Alladi Ramakrishnan Hall

Knot invariants, topological strings, and 3d/3d correspondence I

Satoshi Nawata

Fudan University

In this lecture series, I will explain relationship among knot invariants, topological strings, and 3d/3d correspondence. Recent study reveals that these seemingly different topics can be comprehensively understood from bird eyes' view of M5-branes. Hence, the goal of this lecture is to see how geometry of 3-manifolds and knots can be understood by quantum field theories and string theory involving M5-branes. The lecture will be pedagogical and hopefully it is meaningful even to mathematicians. The following topics will be covered.

1. Chern-Simons theory and knot invariants
2. Topological string theory and knot invariants
3. Volume conjecture and A-polynomials
4. 3d/3d correspondence and exact result of 3d N=2 theories