Aspects of geometry and supersymmetry

A single mathematical object—a supersymmetric quantum field theory—can look completely different depending on how you examine it, and Gurman Woodwal’s thesis project aims to map those hidden connections. This is fundamental science, not applied engineering. The work sits in physical mathematics, a field that uses the tools of theoretical physics to solve problems in pure mathematics. Woodwal will explore three linked areas: dualities in supersymmetric quantum mechanics (where two seemingly different theories describe the same physics), exact calculation methods in supersymmetric quantum field theory, and whether one-dimensional superconformal models can encode information about a two-dimensional holographic world. These are deep, structural questions about the mathematical fabric of quantum theory. Because this is curiosity-driven research, there is no immediate practical application. But similar fundamental work on dualities and holography has, in the past, reshaped how mathematicians understand geometry and how physicists approach quantum gravity. A clearer picture of these relationships could, over decades, influence how we model complex quantum systems—potentially relevant to future quantum computing architectures or to understanding the early universe. For now, the value is in the mathematics itself.