Author Date

2023-11

Degree Name

Department

Mathematics

College

Physical and Mathematical Sciences

Defense Date

2023-11

Publication Date

2024-01-30

First Faculty Advisor

Mark Hughes

First Faculty Reader

Dan Ventura

Honors Coordinator

Davi Obata

Keywords

Deep Reinforcement Learning, Topology, Knots, PPO

Abstract

Deep reinforcement learning (DRL) has proven to be exceptionally effective in addressing challenges related to pattern recognition and problem-solving, particularly in domains where human intuition faces limitations. Within the field of knot theory, a significant obstacle lies in the construction of minimal-genus slice surfaces for knots of varying complexity. This thesis presents a new approach harnessing the capabilities of DRL to address this challenging problem. By employing braid representations of knots, our methodology involves training reinforcement learning agents to generate minimal-genus slice surfaces. The agents achieve this by identifying optimal sequences of braid transformations with respect to a defined objective function.