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EducationPh.D. (1977) University of California at Berkeley Research Area: Topology, geometric group theoryA fundamental technique for studying a group G is to view G as a group of automorphisms of a geometric object X. Geometric and topological properties of X can then be used to study algebraic properties of G. Beautiful classical examples of this are the theory of arithmetic and S-arithmetic groups acting on homogeneous spaces and buildings, including work of Borel and Serre on cohomological properties of these classes of groups, and the theory of groups of surface homeomorphisms acting on the Teichmüller space of the surface. I am interested in developing geometric theories for other classes of groups. In particular, I have worked with orthogonal and symplectic groups, SL(2) of rings of imaginary quadratic integers, groups of automorphisms of free groups, and mapping class groups of surfaces. My main focus in recent years has been on the group of outer automorphisms of a free group, where the appropriate geometric object is called Outer space. This space turns out to have surprising connections with certain infinite-dimensional Lie algebras (discovered by Kontsevich) and also with the study of phylogenetic trees in biology. Selected PublicationsModuli of graphs and automorphisms of free groups (with M. Culler), Inventionnes 84 (1986), 91–119. Cerf theory for graphs (with A. Hatcher), J. London Math. Soc. 58 part 3 (1998), 633–655. The symmetries of Outer space (with M. Bridson), Duke Math Journal 106 no. 2 (2001), 391–409. Geometry of the space of phylogenetic trees (with L. J. Billera and S. Holmes), Advances in Applied Math 27 (2001), 733–767. Infinitesimal operations on complexes of graphs (with J. Conant), Math. Ann. 327 (2003), 545–573. Last modified: October 31, 2006 |
