Faculty
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I am interested in applications of Combinatorics to: Representation Theory, Commutative Algebra, Algebraic Geometry,
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Complex Algebraic Geometry, Irreducible Holomorphic symplectic Manifolds
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Fully nonlinear degenerate elliptic PDE's, Subelliptic PDE's, SubRiemannian structures
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simplicial volume, bounded cohomology, geometric group theory, topology of manifolds
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sums of squares of vector fields, hypoellipticity, a priori estimates, pseudodifferential operators
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asymptotic behavior, thermo-viscous-elastic plate, phase transition , porous-thermo-elasticity, thermodynamics,
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Lie and Noether Symmetries
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matroids, arrangements, cohomology, configuration spaces
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Stochastic differential equations, McKean/Vlasov diffusions, Hypoelliptic diffusions, Analytical approximations,
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Numerical Analysis, Numerical Linear Algebra, Matrix Equations
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Combinatorics, Topology, Group theory, Deep learning, Natural language processing
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Geometric analysis of PDEs, Solvability, Lower-bound estimates, Spectral theory