My research mostly concerns Partial Differential Equations, and uses techniques from harmonic analysis and operator theory. A central problem is the well posedness of boundary value problems for PDEs with non-smooth coefficients or domains. With functional calculus and harmonic analysis we construct new operators beyond singular integrals, with which non-smooth PDEs can be solved constructively.
My focus is on systems of first order PDEs, motivated by Dirac operators from mathematical physics. In algebra and geometry I work much with differential forms, exterior algebra, Clifford algebra and spinors.
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