Lattices of Paths and Flat Dihomotopy Types

Cameron Calk
LIS, Aix-Marseille

Date(s) : 01/02/2024   iCal
11 h 00 min - 12 h 30 min

In this talk, I will describe ongoing work relating rewriting, quantales, and (directed) topology. The goal of this work is to describe the congruences of multinomial lattices and their continuous analogs, in particular the quantale of sup-continuous endomorphisms of the ordered unit interval. The former, generalizing the permutohedra, provide a lattice-theoretic description of the rewriting system associated to commutativity on finite words, while the latter are studied in the context of categorical linear logic. These structures all have an interpretation as directed spaces, which provide a geometric semantics for concurrency. Moreover, the homotopy types of these spaces are closely related to the congruences of the associated lattices. I will describe this connection between multinomial lattices and certain cubical complexes, providing a concrete result in dimension two. Finally, I will briefly discuss the continuous case, in particular the use of topological duality in our ongoing study of these structures.

Site Sud, Luminy, TPR2, Salle 210-212 (2e étage)


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