“…Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. …”
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“…His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. …”
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“…Flag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. …”
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“…MANIFOLDSIntroductionReview of topological conceptsSmooth manifoldsSmooth mapsTangent vectors and the tangent bundleTangent vectors as derivationsThe derivative of a smooth mapOrientationImmersions, embeddings and submersionsRegular and critical points and valuesManifolds with boundarySard's theoremTransversalityStabilityExercisesVECTOR FIELDS AND DYNAMICAL SYSTEMSIntroductionVector fieldsSmooth dynamical systemsLie derivative, Lie bracketDiscrete dynamical systemsHyperbolic fixed points and periodic orbitsExercisesRIEMANNIAN METRICSIntroductionRiemannian metricsStandard geometries on surfacesExercisesRIEMANNIAN CONNECTIONS AND GEODESICSIntroductionAffine connectionsRiemannian connectionsGeodesicsThe exponential mapMinimizing properties of geodesicsThe Riemannian distanceExercisesCURVATUREIntroductionThe curvature tensorThe second fundamental formSectional and Ricci curvaturesJacobi fieldsManifolds of constant curvatureConjugate pointsHorizontal and vertical sub-bundlesThe geodesic flowExercisesTENSORS AND DIFFERENTIAL FORMSIntroductionVector bundlesThe tubular neighborhood theoremTensor bundlesDifferential formsIntegration of differential formsStokes' theoremDe Rham cohomologySingular homologyThe de Rham theoremExercisesFIXED POINTS AND INTERSECTION NUMBERSIntroductionThe Brouwer degreeThe oriented intersection numberThe fixed point indexThe Lefschetz numberThe Euler characteristicThe Gauss-Bonnet theoremExercisesMORSE THEORYIntroductionNondegenerate critical pointsThe gradient flowThe topology of level setsManifolds represented as CW complexesMorse inequalitiesExercisesHYPERBOLIC SYSTEMSIntroductionHyperbolic setsHyperbolicity criteriaGeodesic flowsExercisesReferencesIndex.…”
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“…All these mathematicians work at the interface of analysis and geometry, and Mikael’s impact on their research cannot be underestimated. …”
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“…From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. …”
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“…This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. …”
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“…This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. …”
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“…This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. …”
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