A landscape of knots
Thursday, June 27, 2019 - 2:30pm - 3:30pm
Knots are fascinating objects: featured in low dimensional topology, while gaining a strong visibility in biology, physics, material science and more. A multitude of knot invariants have been introduced to characterize and classify knots. The computational complexity often turns out to be exponential in the number of crossings of a knot, which is prohibitively expensive. Moreover, relations between different invariants and their relative strengths at distinguishing knots are still mostly elusive. We examine the structure of data consisting of various knot invariants using TDA and machine learning tools, such as Ball Mapper by P. Dlotko and dimension reduction methods. We gain insights into the correlations between invariants, and a tool for generating hypotheses about properties of knots and knot invariants.