Knots are fundamental objects of study in low dimensional topology and geometry, and the subject has seen tremendous progress in the recent years. The aim of this program is to familiarise and enthuse younger researchers in India about the latest advances in the subject with a particular emphasis on computational aspects of (co)homological, combinatorial and polynomial invariants of knots. The program will also discuss some important aspects of knot theory from physics point of view.
The program will have two components, an advanced workshop (23 - 28 March 2020) followed by a discussion meeting (30 March - 03 April 2020). The advanced workshop will consist of mini courses on current aspects of knot theory by renowned experts. These topics will cover some of the latest advances in the subject, and will also prepare the participants for the discussion meeting which will consist of talks by well-known researchers in the field.
Topics to be covered during the advanced workshop:
- Colored Jones Polynomial and Volume Conjecture: Abhijit Champanerkar and Hitoshi Murakami
- Introduction to Knots, Knotoids and Virtual Knots: Louis H. Kauffman
- Khovanov Homology and Yang-Baxter Homology: Jozef H. Przytycki
- Quandles Cohomology and Knot Invariants: Seiichi Kamada
- Algebra of Quandles: Valeriy Bardakov
- Diagrammatic Algebra: Scott Carter
- Quantum Fields, Knots, and Strings: Piotr Sulkowski
The primary audience of the program (especially the advanced workshop) will be PhD students, post doctoral fellows and young faculty members working in low dimensional topology and adjoining areas. There will be some slots in the program for contributed talks by younger researchers and a poster session is also planned.
PhD students, post doctoral fellows and faculty members working in low dimensional topology and adjoining areas. A few motivated master level students with demonstrable mathematical maturity may also be considered.