Here are the slides and videos from a few select talks that I have delivered.
A Tour of Skein Modules (Knots Through Web, ICTS, Bengaluru, India, August 26, 2020)
Abstract: Skein modules were introduced in 1987 by Józef H. Przytycki as generalisations of 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 algebraic and hyperbolic geometry, quantum cluster algebras, and the Witten-Reshetikhin-Turaev Topological Quantum Field Theories, to name a few. In this talk we will give the audience a tour of the development of the various kinds of skein modules, focusing primarily on the Kauffman bracket skein module.
Here is the YouTube recording of my talk at the International Centre for Theoretical Sciences.
Here is a talk I gave at the Stanford Topology Seminar about some of my more recent work in quantum topology and skein modules.
Gram Determinants Motivated By Knot Theory (Student Research Talks (StReeTs), George Mason University, October 25, 2019)
Abstract: The study of Gram determinants in knot theory dates back to Lickorish when he used Gram matrices arising from the Temperley – Lieb algebra and constructed the Witten-Reshetikhin-Turaev invariant of 3 – manifolds combinatorially. In this talk, I will first discuss Gram determinants of type A and Gram determinants of type B. A closed formula for the latter was given by Chen and Przytycki which answered a question posed by the late combinatorialist Rodica Simion about the relationship between matrices of chromatic joins and Gram type matrices. Finally, I will describe our work on the Gram determinant of generalised type A and the Gram determinant of type Mb.