The Algebra & Geometry of Modern Physics

In this talk we first recall the functorial definition of closed and open/closed TFTs, as well as their equivalent algebraic descriptions (in terms of Frobenius algebras and Calabi-Yau categories). Both are special cases of "TFTs with defects" which we shall study in some detail. In particular we will discuss a construction of new TFTs by covering worldsheets with appropriate networks of defect lines. If these defect lines encode the action of an orbifold group, then the new TFT precisely recovers the orbifold theory. However, there are also other allowed defect networks, and such "non-group symmetries" lead to interesting relations between TFTs. Much of this is based on joint work with Ingo Runkel.