Mathematics Symposium, organised by the Department of Mathematical Sciences of CIÊNCIAS, featuring Antonio Lei (Univ. Ottawa, Canada).
Abstract: Classical Iwasawa theory investigates how arithmetic invariants from number theory and arithmetic geometry, including ideal class groups, elliptic curves, modular forms, and abelian varieties, behave along infinite towers of number field extensions. More recently, an analogue of Iwasawa theory has been developed in a combinatorial context, where one studies invariants associated with infinite towers of graph coverings. In this talk, I will survey some recent progress in this area and illustrate how these ideas can be used to establish connections between isogeny graphs and modular curves over finite fields.