Après-midi de Topologie - 25 septembre 2024
Organisée par Christian Ausoni (LAGA), Geoffroy Horel (LAGA), Muriel Livernet (IMJ-PRG), Najib Idrissi (IMJ-PRG).
Francesca Pratali : Rectification of operadic left fibrations
By a result of Heuts-Moerdijk, the oo-category of simplicial diagrams on the nerve of a discrete category A is equivalent to that of left fibrations over the nerve of A. This is an instance of the well known Grothendieck-Lurie straightening-unstraightening theorem.
In this talk, we will explain how one can generalize this result to the operadic case. More specifically, by working with the dendroidal formalism we show how, given any discrete operad P, one can functorially rectify an operadic left fibration over the dendroidal nerve of P and obtain a simplicial algebra on P. After explaining how this extends an analogous functor for categories, we prove that it establishes an equivalence of oo-categories between operadic left fibrations over the nerve of P and simplicial P-algebras. A first step towards operadic straightening-unstraightening! If time permits, we will conclude the exposition by presenting possible future applications.
Birgit Richter : Involutive Hochschild homology and reflexive homology as equivariant Loday constructions
In joint work with Lindenstrauss and Zou we identified real topological Hochschild homology of a nice genuine commutative C_2 ring spectrum A with the C_2-Loday construction for the one-point compactification of the sign representation. The same C_2-Loday construction applied to the fixed Tambara functor associated to a commutative ring R with involution can be identified with a Tambara functor of a two-sided bar construction and this in turn relates in good cases to the involutive Hochschild homology and the reflexive homology of R. In work in progress our aim is to get rid of the assumption of commutativity. This is joint work with Ayelet Lindenstrauss. | 
