Titolo della tesi: Projective 2-representations and 2d TQFTs
The thesis explores the interaction between projective 2-representations of 2-categories and 2-dimensional topological quantum field theories (TQFTs) with defects. On one hand, the language of projective 2-representations precisely encodes the concept of anomalous TQFTs. On the other, the language of 2D TQFTs with defects provides an efficient framework for constructions that apply to projective 2-representations of arbitrary 2-categories. In the first chapter, we show how projective representations of groups are naturally described in terms of 2-categories. In the next chapter, we generalize this framework to arbitrary 1-categories, establishing generalizations of classical results about projective representations and central extensions (which recover the group case when restricted to the category with a single object and the group as its morphisms). Following this, we extend the theory to projective representations of 2-categories, proving analogous results. Finally, we apply this formalism to reconstruct the (non-extended) chiral anomaly of the free fermion CFT, as recently demonstrated by Ludewig and Roos.