The Lambrechts–Stanley Model of Configuration Spaces

Invent. Math, 68 pp (2018).

Formality of a higher-codimensional Swiss-Cheese operad

Prépublication v1, 40 pages (2018).

Curved Koszul Duality for Algebras over Unital Operads

Prépublication v2, 32 pages (2018).

A model for framed configuration spaces of points

Ricardo Campos, Julien Ducoulombier, N.I, Thomas Willwacher. Prépublication v1, 27 pages (2018).

Configuration Spaces of Manifolds with Boundary

Ricardo Campos, N.I, Pascal Lambrechts, Thomas Willwacher. Prépublication v1, 107 pages (2018).

Formalité opéradique et homotopie des espaces de configuration

Thèse de doctorat, Université Lille 1 (2017).

Swiss-Cheese Operad and Drinfeld Center

Israel J. Math 221.2, pp. 941–972 (2017).

Structures supérieures

23/01/2019 – Centre international de rencontres mathématiques (CIRM), Luminy, France

Configuration spaces and operads
Résumé: Configuration spaces consist of tuples of pairwise distinct points in a given space. Studying the homotopy type of configuration spaces of manifolds is a classical problem in algebraic topology. In this talk, I will explain how to use the theory of operads - 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 simply connected closed smooth manifolds. I will also talk about generalizations and applications: manifolds with boundary, framed configuration spaces, factorization homology, and work in progress on complements of submanifolds.

Séminaire de Topologie de Stockholm

11/12/2018 – Université de Stockholm + Institut Royal de Technologie (KTH), Stockholm, Suède

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

08/11/2018 – Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France

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 (orateur junior)

20/06/2018 – Institut Fields, Toronto, Canada

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

05/06/2018 – Université de Regina, Regina, Canada

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.

En français, s'il-vous-plaît !

29/12/2017 #blog