Graduate Quantum Algebra and Topology Seminar at UC Santa Barbara
Organizers: Aaron Bagheri and Melody Molander
For Spring 2022, this seminar will be joint with the UCSB Quantum Algebra & Topology Seminar. You can view the schedule for Spring here. For Fall 2021 and Winter 2022 we went through the paper: Ribbon graphs and their invariants derived from quantum groups by Reshetikhin and Turaev.
Winter 2022 Schedule:
- 01/13: 0. Introduction and 1. The invariants of Reshetikhin and Turaev
- 01/20: 2.1 The Algebra A
- 01/27: 2.2 Representations of A
- 02/03: Patrick Vecera (UCSB)
- 02/10: 2.3 The R-matrix
- 02/17: 3.1 Tangles and 3.2 Colored Framed Tangle Operators
- 02/24: 3.3 Properties of Tangles and 3.4 Orientations
- 03/03: 3.5 Tangle Operators for A and 4.1 Skein Theory, the Jones Polynomial, & the Kauffman Bracket
- 03/10: 4.2 Cabling and 4.3 The Symmetry Principle
Fall 2021 Schedule:
- 10/06: Ch 1.1 Ribbon categories
- 10/13: Ch 1.2 Operator invariants of ribbon graphs
- 10/20: Ch 2.1 Modular tensor categories and Ch 2.2 Invariants of 3-manifolds
- 10/27: Ch 2.3.1 Kirby calculus and Ch 2.4 Computations in semisimple categories
- 11/03: Ch 2.5 Hermitian and unitary categories and Ch 3.1 Axiomatic definition of TQFT's
- 11/10: Ch 3.2 Fundamental properties and Ch 3.3 Isomorphisms of TQFTs