A landscape of knots: TDA and dimension reduction techniques in theoretical mathematics

Radmila Sazdanovic (NC State University)

Abstract

A multitude of knot invariants, including quantum invariants and their categorifications, have been introduced to aid with characterizing and classifying knots and their topological properties. Relations between knot invariants and their relative strengths at distinguishing knots are still mostly elusive. In addition to Ball Mapper, and machine learning techniques, we develop a new approach using filtrations to analyze infinite data sets where representative sampling is impossible or impractical, an essential requirement for working with knots and the data from knot invariants. Although of different origins, these methods confirm and illuminate similar substructures in knot data created for 10 million knots up to 17 crossings

Date

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