Distinguished, Speculative, First of April Talk and University Seminar-Speculations on the Jones Hypothesis via the Burau Representation

Time: Wednesday, April 1, 5:00–6:00 pm

Place: Phillips Hall, Room 108

Speaker:  Anzor Beridze, Batumi Shota Rustaveli State Univ., Batumi, Georgia

   and A. Razmadze Math. Institute of I. Javakhishvili Tbilisi State Univ., Tbilisi, Georgia

Title: Speculations on the Jones Hypothesis via the Burau Representation

Abstract: In this talk, using Hecke algebras, we will demonstrate a connection between the Jones hypothesis (Jones polynomial detects the unknot) and the faithfulness problem of the Burau representation for n=4. Moreover, different approaches will be considered, and new hypotheses will be formulated that are equivalent to the faithfulness of the Burau representation for B_4. In particular, we will discuss a homological approach, Garside-theoretic analysis, and algebraic as well as computer-assisted methods.