Knots and Graphs

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.

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

Schedule

Week 1
Mo. June 2	S.Chmutov,  Introduction. Knots.    Handout.
Fr. June 6	S.Chmutov,  The Jones and arrow polynomials.    Handout.
Week 2
Mo. June 9	S.Chmutov,  Graphs and their polynomials.    Handout.
Fr. June 13	S.Chmutov,  Ribbon graphs and Thistlethwaite's theorem.    Handout.
Week 3
Mo. June 16	S.Chmutov,  Topology of surfaces.    Handout.
Fr. June 20	E.Lu,  The Penrose Bracket and it’s Extension.    Slides. J.Case,  Multivirtual Knot Theory.    Slides.
Week 4
Mo. June 23	Levi Keck, Jason Tu,  Arrow Polynomial Collapses for Almost-Classical Virtual Links.     Slides.
Fr. June 27	Yile Huang,  Partial Dual and Delta-Matrix.    Slides. Logan Keck, Rohan Mawalkar,  Recurrence Relationships in Quasi-Tree Subgraphs.    Slides.
Week 5
Mo. June 30	Ethan Lu,  The Penrose-Kauffman Polynomial and Chromatic Bracket.    Slides. Jeremy Case,  Racks, Quandles, and Their Relation to Knot Theory.    Slides.
Week 6
Mo. July 7	Levi Keck,  Arrow Polynomial of Mod k Almost Classical Virtual Links.     Slides.
Fr. July 11	Logan Keck,  Recurrence Relationships in Ribbon Graphs.    Slides.