One Day Meeting on
Topology and its Applications

Michael Farber (Queen Mary Univ. London)
Autonomous robot motion and topology

I will survey recent progress in understanding algorithmic aspects of autonomous motion and will focus on relevant geometric and topological problems and techniques.

Nicolas Heitz (ENS-PSL Paris)
On the topological complexity of certain connected sums

David Mosquera Lois (Univ. Vigo)
Homotopic distance I

Ricardo Brasil (Univ. Minho)
Some maps between Grassmannians

For positive integers k ≤ n, the Grassmannian Gr(k, n) is the manifold of linear subspaces of dimension k in euclidean space ℝⁿ. In particular, Gr(2,n) is the manifold of linear planes in ℝⁿ and Gr(1,n) is the (n-1)- dimensional projective space ℝP^n-1. In this talk, we will use the quaternions and octonions to construct examples of maps from Gr(2,n) to ℝP^m, where m is less than the dimension of Gr(2,n), that is, less than 2(n-2).

María José Pereira Sáez (Univ. A Corunha)
Social Choice and Topological Complexity

Social Choice theory studies how to aggregate the preferences of various individuals to obtain a common group preference. From the point of view of Artificial Intelligence, this may be viewed as the design of decision-making algorithms. For two people, a global social choice map exists exactly when the space of preferences is contractible. In 2018, Carrasquel, Lupton and Oprea applied the concept of Topological Complexity to this field in the case of two individuals. These authors defined the social choice complexity of a space as the least number of sets needed to cover X x X such that in each set a local social choice map is given. In this talk, we will introduce a notion of higher social choice complexity and prove that is bounded between the higher topological complexity and its symmetric version. The relevance of this generalization comes from the fact that, in practice, we will be interested on aggregating the preferences of a whole society and not only of a pair of individuals.

João Nogueira (Univ. Coimbra)
On the unknottability and splittability of 2-string tangles

A tangle T is a pair formed by a ball B and collection of properly embedded disjoint arcs in B. Tangles are useful for decomposing links and have presence in applications in science. In this talk we will discuss the case where the unknot and split links have decompositions with a given tangle T as a factor. As an application we obtain a complete classification for tangles up to seven crossings with such properties. This is joint work with António Salgueiro.

Catarina Faustino (Univ. Minho)
On the topology of concurrent systems

As amply demonstrated in the literature, concepts and methods from algebraic topology can be profitably employed in concurrency theory, the field of computer science that studies systems of simultaneously executing processes. A powerful combinatorial-topological model for concurrent systems is given by higher-dimensional automata, i.e., pointed labeled precubical sets. The purpose of this talk is to show that the topology of an HDA model of a concurrent system can be arbitrarily complex. More precisely, I will show that for every connected polyhedron there exists an accessible transition system that admits an HDA model with the same homotopy type as the polyhedron. This is joint work with T. Kahl and R. Lopes.

Enrique Macias Virgos (Univ. Santiago de Compostela)
Homotopic distance II