Exact Results in Quantum Theory

Volume conjecture relates knot invariants to hyperbolic geometry and the volume of knot complements. In this talk we will present physical formulation of the volume conjecture in terms of Chern-Simons theory, its relations to string theory, and phenomena such as emergent and noncommutative geometry arising in this context, which are currently actively studied.Note: This is the second (albeit self-contained) of the two talks devoted to knots, strings and quantum fields. The first talk will be presented as the "Gravity seminar", also on May 18th. See also: www.stringtheory.pl/seminaria/