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Michael Robinson
Email: mr332 cornell.edu
Research Interests: I am currently examining the
global behavior of solutions to semilinear parabolic equations with
certain polynomial nonlinearities. My work lies at the intersection
of several mathematical topics. On one hand are traditional topics
in partial differential equations, such as maximum principles and
numerical approximation. On the other are newer topics from bifurcations
of dynamical systems and the topology of function spaces. I build
intuition in one of these fields, and then employ methods from the
others for proofs. The analogy of parabolic equations with systems
of ordinary differential equations has been particularly fruitful,
especially where it falls apart. For instance, a critical point of
a parabolic equation whose linearization is stable need not be stable
itself. In this case, undestanding the topology of the (infinite dimensional)
stable and unstable manifolds for the critical point is essential,
and provides much of the motivation for my work.
Office phone: 5-8272
Advisor: John Hubbard
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