Global Iwasawa theory of graphs and p-adic Mahler measures

par Riccardo Pengo

jeudi 25 juin 2026, 14:00 → 19:00 Europe/Paris

The number of spanning trees of a finite graph can be seen as an analogue of the class number of a number field. In this talk, we will first of all explain how one can study how the number of spanning trees varies in certain particular inverse systems of graphs, parametrized by the natural numbers, using the Archimedean and p-adic Mahler measures of certain polynomials with integer coefficients. This part will be based on joint work with Daniel Vallières. If time permits, we will explore the connections between this question and other more Diophantine problems, such as a famous question asked by Lehmer on the smallness of the Archimedean Mahler measure.