Categorical Interactions in Algebra, Geometry and Representation Theory

Abstract: There are several fundamental interactions between combinatorics, algebra and geometry, where the combinatorial structures give representations and suitably interpreted encode cells for a geometric realization. A prime example of this is Deligne's conjecture, where the representation of certain graphs yields 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 out of them. More generally they yield the representations can also be algebras of certain types. In the functorial formalism one has restriction, reduction and Frobenius reciprocity. To make these geometric, one can use a so-called W-construction. For trees and graphs, this program leads to the construction of moduli spaces of graphs and Riemann surfaces. These are versions of the commutative and associative geometries studied by Kontsevich. Staying inside the algebraic world, one can use functors to enrich Feynman categories. The enriched categories play the role of algebras and the representations are modules - all with possible higher operations. The enrichment is made by using a plus construction, which has a connection to bi-algebras and Hopf algebras based on the morphisms of a Feynman category.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )

Comments: Meeting Link us02web.zoom.us/j/89958893469?pwd=aWFWQXZnMXczUFdJc282bWx3bE5Idz09 Meeting ID: 899 5889 3469 Passcode: Lagoon

---

Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.

---