分野別セミナー

アブストラクト：Iwasawa theory for graphs describes the asymptotic behavior of the numbers of the spanning trees in a compatible system of $\mathbb{Z}/p^n\mathbb{Z}$-covers of graphs, where $p$ is a fixed prime number. In this talk, we will generalize
Iwasawa theory for graphs to that for weighted graphs, and this allows us to estimate the behavior of the weighted
complexities instead of the numbers of spanning trees. Depending on how we set the weights on graphs, the
information we can extract from weighted complexities changes. Our generalization contains theories on compatible
systems of $(\mathbb{Z}/p^n\mathbb{Z})^d$-covers including Kida’s formula, which is the Iwasawa theoretical analogue of the Riemann—Hurwitz formula. We also provide several examples. We will start explaining historical backgrounds of Iwasawa
theory and rudimentary theories of graphs without being overly pedantic. This is a joint work with Taiga Adachi and
Kosuke Mizuno.

URL: https://sites.google.com/view/mathpolynomial