Knots and Graphs

Working Group [Summer 2024] MATH 4193, class number 16239 June 3 --- July 26, 2023 Instructor: Sergei Chmutov CLASSES: Mondays, Friday of the first two weeks June 3, 7, 10, and 14 at 3:00-4:00pm Starting from June 17 online classes on ZOOM: Monday, Friday 3:00-4:00pm + one hour zoom meeting with each smaller group.

Past year programs        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 3	S.Chmutov,  Introduction. Knots.    Handout.
Fr. June 7	S.Chmutov,  The Jones and arrow polynomials.    Handout.
Week 2
Mo. June 10	S.Chmutov,  Graphs and their polynomials.    Handout.
Fr. June 14	S.Chmutov,  Ribbon graphs and Thistlethwaite's theorem.    Handout.
Week 3
Mo. June 17	S.Chmutov,  Partial duality of ribbon graphs.    Handout.
Fr. June 21	G.Black,  Polynomials on Graphs with Applications.    Slides.
Week 4
Mo. June 24	W.Wu,  Partial-Dual Genus Polynomial.    Slides.
Fr. June 30	S.Wu,  Chromatic Polynomials of 2-Edge-Colored Graphs.    Slides.
Week 5
Mo. July 1	A.Praturi  Contraction - Deletion Relations for the Bollobás-Riordan polynomial.     Slides.
Fr. July 5	C.Li,  Intersection Graphs and Partial Duality.     Slides.
Week 6
Mo. July 8	J.Case,  Deletion Contraction and Whitney Broken Circuits for2-Edge Colored Graphs.     Slides.
Fr. July 12	D.Kruzel,  Calculating Boninger's Polynomials.    Slides.
Week 7
Mo. July 15	C.Li,  Cut-vertex Recursion for the Intersection Polynomial.    Slides.
Fr. July 19	J.Case,  N-Coloring of 2-Edge Colored Planar Graphs.    Slides.
Week 8
Mo. July 24	G.Black,  Boninger’s Mistake.     Slides. D.Kruzel,  Analyzing Boninger’s Result On The Torus.     Slides.
Fr. July 26	C.Li,  Cut-vertex Recursion for the Twist Polynomial on Looped Simple Graphs.     Slides.