Research lines
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Algebraic and differential topology, Lusternik-Schnirelmann cathegory, topological complexity, Morse theory.
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Dynamical systems. Applications of differential and difference equations. Biomathematics.
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Foliation theory, Global analysis on foliated spaces, Global analysis on stratified spaces.
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Homological algebra, derived categories, Hopf algebras, Lie algebras and Leibniz algebras, duality in algebraic geometry, monoidal structures, homology of singular spaces, Galois theory
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Riemannian and Lorentzian geometry, curvature, geometric evolution equations, isometric actions, isoparametric submanifolds, constant principal curvatures.