K. Fujiwara: Schottky subgroups in mapping class groups.

Abstract: Let S be a compact orientable surface and MCG(S) the mapping class group. It was known that if a and b are independent pseudo-Anosov elements in MCG(S), then the subgroup is free for sufficiently large n,m >0. This result was used to show Tits' alternative of MCG(S). We show that there exists a constant Q(S) such that for any independent pseudo-Anosov elements a and b in MCG(S), the subgroup is Schottky, namely free and convex-cocompact in the sense of Farb and Mosher, if both n and m are at least Q. This effective version is used by Mangahas to show that subgroups in MCG(S) have uniform exponential growth if they are not virtually abelian. We may discuss that if time permits.