Back to WTC Winter 2004

Noel Brady
Filling invariants for finite groups

    We will describe a collection of simple geometric
constructions  which yield groups with interesting first and
second order Dehn functions. The second order Dehn function is a
higher dimensional analogue of the standard Dehn function (or isoperimetric function).

Tadeusz Januszkiewicz
Simplicial nonpositive curvature

Ian Leary
Elements of finite order in VF groups

    A group G is VF if it has a finite-index subgroup
admitting a finite classifying space.  K. S. Brown showed that
each VF group contains only finitely many conjugacy classes of
elements of prime power order.  I shall give a construction of
a VF group containing infinitely many conjugacy classes of
elements of order 6.  This is based on earlier joint work of
mine with B. E. A. Nucinkis.

Kevin Wortman
Finiteness properties of arithmetic groups over function

In this talk we'll focus on proofs of Nagao's theorem that SL_2(F[t])
is not finitely generated, and of Behr's theorem that SL_3(F[t]) is not
finitely presented. Here F[t] is a ring of polynomials in one variable t
with coefficients in a finite field F.

The proofs I will present are special cases of the proof Kai-Uwe Bux and I
used to verify the conjecture that an arithmetic subgroup of a reductive
group G defined over a global function field K is of type  FP_\infty  if
and only if the semisimple K-rank of G equals 0.

This conjecture had its roots in the work of Serre and Stuhler. Our proof
is motivated by the Epstein-Thurston proof that SL_n(Z) is not combable
when n>2.