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Algebra and number theory, arithmetic of automorphic forms and Galois representations.
Fourier analysis, oscillatory integrals, singular integrals, Hardy spaces.
Chaotic properties of dynamical systems. Math and science education. Linking mathematics education to issues of sustainability.
Applied mathematics, mathematical biology, mathematical physiology.
Geometric and quantum topology, 3- and 4-dimensional manifolds.
Global analysis, automorphic forms, analytic number theory, and spectral theory.
Symplectic topology, differential geometry, and topology.
Algebra, algebraic number theory, analytic number theory
Functional analysis, operator theory, ill-posed partial differential equations
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