Graduate Quantum Algebra and Topology Seminar at UC Santa Barbara
Organizers: Aaron Bagheri and Melody Molander
For Fall 2022, this seminar will be joint with the UCSB Quantum Algebra & Topology Seminar.
Winter 2023 Schedule: (mostly following "Braid Groups" by Kassel and Turaev)
- 01/09: 1.1.1-1.2.3 (Melody Molander)
- 01/16: MLK Jr. Day (No Talk)
- 01/23: 1.2.4-1.3.2 (John White)
- 01/30: 1.3.3-1.4.4 (Sam Sehayek)
- 02/06: 1.5.1-1.7.1 (Troy Kling)
- 02/13: 1.7.2-2.1.3 (Choom Moos)
- 02/20: President's Day (No Talk)
Fall 2022 Schedule: (mostly following "Exercises in Quantum Algebra" by Penneys)
- 09/28: The Temperley-Lieb algebras (Melody Molander)
- 10/05: The Kauffman bracket & 3.1.1 Basic facts about \(\text{M}_n(\mathbb{C})\) (Melody Molander)
- 10/12: Exploring Finite-Dimensional *-Algebras (Daniel Halmrast)
- 10/19: Exploring Finite-Dimensional *-Algebras (Part 2) (Daniel Halmrast)
- 10/26: Jones' Basic Construction in Finite Dimensions (Daniel Halmrast)
- 11/02: Diagrammatic Presentation of Index 4 Subfactor Planar Algebras (Melody Molander) (Quantum Seminar Talk)
- 11/09: An Exploration of Linear Categories (Jeremy Khoo)
- 11/16: Cauchy Completion and Semisimplicity (Quinn Kolt)
Winter 2022 Schedule: (following "The 3-manifold invariants of Witten & Reshetikhin-Turaev for sl(2,\(\mathbb{C})\)" by Kirby and Melvin)
- 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: (following "Quantum Invariants of Knots and 3-Manifolds" by Turaev):
- 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