Thestudyofthesubgroupgrowthofin? nitegroupsisanareaofmathematical research that has
grown rapidly since its inception at the Groups St. Andrews conferencein1985. Ithasbecomearichtheoryrequiringtoolsfroma …

We study representation zeta functions of finitely generated, torsion-free nilpotent groups
which are groups of rational points of unipotent group schemes over rings of integers of …

We introduce new methods from p-adic integration into the study of representation zeta
functions associated to compact p-adic analytic groups and arithmetic groups. They allow us …

We prove that the theory of the p-adics Qp admits elimination of imaginaries provided we
add a sort for GLn (Qp)/GLn (Zp) for each n. We also prove that the elimination of …

We construct an uncountable family of finitely generated groups of intermediate growth, with
growth functions of new type. These functions can have large oscillations between lower …

Let be a number field with ring of integers. We compute the local factors of the normal zeta
functions of the Heisenberg groups at rational primes which are unramified in. These factors …

We introduce and study a class of multivariate rational functions associated with hyperplane
arrangements, called flag Hilbert–Poincaré series. These series are intimately connected …

We develop techniques for computing zeta functions associated with nilpotent groups, not
necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the …

Let O be a compact discrete valuation ring of characteristic 0. Given a module M of matrices
over O, we study the generating function encoding the average sizes of the kernels of the …

We consider pro-isomorphic zeta functions of the groups $\Gamma (\mathcal {O} _K) $,
where $\Gamma $ is a unipotent group scheme defined over $\mathbb {Z} $ and $ K …