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Degrees & Accolades:

Ph.D. (Caltech)
M.Sc. (Caltech)
B.Sc. (New Brunswick)

Research Profile:

I am interested in geometric analysis on manifolds, especially real analytic manifolds. This work combines geometric, topological, and algebraic methods. I am especially interested in applications of such methods to problems in geometric control theory, where the resolution of fundamental structural problems seems to require going deeply into some mathematics.

I am interested in hiring graduate students who love mathematics and who want to broaden their mathematical horizons, while being connected to "applied" mathematics.

Research Areas:

Thing 1: I am interested in function space methods involving multiple sorts of “smoothness,” e.g., finitely differentiable, infinitely differentiable, complex or real analytic. I am also interested in methods where nondifferentiable regularity arises, e.g., locally Lipschitz, absolutely continuous, Sobolev-style regularity, etc. Problems of regularity of operations on or between function spaces are of particular interest to me. Work in this area (and those of the other two Things) involves function analytic techniques beyond classical Banach and Hilbert spaces.

Thing 3: A more recent Thing in which I have become interested is infinite-dimensional geometry, which combines my existing interests in differential geometry and functional analysis. Here one is interested in understanding what can be done, and when, when working with manifolds whose model space is infinite-dimensional. The infinite-dimensionality introduces subtleties that do not arise in f inite-dimensional differential geometry.

Thing 2: A particular area where I have made use of the function space methods in my previous Things is connected to problems in differential equations, both ordinary and partial. For ordinary differential equations, I am interested in such equations in infinitedimensional spaces where one can prove useful existence and uniqueness theorems. For partial differential equations, I am interested in such evolution equations as admit a useful representation as an ordinary differential equation in infinite dimensions.