From Link Homology to Topological Quantum Field Theories

This lecture explores how Khovanov's categorification of the Jones polynomial suggests higher categorical structures connecting to 4- and 5-dimensional topological quantum field theories (TQFTs). Discover the foundations of quantum topology, where knot and link invariants originate from braided monoidal categories of quantum group representations. Learn about four distinct types of TQFTs that emerge from link homology—4-dimensional, 5-dimensional, linear, and derived—and examine concrete examples that illustrate these theoretical frameworks. Gain insights into how braided monoidal 2-categories potentially bridge link homology with higher-dimensional topological quantum field theories.