Abstracts for Conference for Young researchers in homotopy theory and categorical structures, February 13-15, 2017

I will describe a construction providing Lie algebras with enveloping algebras over the operad of little $n$-dimensional
disks for any $n$. These algebras enjoy a combination of good formal properties and computability, the latter afforded
by a Poincaré-Birkhoff-Witt type result. The main application pairs this theory with the theory of factorization homology
in a study of the rational homology of configuration spaces, leading to a wealth of computations, improvements of classical results, and a combinatorial proof of homological stability.

Handling higher structures such as higher categories usually involves conceiving them as conglomerates of
cells of certain shape. Such shapes include simplices, globes, or cubes. The aim of this talk is to bridge the
gap between two such results:

The first one is the equivalence between cubical and globular $\omega$-groupoids. Although this equivalence
is useful in theory, in practice it is complicated to make explicit the functors composing this equivalence. This

Speakers, titles and abstracts, see this PDF.
 

$2$-Segal objects, which are a generalisation of ordinary Segal objects, were introduced and studied by
Dyckerhoff-Kapranov and Gálvez-Kock-Tonks. An important example of a $2$-Segal object is the Waldhausen
construction of an exact category. The Waldhausen construction makes sense for a more general input, and the
goal of the talk is to explain that, in the discrete setting, the Waldhausen construction is in fact quite exhaustive.
More precisely, it induces an equivalence between the category of stable pointed double categories and the