Author Date

2024-12-13

Degree Name

Department

Mathematics

College

Physical and Mathematical Sciences

Defense Date

2024-12-13

Publication Date

2024-12-13

First Faculty Advisor

Mark Hughes

First Faculty Reader

Mark Kempton

Honors Coordinator

Davi Obata

Keywords

Braids, Band Rank, Supervised Learning, Neural Networks

Abstract

Supervised learning has emerged as a powerful tool for solving complex classification problems across various domains, including mathematical structures. In the realm of braid theory, an intriguing challenge involves determining the number of bands in a mathematical braid, which is crucial for understanding braid complexity and its applications. This thesis introduces an approach leveraging supervised learning to tackle this problem. Using different representations of a braid (namely braid words and Lawrence-Krammer representations), we train a supervised learning model to predict the number of bands in a given braid. The approach involves constructing a labeled dataset of braids with known band counts and employing neural networks to discern patterns and relationships within this dataset. The efficacy of the proposed method is evaluated, demonstrating its potential to enhance the accuracy and efficiency of band-counting in mathematical braids.