Aaron Lauda

TITLE: Categorified Frobenius Algebras

ABSTRACT: Frobenius structures naturally arise in the study of 2D TQFT.  I will describe a categorical framework for understanding Frobenius structures that naturally lends itself to generalization (categorification). I will use this categorical framework to define a weak 2-Frobenius algebra and sketch some possible applications to 3D TQFT.  Should this generalization prove fruitful for 3D TQFT, higher-dimensional category theory can be used to iterate this process yet again.  Diagrammatic methods will be used throughout the talk.