special values of L-functions.
The other approach uses congruences between modular forms to construct nontrivial elements in Selmer groups arising from special L-values.
The purpose of this lecture is to survey important examples studied via the method of modular form congruences and to report on some recent progress in this direction.

◆No registration is required for Kyoto University students.

◆This lecture is part of the Kyoto University Super Global Education Program, Super Global Course (Mathematics).
For more details about the course, please visit:　 https://www.math.kyoto-u.ac.jp/ja/ktgu/ktgu