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Classification of manifolds.
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Higher order connections on frame bundles.
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Affine Differential Geometry.
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Differential Geometry and Mathematical Physics
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Spectral Geometry.
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Lorentz Geometry and Relativity.
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Semi-Riemannian Geometry.
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Finsler Geometry.
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Global analysis in Lorentz manifolds: geodesics, convexity.
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Rational mechanics: particles under the action of potentials, magnetic fields and forces.
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Causal structure of a space-time: trapped surfaces, black holes, causal and conformal boundary.
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Busemann and Gromov constructions: compactification of Finsler manifolds, generalization of Busemann functions.
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Geodesic curves, conjugate points and curvature in Lorentz manifolds.
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Maximal spacelike hypersurfaces with constant curvature.
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Hypersurfaces in symmetric spaces.
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Spaces with symmetries: generalizations of symmetric spaces and circles acting on space-times.
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Equivalence between different geometric structures.
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(pseudo-)Riemannian conformal structures.
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Hypersurfaces and submanifolds.
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Isometric immersions.
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Geometric inequalities in metric measure spaces.
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Potential theory.
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Variational problems in Differential Geometry.
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Variational Problems associated to elliptic operators.
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Variational problems related to relative perimeter and isoperimetric inequalities in Euclidean convex sets.
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Variational problems related to area in manifolds with densities.
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Variational problems related to the Minkowski content in metric measure spaces.
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Variational problems related to sub-Riemannian area in sub-Riemannian geometry.
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Extensions of G-structures.
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Colour symmetry.
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Differential Systems.
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Finite-type submanifolds.
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Extremal submanifolds.
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Minimal surfaces.
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Constant curvature surfaces.
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Surfaces with prescribed mean curvature.
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Tessellations and mosaics.