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Thank you for your interest in the Purdue Quantum Topology Student Seminar! This website will host the schedule and meeting notes as well as links to helpful resources/papers.
Thank you for your interest in the Purdue Quantum Topology Student Seminar! This website will host the schedule and meeting notes as well as links to helpful resources/papers.
The schedule for the seminar is below. We meet on Fridays at 3:30pm in SCHM 122. If we are not meeting, then that date will not be in the calendar.
The schedule for the seminar is below. We meet on Fridays at 3:30pm in SCHM 122. If we are not meeting, then that date will not be in the calendar.
Overview
Overview
For Fall 2026, the goal of the seminar is to understand the tool of skein modules for studying 3-manifolds. Described as an "algebraic topology based on knots," skein modules are a knot theoretic construction that has close connections to character varieties, representations of quantum groups, and 3-manifold invariants. The goal of this seminar is to understand some of these connections specifically in the case of the Kauffman bracket skein module.
Books & Papers
Books & Papers
For the definition of skein modules and the Kauffman bracket
Lectures in Knot Theory,'' by Józef Przytycki et al, Chapters 11-12.
Gives a good introduction to skein modules in general and provides some exercises to work with. The Kauffman bracket skein module is well studied.
Connections to Quantum Groups
Quantum Invariants of Knots and 3-Manifolds,'' by Vladimir Turaev, Chapter 12. (Ask the organizers for a copy.)
Considers the same skein module construction but in the case of tangles and interprets this as the construction of a tensor category. This chapter also ties the Kauffman bracket to the Temperley-Lieb algebra."A minus sign that used to annoy me but now I know why it is there," by Peter Tingley.
Gives the relationship between the Kauffman bracket skein module and the quantum group Uq(sl2).
Connections to 3-Manifold Invariants
"Quantum Invariants of Knots and 3-Manifolds," by Vladimir Turaev, Chapters 3-4.
Connections to Character Varieties
"Lectures in Knot Theory," by Józef Przytycki et al, Chapters 13.
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