Iwasawa Theory on Graph

BIMSA-YMSC Number Theory Lunch Seminar

Organizers：

Yong Suk Moon, Koji Shimizu

Speaker：

Xiuwu Zhu

Time：

12-1 pm on Thursdays

Oct. 30, 2025

Venue：

BIMSA A4-1

Title:

Iwasawa Theory on Graph

Abstract:

In graph theory, certain covering maps satisfying specific symmetry conditions can be viewed as analogues of Galois extensions in number theory. Recent studies have revealed that, along the $\mathbb{Z}_p$-extension tower of graphs, the sizes of the Jacobian groups exhibit distributional behaviors strikingly similar to those in classical Iwasawa theory. This talk will present the main results of this analogy and highlight a particular example of a $\mathbb{Z}_p$-extension arising from the isogeny graphs of elliptic curves with level structures.