Research
Research themes, methods, current directions, and collaborations.
Research
My work develops scalable numerical methods for large scientific problems, with emphasis on structure, adaptivity, and efficient use of matrix or operator information.
Research themes
Numerical linear algebra
Structure-aware algorithms for large matrices and operators, including low-rank approximation, hierarchical methods, factorization, and fast solvers.
Randomized algorithms
Adaptive randomized sampling and compression methods that discover useful numerical structure with limited operator access.
Inverse problems
Computational methods for inference and optimization in scientific models, including large-scale PDE-constrained settings.
Current directions
Structured approximation
Many dense operators arising in scientific computing are expensive to assemble explicitly but can be applied efficiently to vectors. I am interested in adaptive methods that identify low-rank and hierarchical structure directly from these matrix-vector products and use that structure for compression, factorization, and solution.
Inverse problems and optimization
Regularized inverse problems provide a natural setting in which numerical linear algebra, modeling, and optimization interact. A representative objective is
\[\min_x \; \frac{1}{2}\lVert Ax-b\rVert_2^2 + \frac{\lambda}{2}\lVert Lx\rVert_2^2.\]The computational challenge is often not the expression itself, but how to exploit structure in the forward model, Hessian, or related operators when dimensions become large.
Computational toolkit
Collaboration
I am interested in collaborations at the intersection of numerical linear algebra, inverse problems, scientific computing, and large-scale simulation, especially when mathematical structure can be translated into substantial computational savings.