Title:  Aut(F_2) is a CAT(0) group.
<p>
 Abstract:  T. Brady showed that a finite index subgroup of Aut(F_2) acts properly and cocompactly by isometries
 on a CAT(0) space.  In general, this does not imply the bigger group admits such an action.  In this talk, we will show the full automorphism group of F_2 does act geometrically on a CAT(0) space.  The proof uses the fact that Aut(F_2) is isomorphic to Aut(B_4) where B_4 denotes the braid group on 4 strands, thus showing Aut(B_4) is also a CAT(0) group.