Topological Strings, Knots, and Quivers - Lecture 1

Explore the fascinating intersection of mathematics and physics in this lecture on topological strings, knots, and quivers. Delve into the world of knot theory, beginning with closed loops in 3D manifolds and topological equivalence. Learn about polynomial knot invariants, including the HOMFLY-PT polynomial, and their connections to Chern-Simons theory. Discover cabling formulas and tackle exercises to reinforce understanding. Investigate the A-polynomial, recursion relations, and the volume conjecture, including its quantum counterpart. Examine knot homology and superpolynomials, with practical examples provided. Gain insights into the deep connections between quantum field theory, geometry, and representation theory in this comprehensive lecture from the International Centre for Theoretical Sciences' program on Quantum Fields, Geometry and Representation Theory.

Quantum Fields, Geometry and Representation Theory
Topological strings, knots, and quivers Lecture 1
KNOTS - Closed loops in 3D manifold
Topological Equivalence
Polynomial KNOT Invariants
Exercise
Homfly - PT
Chern-Simons Theory
We will often consider symmetric reps R=St
Cabling Formulas
Exercise 2
A- Polynomial & Recursion Relations
Under they are rearrested by the commutative matrices, so by conjugation
CCGLS 1995
Volume conjecture & recursion relations
Quantum Volume Conjecture
Remark
Knot Homology
Superpolynomial
Super Polynomials can be found by
Example
Q&A