Knots and Graphs

Working Group [Summer 2018]
MATH 4193, class number 17324
June 5 --- July 27, 2018

Instructor: Sergei Chmutov
Office MA-234. Phone 292-3568

Monday 12:30-1:30, Friday 12:00-1:00, MW-154             

Past year programs

       2017   2016
       2015   2014    2013    2012    2011
       2010    2009    2007    2006    2005

  • Announcement
  • List of participants
  • Research projects
  • Table of Virtual Knots by Jeremy Green
  • Our results

  • Schedule

    Week 1

    Fr. June 8S.Chmutov,  Introduction. Knots and Jones polynomial.    Handout.   

    Week 2

    Mo. June 11S.Chmutov,  The Jones polynomial and the chromatic polynomial.   
    Fr. June 15 S.Chmutov,  The Tutte polynomial.     Handout.    Wikipedia.

    Week 3

    Mo. June 18S.Chmutov,  The Tutte polynomial. (continuation.)   
    Fr. June 22 S.Chmutov,  Symmetric functions.     Handout.

    Week 4

    Mo. June 25A.Vengal, W.Hoffer, V.Winstein,   Tricolorings, Keis, and Quandles.
    Fr. June 29 J.Enouen, E.Fawcett, R.Raghavan, I.Shah,  Symmetric signed chromatic polynomial.

    Week 5

    Mo. July 2J.DePascale, M.Fava, J.Park,  Gauss diagrams, virtual knots, and their polynomals.
    Fr. July 6 J.Huryn,   Symmetric chromatic polynomial for trees.

    Week 6

    Mo. July 9A.Vengal, W.Hoffer, V.Winstein  Two cocycles of quandles and the state sum invariants.
    Fr. July 13 J.Enouen, E.Fawcett, I.Shah,  Contraction-deletion for the symmetric chromatic polynomial of signed graphs.

    Week 7

    Mo. July 16N.Wang  Invariance of the Tutte polynomial.
    J.Huryn,  Symmetric chromatic polynomial of modified spiders.
    Fr. July 20J.Beck, J.DePascale, M.Fava, J.Park,  Estimate for the number of Reidemeister moves.

    Week 8

    Mo. July 23A.Vengal, W.Hoffer, V.Winstein,   Cohomology, biquandles, and bracket invariants.
    Fr. July 27J.Enouen, E.Fawcett, R.Raghavan, I.Shah,   Symmetric chromatic polynomial for trees and hypergraphs.