Noah Ringrose’s Personal Website

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Hi! I’m a first-year physics PhD student at NYU advised by Yifan Wang and Aditi Mitra. My research interests lie in understanding how methods from topology and category theory can be used to reinterpret discrete and subtle physical quantities within a deeper geometric framework, and how physical techniques can, in turn, be used to compute and illuminate rich mathematical invariants. To first-order approximation, it’s fair to say that I am interested in physical mathematics.

Currently, I am interested in learning about anything related to the following:

While I have a LONG way to go, I am ultimately interested in the non-perturbative structure of the space of quantum lattice models and QFTs, and in the development of a higher-categorical calculus for computations within and between them.

In Spring 2025, I finished my undergraduate studies in math and physics at Penn State University, where I was mentored by Adrian Ocneanu. Adrian liked to say that matter and spacetime are computation machines, and in order to study physics non-perturbatively, we need to literally “fill space around us with computations.” Formally, this amounts to considering the higher representation theory of networks of extended defects and computing physical quantities via some kind of higher-dimensional diagrammatic calculus. My goal in some sense is to learn how to apply this perspective to understand various aspects of physics.

I also spent a summer at Ohio State University, where I researched how to compute categorical data directly from the movement and fusion of anyonic excitations in a unitary fusion category’s associated Levin-Wen model. This was done under the supervision of Dave Penneys and Kyle Kawagoe. There, I learned the formal language of tensor categories and of the physical theory of topological phases of matter which it describes exactly.

This website is my personal space where I share my ideas and perspectives on math and physics and keep track of my progress as a physicist, mathematician, natural philosopher, or whatever I choose to identify as on a given day.

I’m only just getting started, but if you’re itching for a first taste of my work, you should check out my senior honors thesis, Higher Structures from Simple Lattice Models. I believe that young physicists shouldn’t have to spend years delving into an intense study of mathematics to build up the necessary vocabulary to penetrate the seriously cool aspects of physics; nor should they have to wait around for years for cutting-edge mathematical techniques to be translated into a physics-friendly language. I believe that physics and mathematics should be developed side-by-side in a common language and that the usage of ‘abstract nonsense’ — like category theory — can be destigmatized in physics by building visually intuitive mathematical frameworks. This thesis is a testament to this belief; my goal was to motivate the study of topological defects, fusion categories, and non-invertible symmetries in physics from the ground up with very few prerequisites, showing how these structures arise naturally when studying the simplest classical lattice model — the 2d Ising model.

Outside of physics and math, I try to eat food from as many different cultures as I can and experiment with the fusion of their flavors in my own kitchen. From time to time I dabble in bouldering and I am particularly passionate about the long conversations/one-sided-ramblings that take place between the time spent on the climbing wall. I also enjoy reading novels and philosophy on the subway and listening to Suki Waterhouse while aimlessly walking through New York City. I look forward to getting lost in more cities, flavors, books, music, and problems during my journey as a physicist.

If you are curious about my background, you can check out my CV, though it may or may not be a bit out of date depending on when you are reading this.

I love talking to anyone who shares even a passing interest in these ideas, so if you want to chat about anything, feel free to reach out via email at noah.ringrose@gmail.com!