La onzième session des Après-midi de Topologie, co-organisées par Christian Ausoni (LAGA), Geoffroy Horel (LAGA), Najib Idrissi (IMJ-PRG) et Muriel Livernet (IMJ-PRG).
Basile Coron: Matroid complexes and Orlik-Solomon algebras.
The (co)operad of admissible graphs is an important object introduced by M. Kontsevich, which can serve as a middle-man between the cooperad of forms on the Fulton-MacPherson operad (an E_2 operad), and its cohomology. In this talk we will explain how this whole picture can be painted from the point of view of braid arrangements, and how one might extend this picture to other well-behaved hyperplane arrangements.
Interestingly, the construction of the model can be done at the purely combinatorial level of matroids.
Gijs Heuts: Koszul duality for E_n-operads and E_n-algebras
I will describe a direct relation between bar-cobar duality for E_n-algebras and the Koszul self-duality of the E_n-operad proved by Ching—Salvatore; in fact, the second may be deduced from the first. The main technical tool is a result that allows one to manipulate (stable) E_n-operads by manipulating their categories of algebras. I will discuss several other consequences for the theory of E_n-algebras that may be deduced in this way, e.g. analogs of the Poincare—Birkhoff—Witt theorem in higher algebra. Parts of this work are joint with Markus Land, others with Lukas Brantner and Omar Antolin-Camarena.
Danica Kosanović: Diffeomorphisms from dancing circles
It is still unknown whether the 4-sphere has trivial smooth mapping class group (diffeomorphisms modulo isotopy). Recently, Gay has shown that any potential class can be realised using a 1-parameter family of embedded 2-spheres. In fact, we showed that all candidate classes constructed so far come from 1-parameter families of embedded circles, and often reduce to a single class. Analogues of such families are nontrivial in some non-simply connected 4-manifolds, as shown by Budney—Gabai and Watanabe. In this talk I will first explain how one can study families of circles, and show that they give rise to nontrivial diffeomorphisms of S^1 \times S^2 \times [0,1], as done in the joint work with E. Fernández, D. T. Gay, and D. Hartman. | 
