BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:	An Algebraic Combinatorial Approach to the Abstract Syntax of Ope
 topic Structures - Marcelo Fiore\, University of Cambridge
DTSTART:20161014T130000Z
DTEND:20161014T140000Z
UID:TALK68200@talks.cam.ac.uk
CONTACT:Dominic Mulligan
DESCRIPTION:The starting point of the talk will be the identification of s
 tructure common to tree-like combinatorial objects\, exemplifying the situ
 ation with abstract syntax trees (as used in formal languages) and with op
 etopes (as used in higher-dimensional algebra). The emerging mathematical 
 structure will be then formalized in a categorical setting\, unifying the 
 algebraic aspects of the theory of abstract syntax of [2\, 3] and the theo
 ry of opetopes of [5]. This realization conceptually allows one to transpo
 rt viewpoints between these\, now bridged\, mathematical theories and I wi
 ll explore it here in the direction of higher-dimensional algebra\, giving
  an algebraic combinatorial framework for a generalisation of the slice co
 nstruction of [1] for generating opetopes. The technical work will involve
  setting up a microcosm principle for near-semirings and subsequently expl
 oiting it in the cartesian closed bicategory of generalised species of str
 uctures [4]. Connections to (cartesian and symmetric monoidal) equational 
 theories\, lambda calculus\, and algebraic combinatorics will be mentioned
  in passing.\n\nReferences\n\n# J.Baez and J.Dolan. Higher-Dimensional Alg
 ebra III. n-Categories and the Algebra of Opetopes. Advances in Mathematic
 s 135\, pages 145–206\, 1998.\n# M.Fiore\, G.Plotkin and D.Turi. Abstrac
 t syntax and variable binding. In 14th Logic in Computer Science Conf. (LI
 CS’99)\, pages 193–202. IEEE\, Computer Society Press\, 1999.\n# M.Fio
 re. Second-order and dependently-sorted abstract syntax. In Logic in Compu
 ter Science Conf. (LICS’08)\, pages 57–68. IEEE\, Computer Society Pre
 ss\, 2008.\n# M.Fiore\, N.Gambino\, M.Hyland\, and G.Winskel. The cartesia
 n closed bicategory of generalised species of structures. In J. London Mat
 h. Soc.\, 77:203-220\, 2008.\n# S.Szawiel and M.Zawadowski. The web monoid
  and opetopic sets. In arXiv:1011.2374 [math.CT]\, 2010.
LOCATION:FW26
END:VEVENT
END:VCALENDAR