Noah Ringrose’s Personal Website

Hi! I’m a first-year physics PhD student at NYU advised by Yifan Wang with broad interests in the higher categorical structures which underlie quantum field theory (QFT). Before this, I was lucky enough to do my undergraduate studies at Penn State University under the mentorship of Adrian Ocneanu and do some research on tensor categories and Levin-Wen models under the supervision of Dave Penneys at Ohio State University.

In the last decade or so, the cultural zeitgeist surrounding QFTs has shifted to become increasingly more Yoneda-esque. By this I mean that physicists have become more conscious of the idea that rather than asking what “is” a QFT, we should instead study the “space” of all defects which can probe the theory.

While we are applying it on a higher level these days, this general approach toward physics is certainly not new. Even Ernest Rutherford knew in 1909 that the question of “what is an atom?” is somehow nonsensical: this question should be rephrased as “how do atoms (in a thin gold film) respond to all possible probes (charged alpha particles) that we can throw at it?”

Some things that I am curious about (but certainly do not know nearly enough about) in this direction currently are:

• Generalizations of the tube algebra and Drinfeld center constructions, and their interactions with quiches, higher representation theory, and ideas from factorization homology. In particular, how can this technology be used to go beyond finite semisimple symmetries, and eventually beyond topological defects altogether? More broadly, what is the general mechanism behind bulk-boundary correspondence in QFT?
• How can we connect ideas from extended functorial field theory and algebraic QFT with what physicists actually do? I am especially interested in the question: “What is a morphism of a field theory?” For instance, what is the proper way to formulate questions about how RG flows act on higher categories of defects in this language? I am interested in exploring these ideas in concrete low-dimensional examples such as 3d TFTs (state-sum models, lattice models, homotopy sigma models) and 2d CFTs.
• Despite being two central features of physical theories, fermions and unitarity have received comparatively little in-depth treatment in much of the literature on category-theoretic structures in QFT. I am interested in further developing the rich but subtle extensions of these structures needed to incorporate them naturally.
• The role of generalized cohomology theories and spectra in classifying spaces of physical theories. For instance, I have passing interests in invertible field theories and homotopy theory, as well as differential cohomology.

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!