Talk by Dr. Nathan Geer (Dept of Mathematics & Statistics, Utah State University)

1/10/2019   Wilson Hall 1-144   4:10-5:00pm


In the last few years, C. Blanchet, F. Costantino, M. De Renzi, B. Patureau, N. Reshetikhin, V. Turaev and myself (in various collaborations) have developed a theory of renormalized quantum invariants of links and 3-manifolds which lead to TQFTs. This talk will start out by giving an overview of this work. In the second part of the talk I will discuss the renormalized quantum invariants of links coming from quantized sl(2) at a root of unity. These link invariants contain Kashaev's quantum dilogarithm invariants of knots, the Akutsu-Deguchi-Ohtsuki invariant of links and the multivariable Alexander Polynomial. Moreover, these re-normalized invariants of knots are meromorphic functions whose residues are closely related to the colored Jones polynomials.