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Bay Area Topology Seminar Talk 2: Braids, Morse Theory and Parabolic PDEs
Special Events| Speaker: | Robert Ghrist, Univ. of Illinois, Urbana-Champaign |
| Location: | 693 Kerr |
| Start time: | Tue, Apr 26 2005, 4:00PM |
Nonlinear generalizations of the heat equation (curve shortening, e.g.) entwine topological, geometric, and dynamical features in ways increasingly relevant to topologists. We describe a homotopy Morse index for spaces of braids that is specially adapted to parabolic PDEs. This yields a braid theoretic version of the `comparison principle' and allows for topological solutions to a variety of dynamical questions. (Joint work with R. Vandervorst, VU Amsterdam.)