DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Co-organizers:

Matthew Russell, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)

Doron Zeilberger, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Quantum A-polynomials for knots using the q-Zeilberger algorithm

Speaker: Semeon Artamonov, Rutgers University

Date: Thursday, February 20, 2014 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

My talk is devoted to application of the q-Zeilberger algorithm to knot theory and my recent research in that area. I will start with a basic introduction to knot invariants for graduate students and define braid group and Hecke algebras. Using the Turaev R-matrix approach I will explain how to evaluate one of the most powerful knot invariants, namely the colored HOMFLY polynomial. However, the naive application of the Turaev approach quickly makes evaluations impossible on today's computers. To overcome that issue I will explain the recent developments on cabling techniques and tricks I used in my programs.

See: http://www.math.rutgers.edu/~russell2/expmath/