|ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU
PROGRAM ZA SEPTEMBAR 2018.
PETAK, 21.09.2018. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Jovana Obradović, Charles University, Prague
CATEGORIFIED CYCLIC OPERADS IN NATURE
In the last talk I gave at the Mathematical Institute, I introduced a notion of categorified cyclic operad. A question of justifying the need of such a level of generality (weak rather than strict cyclic operads) arose back then. In this talk, I will address this questions by exhibiting the place and the use of categorified cyclic operads "in nature".
I will first give an example of a categorified cyclic operad in the form of an easy generalisation of the structure of profunctors of Benabou. I will then show how to exploit the coherence conditions of categorified cyclic operads in proving that the Feynman category for cyclic operads, introduced by Kaufmann and Ward, admits an odd version.
I will finish with combinatorial aspects of categorified cyclic operads, i.e. with their possible characterisations in convex and discrete geometry. This investigation aims at finding polytopes which describe the coherences of categorified cyclic operads, in the same was as the geometry of symmetric monoidal categories is demonstrated by permutoassociahedra, or the geometry of categorified operads by hypergraph polytopes.