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CATEGORIES:Category Theory Seminar
SUMMARY:The Algebra of Directed Acyclic Graphs - Marco Dev
 esas Campos\, Computer Laboratory\, Cambridge
DTSTART;TZID=Europe/London:20120522T141500
DTEND;TZID=Europe/London:20120522T151500
UID:TALK38082AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/38082
DESCRIPTION:In this talk I'll present the work that Marcelo Fi
 ore and I did on a finitary algebraic characterisa
 tion of directed acyclic graphs (dags).\n\nWe expr
 ess the algebra of dags as a product and permutati
 on category (PROP)\, a symmetric monoidal variant 
 of Lawvere theories. In the talk\, I'll survey sim
 ple examples of symmetric monoidal theories and th
 e PROPs they give rise to and explain how they can
  be combined to express the dag structure.\n\nSpec
 ifically\, I'll characterise the algebra of dags a
 s the PROP generated by the  theory of bialgebras 
 that are commutative\, co-commutative and degenera
 te\, together with a generic endomorphism. The cru
 x of the problem lies in how to combine two differ
 ent algebras without the aid of a distributive law
 \, as we commonly have for monads. Technically\, t
 his is circumvented by a careful choice and analys
 is of canonical forms. I'll end by showing how our
  work can be further generalised to the cases wher
 e the dag links are weighted by natural and intege
 r numbers.\n\nAs for practical applications\, this
  work originated from a question by Robin Milner i
 n the context of distributed systems. He wished to
  extend of his bigraphical model to place graphs t
 hat allowed for sharing\, thus generalising them f
 rom tree-like structures to dags. With this work w
 e provide the necessary axioms to formalise this g
 eneralisation.\n\n
LOCATION:MR5\, Centre for Mathematical Sciences
CONTACT:Julia Goedecke
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