Structures supérieures
~2019-01-21Centre international de rencontres mathématiques (CIRM), Luminy, France

Séminaire de Topologie de Stockholm
2018-12-11Université de Stockholm + Institut Royal de Technologie (KTH), Stockholm, Suède
Diapositives

Configuration spaces and Operads
Résumé: Configuration spaces of manifolds are classical objects in algebraic topology, but studying their homotopy type is a difficult task. In this talk, I will explain how to use ideas coming from the theory of operads (and more precisely Kontsevich's proof of the formality of the little disks operads) to obtain results on the real homotopy type of configuration spaces of compact manifolds. I will also talk about recent applications.

Séminaire Géométrie et Topologie
2018-11-08Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France
Diapositives

Espaces de configuration et Opérades
Résumé: Les espaces de configuration de points sont des objets classiques en topologie algébrique. L'étude de leur type d'homotopie engendre de nombreuses questions et applications dans différents domaines des mathématiques. Dans cet exposé, je présenterai des idées qui viennent de la théorie des opérades et qui permettent d'obtenir des résultats concernant le type d'homotopie rationnel des espaces de configuration de variétés.

Derived Geometry and Higher Categorical Structures in Geometry and Physics
2018-06-20Institut Fields, Toronto, Canada
Diapositives Vidéo

Curved Koszul duality and factorization homology
Résumé: Koszul duality is a powerful tool that can be used to produce resolutions of algebras in many contexts. In this talk, I explain how to use curved Koszul duality for algebras over unital operads to compute the factorization homology of a closed manifold with values in the algebra of polynomial functions on a standard shifted symplectic space.

Colloque du département
2018-06-05Université de Regina, Regina, Canada
Diapositives

Configuration Spaces and Graph Complexes
Résumé: Configuration spaces of points are classical objects in algebraic topology that appear in a wide range of applications. Despite their apparent simplicity, they remain intriguing. Kontsevich proved in the 90's that they are intimately related to "graph complexes", combinatorial objects that can be used to explicitly describe the homotopy type of configuration spaces in a Euclidean space. After recalling the above story, I will explain a conjecture of Lambrechts and Stanley about configuration spaces of simply connected closed manifolds. I will then give an idea of the proof of this conjecture, using graph complexes similar to the ones appearing in the works of Kontsevich. I will also describe recent generalizations: for manifolds with boundary, and for so-called "framed" configuration spaces (j/w Campos, Ducoulombier, Lambrechts, and Willwacher). Finally, I will talk about applications of these results.

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