Time: 16:30-18:00

Location: Mondi 3 / Central Building

Speaker 1: Alberto Avitabile (Tor Vergata University of Rome)

Title: On the Real Homotopy Type of Orbit Configuration Spaces

Abstract: Configuration spaces $Conf_k(X)$ parametrize k-tuples of -- pairwise distinct -- points in a fixed space $X$. Euclidean configurations provide a concrete geometrical model for the operad $\mathbb{E}_n$ and, more generally, manifold configurations are natural modules over $\mathbb{E}_n$-algebras, which constitute a central topic in modern homotopy theory. Despite their simple definition, the task of understanding the homotopy type of $Conf_k(X)$ in terms of $k$ and the homotopy type of $X$ in full generality is simply impossible. Recent works in a slightly simplified setting ultimately led to explicit models for the \emph{real} homotopy type of $Conf_k(M)$ in terms of the \emph{real} homotopy type of $M$, for $M$ a simply connected closed orientable $n$-manifold. The aim of this talk is to highlight the key ideas contained in the proof and at the same time to present a partial generalization of this result for \emph{orbit} configuration spaces, an equivariant version of $Conf_k(X)$ which naturally arises when a free action of a finite group $G$ on $X$ is involved.

Speaker 2: Sergio Alejandro Fernandez de soto Guerrero (TU Graz)

Title: Positroidal magic

Abstract: Positroids are a subclass of matroids born in the study of the non-negative Grassmanian by Postnikov in 2006. Since then, there have been a plethora of combinatorial objects indexing positroids, two of these being the families of decorated and bicolored permutations, which are generalizations of classical permutations. These two families can be used to study properties of positroids, and as a byproduct we end up with useful ways to describe a group action on a deck of cards. In this context, we give a definition of invariants under this group action allowing us, as an application, to develop new magic tricks with unusual ways of shuffling cards.