Tensor categories give a shared algebraic language for how objects combine, how duals behave, and how exchange or 'twist' data appear. They arise naturally in two-dimensional conformal field theory (CFT). At the start, I will briefly point out how fusion, braiding, twists, and modular constraints connect to topics such as topological phases of matter and braid-based approaches to quantum computation, to set context for the broader ICTS audience.
The main focus is logarithmic CFT and the representation categories of vertex operator algebras (VOAs). A useful approach is to study a few key families (building on work of Feigin, Frenkel, Kazhdan, Lusztig, etc) and then relate many further examples by using constructions like extensions, cosets, and orbifolds. I will concentrate on VOA extensions and the categorical mechanism behind them: commutative algebra objects and their local modules. This gives a clean way to carry properties such as rationality and rigidity from one VOA to another (which we will illustrate in examples).
Zoom link: https://icts-res-in.zoom.us/j/96419966420?pwd=1VWojfqUpPruUSbTxu5vyD6hSnW8pd.1
Meeting ID: 964 1996 6420
Passcode: 202030