Invariants of Tangles with Flat Connections in the Complement

Watch a 54-minute lecture exploring the construction of invariants of tangles with flat connections in the complement, based on quantum groups at roots of unity. Delve into the collaborative work of Reshetikhin and Kashaev from 2005, examining its connection to Turaev's homotopy quantum field theory. Learn about the construction of these invariants and discover why Poisson structures on the center of quantum groups at a root of unity emerge naturally when considering the geometry of flat connections in tangle complements. Gain insights into the De Concini-Kac version of quantum groups, featuring their distinctive large center characteristics.