Quantum Topology Seminar
Rhea Palak Bakshi
Institute for Theoretical Studies at ETH Zürich.
Skein Modules and Chebyshev Polynomials
Abstract: Skein modules were introduced by Józef H. Przytycki as generalisations
of all the various polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. Over time, they have evolved into one of the most important objects in knot theory and quantum topology having strong ties with many fields of mathematics such as algebraic geometry, hyperbolic geometry, and the Witten-Reshetikhin-Turaev 3-manifold invariants, to name a few. Chebyshev polynomials are an important class of polynomials related to the sine and cosine functions, which have made surprising appearances, and have been rather indispensable, in the study of Kauffman bracket skein modules and algebras. In this talk we will discuss some of these connections between Chebyshev polynomials and skein modules and algebras.
Thursday December 1, 2022 at 12:00 PM in Zoom