I am a Professor of Mathematics at the University of Louisville. My research lies at the intersection of applied analysis, partial differential equations, and computation, with a focus on problems arising in fluid mechanics and related systems. I study mathematical models in which small physical parameters lead to complex multi-scale behavior, and I develop analytical and computational frameworks that remain reliable in such singular regimes.

A unifying theme of my work is the use of problem structure and analytical insight to guide the design of robust numerical and learning-based methods. By incorporating asymptotic information and conservation principles, my research aims to bridge rigorous mathematical analysis with modern computational approaches for challenging partial differential equations. The question that guides my recent work is where to build this structure into a learning-based method: in the trial space, in the discrete residual, or in the learned solution operator.

CV (PDF) · Email · Publications · Research