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Nathan Totz My research concentrates on studying PDEs arising from modeling fluid flow from a variety of perspectives. I received my Ph.D. At the University of Michigan under Sijue Wu, and before joining the faculty of the University of Miami I have done postdoctoral work at Duke University with J. Thomas Beale and at the University of Massachusetts Amherst with Andrea Nahmod. In the continuum of pure vs. applied math I place myself on the applied side of pure math. My thesis and some subsequent papers published in Communications in Mathematical Physics are in justifying quantitatively that certain model equations for PDEs govern the motion of wave packet-like water waves. From this line of work, I've springboarded into considering these modeling methods not just as tools from applied mathematics for shedding light on physical problems, but as mathematical tools in their own right to attack more fundamental questions about the long-time well-posedness of solutions to PDEs generally considered in a more pure context. My first foray into this program is a paper that recently appeared in the Journal of Differential Equations, and I received an NSF grant last year to continue investigating this approach. Finally, I've of late become interested in studying PDEs that incorporate elements of randomness using statistical tools. In my free time, I'm a fan of classical music, weightlifting, and spending time with my wife Kathryn and daughter Evie. |
