Research Interests

My main goal is to find concrete, real life applications of mathematics (all kinds of mathematics).

More concretely, my general research interests are centered around

• Numerical Analysis,
• Mathematical Physics,
• Partial Differential Equations on singular spaces,
• Geometric Analysis, and
• Scientific Computing.

Even more specifically, I am currently working on "quasi-optimal rates of convergence for the Finite Element Method", the "Generalized Finite Element Method" (distributional data, enforcement of Dirichlet boundary conditions, numerical integration and implementation). I am using these results for "eigenvalue estimates for Schrodinger operators" and "Multigrid methods in Quantum ChromoDynamics." I am also planning some applications to Elastography and the Black-Scholes partial differential equation.

In the past, I also worked on "Pseudodifferential operators on singular spaces," on "Operator algebras," and "Non-commutative Geometry." Occasionally, these ideas are still useful.

See Preprints and Publications for latest work and publications and reprints for older work.