Event
Alexander Kolpakov, University of Neuch芒tel
Friday, October 6, 2017 13:30to14:30
Room PK-4323, Seminar LACIM, 201 Ave. President-Kennedy, Montreal, QC, H2X 2Y7, CA
Counting subgroups and hypermaps: common points.
We derive a generating series for the number of free subgroups of finite index in certain free products of cyclic groups. We also find a generating series for the number of their conjugacy classes. Both solutions rest on a connection between counting free subgroups and counting hypermaps (or their generalisations). We provide non-linear recurrence relations for the number of objects of both kinds, and prove that in some cases the generating series is not D-finite, and in all cases it is not algebraic. The talk will focus on the interplay between algebra, geometry and combinatorics in the above problems.