Rhea Palak Bakshi - Skein Theory in the Semisimple and Non-Semisimple Setting - IPAM at UCLA
Recorded 13 October 2026. Rhea Palak Bakshi of the University of California, Santa Barbara, presents "Skein Theory in the Semisimple and Non-Semisimple Setting" at IPAM's Hyperbolic Structures and Quantum Invariants Workshop.Abstract: Skein modules were introduced independently by Przytycki and Turaev with the goal of building an algebraic topology based on knots, generalising the skein theory for links in $S^3$ to arbitrary 3-manifolds. Turaev introduced the Conway and Kauffman skein modules independently. The Kauffman bracket skein module, which serves as the generalisation of the Kauffman bracket polynomial, has a natural algebra structure given by the stacking of skeins (elements in the skein module) when the 3-manifold is a thickened surface. This algebra, known as the Kauffman bracket skein algebra, has deep connections with algebraic and hyperbolic geometry. The Roger-Yang skein algebra is a generalisation of the Kauffman bracket skein algebra for punctured surfaces, allowing framed arcs between punctures. It is known that this new algebra is related to the decorated Teichmuller space introduced by Penner. Further study of the Roger-Yang skein algebra will help better understand the connections between hyperbolic geometry and quantum topology. In this talk, we talk about some preliminary work, joint with Han-Bom Moon and Sujoy Mukherjee, towards giving a presentation of the Roger-Yang skein algebra of the n-punctured torus, for $n 0$.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-hyperbolic-structures-and-quantum-invariants/?tab=overview Receive SMS online on sms24.me
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