You are cordially invited to the Department of Mathematics Colloquium
Speaker: Shinichi Kobayashi (Kyushu University)
“p-adic Aspects of the Coefficients of the Weierstrass Sigma Function”
Abstract: The coefficients of the Weierstrass sigma function of an elliptic curve are arithmetically significant. In the case of complex multiplication, they are related to special values of Hecke L-functions of imaginary quadratic fields and to anticyclotomic Iwasawa theory. For elliptic curves with ordinary reduction at a prime p, the p-adic properties of the sigma function are well understood, notably through the Mazur–Tate p-adic sigma function and its applications to p-adic height pairings. In contrast, at a prime of supersingular reduction, the speaker has established relations between the p-adic radius of convergence and p-adic periods. In this talk, we explain these results and, time permitting, discuss further recent developments.
Biography: Shinichi Kobayashi is a leading researcher in number theory and arithmetic geometry, with particular emphasis on Iwasawa theory, elliptic curves, and p-adic methods. He is a Professor of Mathematics at Kyushu University, and previously held academic positions at Nagoya University and Tohoku University. His research has made influential contributions to the arithmetic of elliptic curves—especially the study of Selmer groups, supersingular primes, and p-adic L-functions—closely connected with central problems and conjectures in modern arithmetic geometry, including the Birch and Swinnerton–Dyer conjecture. He is a recipient of the Mathematical Society of Japan’s Algebra Prize, recognizing his impact on Iwasawa theory, and his work has appeared in leading journals such as Annals of Mathematics, Inventiones mathematicae, and Duke Mathematical Journal.
Date: Tuesday, March 10, 2026
Time: 11:40-12:40
Place: Mathematics Seminar Room, SA-141