- Series
- Geometry Topology Seminar
- Time
- Monday, April 13, 2015 - 2:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Aaron Lauda – USC – adlauda@gmail.com – http://www-bcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html
- Organizer
- Stavros Garoufalidis
It is a well understood story that one can extract linkinvariants associated to simple Lie algebras. These invariants arecalled Reshetikhin-Turaev invariants and the famous Jones polynomialis the simplest example. Kauffman showed that the Jones polynomialcould be described very simply by replacing crossings in a knotdiagram by various smoothings. In this talk we will explainCautis-Kamnitzer-Licata's simple new approach to understanding theseinvariants using basic representation theory and the quantum Weylgroup action. Their approach is based on a version of Howe duality forexterior algebras called skew-Howe duality. Even the graphical (orskein theory) description of these invariants can be recovered in anelementary way from this data. The advantage of this approach isthat it suggests a `categorification' where knot homology theoriesarise in an elementary way from higher representation theory and thestructure of categorified quantum groups. Joint work with David Rose and Hoel Queffelec