Currently I am interested in geometric analysis, Riemannian geometry, Kähler geometry, partial differential equations. I am working on some problems via geometric flows, e.g. the Ricci flow.
One of my areas of research interest is called “constructive mathematics” where mathematical proofs must be done “constructively”. For example, if a theorem asserts the existence of a function, a constructive proof must actually describe a procedure to compute the function. A nonconstructive existence proof would merely show the impossibility that such a function could fail to exist. A constructive proof is also a valid classical proof, but not vice versa. A constructive theorem is true in the universe of computable functions, but a classical theorem can have wildly noncomputable objects.
Mathematics for Molecular Medicine, Visualization, and Scientific Computation
My mathematical interests are always growing. Most recently they have focused on high-resolution DNA melting analysis and applications to modern molecular medicine; as well as geometry and algorithms for 3d visualization. I am still enthusiastic about the interactions of dynamical systems with cognitive science, turbulent fluid flow, optimization of composite material microstructures, and number theory!
Physical Education and Recreation
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