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Research Themes

• Developing novel integral equation (IE) formulations
• Analyzing IEs, i.e. proving well-posedness, and understanding the structure of solutions in the vicinity of corners and edges (where they tend to be singular)
• Exploiting the analytical structure to create efficient discretizations for representing the solutions, and efficient singular quadrature rules for computing them
• Developing novel algorithms for the resulting rank-structured matrices based on analytic features of the underlying system and the propagation of information therein
• Fast algorithms for problems in statistics, data analysis, and to the continuous setting where it can be viewed as hierarchical compression of integral operators
• Using these tools for the analysis and evaluation of eigenvalues and eigenfunctions of elliptic PDEs.