Filling functions of arithmetic groups

Braids, Galois Groups, and Some Arithmetic Functions

This lecture is about some new relations among the classical objects of the title. The study of such relations was started by [Bi, G, De, Ihj] from independent motivations, and was developed in [A3, C3, A-I, IKY, Dr2, O, N], etc. It is still a very young subject, and there are several different approaches, each partly blocked by its own fundamental conjectures! But it is already allowing one to...

on finite arithmetic groups

let $f$ be a finite extension of $bbb q$‎, ‎${bbb q}_p$ or a global‎ ‎field of positive characteristic‎, ‎and let $e/f$ be a galois extension‎. ‎we study the realization fields of‎ ‎finite subgroups $g$ of $gl_n(e)$ stable under the natural‎ ‎operation of the galois group of $e/f$‎. ‎though for sufficiently large $n$ and a fixed‎ algebraic number field $f$ every its finite extension $e$ is‎ ‎re...

Arithmetic groups

The theory of arithmetic groups deals with groups of matrices whose entries are integers, or more generally, S-integers in a global field. This notion has a long history, going back to the work of Gauss on integral quadratic forms. The modern theory of arithmetic groups retains its close connection to number theory (for example, through the theory of automorphic forms) but also relies on a vari...

Arithmetic Groups

We present detailed summaries of the talks that were given during a weeklong workshop on Arithmetic Groups at the Banff International Research Station in April 2013, organized by Kai-Uwe Bux (University of Bielefeld), Dave Witte Morris (University of Lethbridge), Gopal Prasad (University of Michigan), and Andrei Rapinchuk (University of Virginia). The vast majority of these reports are based on...

Algebraic Groups and Arithmetic Groups