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TZID:Europe/Paris
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UID:5038@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240201T110000
DTEND;TZID=Europe/Paris:20240201T123000
DTSTAMP:20260107T153112Z
URL:https://www.i2m.univ-amu.fr/evenements/lattices-of-paths-and-flat-diho
 motopy-types/
SUMMARY:Cameron Calk (LIS): Lattices of Paths and Flat Dihomotopy Types
DESCRIPTION:Cameron Calk: In this talk\, I will describe ongoing work relat
 ing rewriting\, quantales\, and (directed) topology. The goal of this work
  is to describe the congruences of multinomial lattices and their continuo
 us analogs\, in particular the quantale of sup-continuous endomorphisms of
  the ordered unit interval. The former\, generalizing the permutohedra\, p
 rovide a lattice-theoretic description of the rewriting system associated 
 to commutativity on finite words\, while the latter are studied in the con
 text of categorical linear logic. These structures all have an interpretat
 ion as directed spaces\, which provide a geometric semantics for concurren
 cy. Moreover\, the homotopy types of these spaces are closely related to t
 he 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 con
 tinuous case\, in particular the use of topological duality in our ongoing
  study of these structures.
CATEGORIES:Séminaire,Logique et Interactions
LOCATION:I2M Luminy - TPR2\, Salle 210-212 (2e étage)\, 163\, avenue de Lu
 miny\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163\, avenue de Luminy\, Ma
 rseille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sa
 lle 210-212 (2e étage):geo:0,0
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DTSTART:20231029T020000
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