Seminarium Teorii Względności i Grawitacji

Knot theory is a fascinating field of mathematics, with applications in physics ranging from biophysics to statistical physics, quantum information theory and string theory. It gained an enormous boost in the 1980’s after a discovery of so-called Jones polynomial, and its physical interpretation in terms of a topological quantum field theory with the action functional consisting purely of Chern-Simons term. The last decade has witnessed another series of fascinating developments in this area, in particular (mathematical) discovery of homological knot invariants, and their (physical) realization in terms of Calabi-Yau manifolds. In this talk we will review an approach to knot theory based on Chern-Simons theory, and discuss recent progress in relating its refinement to string theory and homological knot invariants.Note: This is the first (albeit self-contained) of the two talks devoted to knots, strings and quantum fields. The second talk will be presented as the “Exact Results in Quantum Theory and Gravity” seminar, also on May 18th. See also: www.stringtheory.pl/seminaria/

Knot theory is a fascinating field of mathematics, with applications in physics ranging from biophysics to statistical physics, quantum information theory and string theory. It gained an enormous boost in the 1980’s after a discovery of so-called Jones polynomial, and its physical interpretation in terms of a topological quantum field theory with the action functional consisting purely of Chern-Simons term. The last decade has witnessed another series of fascinating developments in this area, in particular (mathematical) discovery of homological knot invariants, and their (physical) realization in terms of Calabi-Yau manifolds. In this talk we will review an approach to knot theory based on Chern-Simons theory, and discuss recent progress in relating its refinement to string theory and homological knot invariants.Note: This is the first (albeit self-contained) of the two talks devoted to knots, strings and quantum fields. The second talk will be presented as the “Exact Results in Quantum Theory and Gravity” seminar, also on May 18th. See also: www.stringtheory.pl/seminaria/