Seminar Autumn 2024
The seminars take place on Wednesdays from 2-3 pm during term time in Horten Lecture Theatre 1 (HLT 1). They are aimed to appeal to most of our staff and PhD students. They are followed by coffee, tea and biscuits in the McCrea building (next to room 0-08). Most times we will go to dinner afterwards.
Everyone is welcome!
18th September: Jan-Christoph Schlage-Puchta (University of Rostock)
Title: Numerical computation of the Witten zeta function of symmetric groups and Fenchel's conjecture
Let G be a group. Then define ζG(s), the Witten ζ-function of G, as the sum over all χ in Irr(G) of χ(1)-s, where Irr(G) denotes the set of irreducible characters. The series of functions ζSn(s) has first been studied by Lulov in the connection with random walks on Sn, later it was used to study the subgroup growth of surface groups and Fuchsian groups.
While the behaviour of ζSn(s) is easy to describe for when n tends to infinity, computing values for specific values of n and s is computationally demanding, as the number of representations of Sn grows like exp(π √(2n/3)).
Here we give an algorithm that produces reasonable approximations for ζSn(s) for medium sized values of n. As applications we prove a stronger versions of Fenchel's conjecture: Every Fuchsian group contains a torsion free subgroup of the minimal index for which such a subgroup is not prohibited by congruence restrictions.
25th September: Heather Leitch (Royal Holloway, University of London)
2nd October at 3pm: Robert Johnson (Queen Mary, University of London)
Starts at 3pm!
16th October: Antony Hilton (University of Reading)
Title: The total chromatic number of a graph
23rd October: Will Cohen (University of Cambridge)
30th October: Revision week - no seminar
6th November: Steve Lester (King's College London)
13th November: Olivea Reade (Open University)
11th December: Julia Wolf (University of Cambridge)
