UBC Math Department Colloquium: Antonio Lei

Classical Iwasawa theory studies the variation of arithmetic invariants, such as ideal class groups, along infinite towers of number field extensions. Over the years, these ideas have been extended to a wide range of arithmetic objects, including elliptic curves, modular forms, and abelian varieties. More recently, an analogue of Iwasawa theory has emerged in a combinatorial setting, where one studies invariants associated with towers of graph coverings. To date, most results in this area have focused on undirected graphs. In this talk, I will survey recent developments and explain how several of these ideas can be extended to the broader setting of directed graphs.