Student Algebra Seminar 2019
This page is for the Semester 2, 2019 seminar. The current seminar is here.
The Student Algebra Seminar is running in Semester 2 of 2019, and provides an opportunity for postgraduate and honours students to come together once a week and share knowledge about aspects of algebra and representation theory. We meet on Monday afternoons at 2pm, in Carslaw 830, for afternoon tea and a talk, which should last 50-80 minutes. Check the schedule below for which day. The seminar is organised by Joel Gibson.
About the seminar
Most talks this semester will be on the topic of Khovanov homology, primarily following the two sets of notes which are listed below. The topic will be in the usual style of the student algebra seminar: approachable, self-contained, and not requiring much more than honours-level knowledge to understand. Each lecture will be around 60 minutes long.
Schedule
| Date | Speaker | Topic | |
|---|---|---|---|
| Week 5 | Monday, 2nd September | Joel Gibson | The Jones polynomial |
| Week 6 | Monday, 9th September | Giulian Wiggins | The chain complex |
| Week 7 | Tuesday, 17th September | Joshua Ciappara | Reidemeister invariance |
| Week 8 | Monday, 23rd September | Gastón Burrull | Applications of Khovanov homology, movies, and functoriality |
| Week 11 | Wednesday, 23rd October | Joseph Baine | Lee Theory |
| Week 12 | Monday, 28th October | Joel Gibson | String diagrams I: Braided monoidal categories |
| Week 13 | Monday, 4th November | Joel Gibson | String diagrams II: Rigidity, ribbons and twists |
| Monday, 18th November | Boris Lishak | Link Framings | |
| Monday, 2nd December | Aiden Suter | Vertex algebras in QFT |
References (Khovanov Homology)
Mikhail Khovanov's original two papers on categorifying the Jones polynomial:
Two sets of notes on Khovanov's work:
- On Khovanov's categorification of the Jones polynomial, Dror Bar-Natan, 2002.
- Five Lectures on Khovanov Homology, Paul Turner, 2006.
Further reading:
- A hitchhiker's guide to Khovanov homology, Paul Turner, 2014.
References (String diagrams)
There will be notes posted here soon…
These two talks are modified versions of a talk given during a reading seminar on Tensor Categories by Etingof et. al. This book is excellent for definitions and theorems in general monoidal categories, but is quite difficult to skim for an overview of the subject, and only touches on diagrammatics. It would be much better to read the following references first, and consult Tensor Categories only to clear up any confusion:
- A survey of graphical languages for monoidal categories, Peter Selinger, 2009 — in particular Section 3 on monoidal categories, and Section 4 on autonomous categories. A word of warning: I used composition as bottom-to-top concatenation of diagrams and monoidal product as left-to-right concatenation of diagrams, but this survey flips those conventions.
Abstracts
Vertex algebras in QFT
Speaker: Aiden Suter
In this talk I will give an overview as to what vertex algebras are and some of the places they have been found to arise in physics. In particular, I will give several canonical examples of vertex algebras and explain how these, as well as other algebraic structures, arise in 2d conformal field theory and 3d and 4d supersymmetric (SUSY) QFTs.