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Quantum invariants and low-dimensional topology: Computational approaches

Developing software for skein computations in knot complements- Rachel Marie Harris (Texas Tech University)

Abstract: Skein manipulations prove to be computationally intensive due to the exponential nature of skein relations. The purpose of this project is to construct an automated tool to generate a library of examples for use in testing new conjectures in Chern-Simons theory.

Finding Structure in Polynomial Invariants using Data Science- Jesse Levitt (UCLA)

Abstract: Authors: Pawel Dlotko, Mustafa Hajij, Jesse Levitt (presenter), Radmila Sazdanovic Abstract: Using Principal Component Analysis and Topological Data Analysis we analyze the distributions of the knot polynomials in coefficient space. These tools prove useful for both distinguishing how well different invariants separate the knots into distinct families and for how these families suggest correlations between different knot invariants. We focus on how the Ball Mapper of P. Dlotko, an exploratory data analysis tool that builds graphs from high dimensional clouds of data using just a radius measure, confirms and further illuminates substructure in this data. This includes some specific ways in which the s-invariant and signature differ through the distribution of the Alexander and Jones polynomials.

2 replies on “Quantum invariants and low-dimensional topology: Computational approaches”

Hi Rachel,

Your video is so awesome! I’m really curious about these conjectures in Chern–Simons theory that the skein computations are related to, can you say more about those?

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