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Research Results
CARLOS TOMEI
My current research stems from years of concentration in certain subjects. My interests in the intertwining of spectral theory with integrable systems led me to the study of concrete eigenvalue algorithms through a conceptual approach to numerical analysis. A concrete example is the interplay between the so called Toda Lattice and the QR method, dating back to the late seventies, which used symplectic geometry as the foundational background. Further developments in the eighties and nineties brought a deeper understanding of familiar algorithms. And recently, a Lie algebraic approach yielded simpler theoretical tools: the dynamics at relevant points of phase space has been reduced to standard local theory. Fundamental numerical methods which have been used for decades are now thoroughly understood, as are basic transversality properties of the underlying vector fields. In a similar vein, my interest on nonlinear functions in the plane, which started in the nineties, developed into the consideration of a collection of cases, ranging from finite dimensional maps associated to spectral properties, to ordinary and partial differential operators. A constant attention is given to both theoretical and numerical implications. The list of collaborators increased accordingly.
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updated (11/18/2019) |
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