Knots and Graphs

https://people.math.osu.edu/chmutov.1/wor-gr-su26/wor-gr.htm

Working Group [Summer 2026]
MATH 4193, class number 15031
June 5 --- July 30, 2026

Instructor: Sergei Chmutov

CLASSES: Mondays, Friday of the first two weeks (June 5, 8, 12, and 15)
on 3:00-4:00pm at Dulles Hall 012.
Starting from June 22 online classes on ZOOM: Monday, Friday 3:00-4:00pm
+ one hour zoom meeting with each smaller group.             

 Past year programs

       2025   2024   2023   2022   2021
       2020   2019   2018   2017   2016
       2015   2014   2013   2012   2011
       2010   2009   2007   2006   2005

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

    Schedule

    Week 1

    		 
    Fr. June 5S.Chmutov,  The Introduction. Knots.    Handout.   

    Week 2

    		 
    Mo. June 8S.Chmutov,  The Jones polynomial.    Handout.
    Fr. June 12S.Chmutov,  Graphs and their polynomials.    Handout.   

    Week 3

    		 
    Mo. June 15S.Chmutov,  Ribbon graphs and Thistlethwaite's theorem.    Handout.

    Week 4

    		 
    Mo. June 22S.Chmutov,  Matroids and delta-matroids.     Slides.
    Fr. June 26Yile Huang,  Partial Dual and Delta-Matroid.    Slides.

    Week 5

    		 
    Mo. June 29Ethan Lu,  The Penrose Polynomial and some Variants.    Slides.

    Week 6

    		 
    Mo. July 6Logan Keck,  Maximum Twist Width of Delta-Matroids.    Slides.

    Week 7

    		 
    Mo. July 13Iain Moffatt,  Guest lecture. The Penrose Polynomial(s?) of a graph.   
    Fr. July 17Maxwell Brown,  Twisted duality and the Penrose polynomial.    Slides.

    Week 8

    		 
    Mo. July 20Ryland Smoot,  Characterizing Delta-Matroid with Twist Monomials.    Slides.
    Fr. July 24Minxiao Wu,  Exploring the Differences and Connections Between Two Generalizations of the Penrose Polynomial via Knot Theory.     Slides.