Stephen Fulling -- Mathematical Physics

Permanent faculty in the TAMU math department who might be classed as "mathematical physicists" include Peter Kuchment, Francis Narcowich, Guy Battle, Philip Yasskin, Alex Poltoratski, Dmitry Panchenko, Andrew Comech, Gregory Berkolaiko, and Yaroslav and Mariya Vorobets. I am the only one with a joint appointment in the physics department, my degrees are in physics, and I have funding from the physics division of NSF. As a physicist, my interests are in quantum theory, general relativity, and their areas of overlap. As a mathematician, I'm concerned with linear partial differential equations as they apply to physical problems in modern ramifications of familiar ways: the spectral theory and asymptotics of differential operators. In the past decade I have been concerned primarily with two related topics: (1) Semiclassical approximations: how solutions of PDEs are related to (sometimes constructible from) the orbits of associated systems of ODEs (e.g., wave functions to classical mechanics, or wave optics to ray optics). (2) Quantum vacuum (Casimir) energy associated with the zero-point oscillations of the normal modes of a field. I have worked with quite a few graduate and undergraduate students from either or both departments.

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