Mathematical Sciences: Manifolds and Algebraic Topology
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This project involves four senior faculty members, one                     junior faculty member, and several advanced graduate students in                a wide variety of topological investigations.  William P.                       Thurston will continue research on low-dimensional manifolds,                   computational geometry and geometric group theory.  For example,                he has defined an automatic group as one that can, in a sense                   that can be made quite precise, be treated by a finite state                    automaton.  Moreover, he has shown that the fundamental group of                any negatively curved manifold is automatic.  Other geometrically               interesting groups also fit this viewpoint, and computer                        algorithms may be written to exploit the situation.                                  John N. Mather and Victor J. Donnay, as well as Thurston,                  will attack problems in dynamics and the theory of foliations.                  Donnay has found the first example of an ergodic geodesic flow on               a two-dimensional sphere equipped with an appropriately chosen                  metric.  The ramifications of this will take some time to                       understand.                                                                          William Browder and Wu-chung Hsiang are engaged in wide-                   ranging research in differential topology and transformation                    group theory, homotopy theory, and algebraic varieties and                      topology.  Hsiang's work also extends into differential geometry.
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[{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}, {'Code': '1267', 'Text': 'TOPOLOGY'}]
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