BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ralph Kaufmann (Purdue University\, USA) DTSTART:20201210T120000Z DTEND:20201210T130000Z DTSTAMP:20260423T024755Z UID:LAGOON/24 DESCRIPTION:Title: Categorical Interactions in Algebra\, Geometry and Representation Theory\nby Ralph Kaufmann (Purdue University\, USA) as part of Longitudinal Al gebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThere are s everal fundamental interactions between combinatorics\, algebra and geomet ry\, where the combinatorial structures give representations and suitably interpreted encode cells for a geometric realization. A prime example of t his is Deligne's conjecture\, where the representation of certain graphs y ields actions on the Hochschild complex and geometrically these graphs can be considered as graphs dual to a system of arcs on a surface. There is a way to encode the combinatorial structures into categorical ones\, the so -called Feynman categories. The representations in this setting functors o ut of them. More generally they yield the representations can also be alge bras of certain types. In the functorial formalism one has restriction\, r eduction and Frobenius reciprocity. To make these geometric\, one can use a so-called W-construction. For trees and graphs\, this program leads to t he construction of moduli spaces of graphs and Riemann surfaces. These are versions of the commutative and associative geometries studied by Kontsev ich. Staying inside the algebraic world\, one can use functors to enrich F eynman categories. The enriched categories play the role of algebras and t he representations are modules - all with possible higher operations. The enrichment is made by using a plus construction\, which has a connection t o bi-algebras and Hopf algebras based on the morphisms of a Feynman catego ry.\n\nMeeting Link\nhttps://us02web.zoom.us/j/89958893469?pwd=aWFWQXZnMXc zUFdJc282bWx3bE5Idz09\nMeeting ID: 899 5889 3469\nPasscode: Lagoon\n LOCATION:https://researchseminars.org/talk/LAGOON/24/ END:VEVENT END:VCALENDAR