Mark Feighn, with Mladen Bestvina and Michael Handel, will continue the study of automorphism groups of free groups. Abelian subgroups will be described. The Torelli subgroup of a mapping class group of a surface or of the automorphism group of a free group is the subgroup that acts trivially on first homology. Morse theoretic techniques will be applied to bordifications of Teichmuller Space or Culler-Vogtmann's Outer Space in order to determine connectedness properties of Torelli groups. Further, the study of coherent groups will be pursued. Groups are fundamental algebraic objects. They describe symmetries of objects and so are important anywhere symmetry appears. For example, the symmetry group of a molecule in part determines the molecule's chemical properties. In a new and exciting field of mathematics, geometric group theory, algebraic properties of the symmetry group of an object are gleaned from geometric properties of the object. Interesting groups occur when the object itself is taken to be a group. Mark Feighn will continue to apply this technique in the study of a fascinating class of groups, the symmetry groups of free groups. Free groups play a central role in the theory of groups, as any group may be obtained from a free group. ***
