SA310, Science Building I, NYCU
(交通大學科學一館 310室)
Determining the sizes of orbits of simplex stabilisers in a Bruhat-Tits building
Rupert McCallum (University of Tübingen)
We will give an account of the notion of an Ihara zeta function and how it may be generalised to the quotient of a Bruhat-Tits tree by a non-uniform lattice. In order to confirm the viability of ideas for generalising this to Bruhat-Tits buildings of higher dimension, certain propositions about the sizes of the orbits of stabilisers of simplices in the lattice on the space of chambers incident to the simplex must be confirmed. We shall present some techniques for determining the sizes of such orbits.
