Knots and Graphs

https://people.math.osu.edu/chmutov.1/wor-gr-su25/wor-gr.htm

Working Group [Summer 2025]
MATH 4193, class number 14974
June 2 --- July 25, 2025

Instructor: Sergei Chmutov

CLASSES: Mondays, Friday of the first two weeks (June 2, 6, 9, and 13)
on 3:00-4:00pm at Cockins Hall 232.
Starting from June 16 online classes on ZOOM: Monday, Friday 3:00-4:00pm
+ one hour zoom meeting with each smaller group.             

 Past year programs

       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

    		 
    Mo. June 2S.Chmutov,  Introduction. Knots.    Handout.
    Fr. June 6S.Chmutov,  The Jones and arrow polynomials.    Handout.   

    Week 2

    		 
    Mo. June 9S.Chmutov,  Graphs and their polynomials.    Handout.
    Fr. June 13S.Chmutov,  Ribbon graphs and Thistlethwaite's theorem.    Handout.   

    Week 3

    		 
    Mo. June 16S.Chmutov,  Topology of surfaces.    Handout.
    Fr. June 20E.Lu,  The Penrose Bracket and it’s Extension.    Slides.
    J.Case,  Multivirtual Knot Theory.    Slides.    

    Week 4

    		 
    Mo. June 23Levi Keck, Jason Tu,  Arrow Polynomial Collapses for Almost-Classical Virtual Links.     Slides.
    Fr. June 27Yile Huang,  Partial Dual and Delta-Matrix.    Slides.
    Logan Keck, Rohan Mawalkar,  Recurrence Relationships in Quasi-Tree Subgraphs.    Slides.    

    Week 5

    		 
    Mo. June 30Ethan Lu,  The Penrose-Kauffman Polynomial and Chromatic Bracket.    Slides.
    Jeremy Case,  Racks, Quandles, and Their Relation to Knot Theory.    Slides.    

    Week 6

    		 
    Mo. July 7Levi Keck,  Arrow Polynomial of Mod k Almost Classical Virtual Links.     Slides.
    Fr. July 11Logan Keck,  Recurrence Relationships in Ribbon Graphs.    Slides.

    Week 7

    		 
    Mo. July 14Jeremy Case,  Multivirtual Quandles Invariants.    Slides.
    Ethan Lu,  The Potts model and Graphs Theory.    Slides.
    Fr. July 18Jason Tu,  Generalization of mod m Alexander numbering with Arrow polynomial variables.    Slides.
    Levi Keck,  Seifert State Ribbon Graphs of Classical Links.    Slides.

    Week 8

    		 
    Mo. July 24Yile Huang,  Partial Dual and Delta-Matrix.    Slides.
    Logan Keck, Rohan Mawalkar,  Counting Quasi-Trees in Non-Orientable Sequences.    Slides.
    Fr. July 25Ethan Lu,  Theoretical Juggling.     Slides.
    Levi Keck,  Tait graphs and Seifert States.    Slides.