Teichmueller groups and their automorphisms (I and II)

These combined talks will provide an introduction to
Teichmueller groups (alias mapping class groups) whose
profinite completions have recently become the subject of
intense study, mostly motivated by Grothendieck-Teichmueller
theory which in particular seeks to determine their automorphism groups.

In the first talk (L.S.) some elementary features of the
discrete groups will be recalled, starting with the structure
of (Artin) braid groups, which provide the simplest (genus 0)
family of such groups. The second talk (P.L) will focus on
the profinite setting and the network of closely related conjectures
which should enable us to understand the structure of these
groups and their automorphism groups. We will also briefly
explain the long standing analogy (and contrast) between these
groups and linear arithmetic groups.