Combinatorics of subgroup counting in free products of cyclic groups, and other stories

Vortrag von Prof. Dr. Alexander Kolpakov

Datum: 11.04.18  Zeit: 15.45 - 18.00  Raum: ETH HG G 43

We shall derive a generating series for the number of free subgroups of finite index in certain free products of cyclic groups. We shall also give a generating series for the number of their conjugacy classes. This computation turns out the same as counting the number of orientable cellular complexes of dimension 2 and 3 (or even higher), as well as their isomorphism classes. Our solution rests on a classical theory by Jones and Singerman, later developed by Lienhardt and co-authors, and on the theory of species by Joyal, Flajolet and Sedgewick. There is also a number of curious facts related to the mentioned functions. The talk will focus on the interplay between algebra, geometry and combinatorics.This is joint work with Laura Ciobanu (Heriot-Watt University, UK).