BYU

Abstract by Andrew Carr

Personal Infomation


Presenter's Name

Andrew Carr

Degree Level

Doctorate

Co-Authors

Christopher Rytting

Abstract Infomation


Department

Computer Science

Faculty Advisor

David Wingate

Title

NMT exploration of knots and their invariants

Abstract

The study of knots in geometric topology has progressed recently with aid from computational methods. In this work, we explore the application of neural machine translation (NMT) to the generation of novel knots and studies of their distributions. Knots can be uniquely represented, up to reflection, by Dowker-Thistlethwaite (DT) codes. Additionally, knots have various invariants which can be derived from their projections. One of these invariants is the Jones polynomial. We use a novel representation of the Jones polynomial and a modern NMT architecture to explore transformations from knot invariants to the unique DT codes.