James M. Scott
I am currently a postdoc in the Department of Applied Physics and Applied Mathematics in the Fu Foundation School of Engineering and Applied Science at Columbia University.
I am an applied mathematician. I analyze systems of partial differential and integro-differential equations which describe constitutive relations in various scientific applications, including continuum mechanics, machine learning, and fractional PDE modeling. I use variational techniques, compensated compactness techniques, and tools from harmonic analysis to study qualitative behavior of solutions, asymptotic regimes, and the structure of associated function spaces.
Current and Previous Positions
2021-present: Postdoctoral Research Scientist at Columbia University
2020-2021: MRC Postdoctoral Associate at the University of Pittsburgh
2014-2020: Graduate Teaching Associate at the University of Tennessee
2017-2018: Graduate Research Associate at Oak Ridge National Laboratory
Research Interests
Variational methods for constitutive models
Modeling: continuum mechanics, supervised machine learning, linear and nonlinear elasticity,
Asymptotics: Γ-convergence, model reduction, moment methods, homogenization
Theory of function spaces associated to elliptic and parabolic equations
Existence, uniqueness and regularity of solutions
Nonlocal integro-differential equations
Education
PhD in Mathematics
University of Tennessee, 2020Masters in Mathematics
University of Tennessee, 2017Bachelor of Science
University of Wisconsin - Stevens Point, 2012