Education & training:
- BS 1977, mathematics and physics, Antioch College.
- MS 1978, physics, University of Cincinnati; thesis: Generation of Solutions to the Einstein Equations
- PhD 1985, theoretical & mathematical physics, The University of Texas at Austin; dissertation: Functional Stochastic Differential Equations with Applications in Field Theory and Statistical Mechanics (under the direction of Cecile DeWitt-Morette)
- Director's Postdoctoral Fellow 1986-87, Los Alamos National Laboratory, Center for Nonlinear Studies
Professional positions:
- Assistant, Associate & Research Professor of Physics, 1987-96, Clarkson University
- Deputy Director, 1994-96, Los Alamos' Center for Nonlinear Studies
- Professor of Mathematics, 1996-present, University of Michigan
Selected honors & awards:
- NSF Presidential Young Investigator, 1989-94
- University of Michigan College of Literature, Science & the Arts Excellence in Education Award, 1998
- Founding Director, 1999-2003, University of Michigan Applied & Interdisciplinary Mathematics Graduate Program
- Fellow of the American Physical Society, 2000
- Humboldt Research Award, 2003
- Plenary Speaker, 2005, SIAM "Snowbird" Conference on Applied Dynamical Systems
- Member of Board of Governors, 2005-10, Institute for Mathematics and its Applications, University of Minnesota
Research interests and activities: My work is generally focused on the
analysis of mathematical models of physical systems with the aim of
extracting reliable, rigorous, and useful predictions. These models range
from stochastic dynamical systems arising in biology, chemistry and
physics, to systems of nonlinear partial differential equations such as
those which (ostensibly) describe turbulent fluid flows. The techniques I
use range from the development of exact solutions, to modern applied
mathematics and careful numerical computations and simulations, to
abstract functional and probabilistic analysis --- often a combination
of all three approaches.
Recently I have been focusing on fundamental questions in fluid dynamics such as: "Are the basic models of turbulent flow predictive, i.e., do the equations of motion have unique solutions?" This question is part of the $1M Clay Institute millennium challenge concerning the regularity of solutions to the equations of fluid dynamics. More concretely, we ask "What physical quantities can be rigorously bounded from the equations, given the existence of possibly non-unique weak solutions?" And most importantly, "What kind of contact can we make between the mathematical analysis, rigorous estimates, and real experiments or direct numerical simulations of turbulent flows?"
Interested students are directed to my book co-authored with J. D. Gibbon, "Applied Analysis of the Navier-Stokes Equations" (Cambridge University Press Series, Graduate Texts in Applied Mathematics, 1995; corrected reprint 2005).
