My name is Cathe**rin**e Ray (they/them), and I’m a mathematician and artist.

My current mathematical research is on arithmetic patterns in homotopy theory and physics. I also work in chronic pain research. Before I was in math, I worked mostly in scientific simulation, autonomous robotics, and medical technology.

I graduated from George Mason University at 16 with a B.S. in Computational Physics, and accepted the Thiel Fellowship in 2014 to study mathematics full time under my mentor, Edward Frenkel. I graduated with my Master’s degree from UChicago working with Peter May, and with my PhD from Northwestern working with Paul Goerss. I am currently a postdoc at Uni-Münster in the Arithmetic and Homotopy Theory Working Group lead by Thomas Nikolaus and Christopher Deninger.

Here is a summary of my work as a graduate student for a general audience, including original illustrations.

### Contact me

Curiosity is welcome: fractalcows@gmail.com

My work email: cray@uni-muenster.de

If you are interested in my research mathematics, here are some fun papers of mine:

### Research publications:

- Automorphisms of Abelian Varieties and Principal Polarizations joint with D. Lee;
*Rendiconti del Circolo Matematico di Palermo Series 2, Volume 71, pages 483–494, 2022*arxiv - Towards Directed Collapsibility joint with R. Belton, R. Brooks, S. Ebli, L. Fajstrup, B. T. Fasy, N. Sanderson, E. Vidaurre;
*Advances in Mathematical Sciences, Volume 21, pages 255–271, 2020*arxiv

### Research preprints:

A Global Crystalline Period Map joint with M. Neaton and A. Pieper

### In progress:

- A Geometric Model of Higher K-theories at Height h=p^{k-1}(p-1) via Families of Ramified Curves — (my thesis, readable arxiv version in progress)
- The homotopy groups of E_6^{hC_9} and the odd primary Kevaire invariant; joint with E. Belmont
- Covers of the Octahedron; joint with D. Lee
- Duality resolutions for general linear groups; joint with E. Belmont, P. VanKoughnett

### Expository writing:

- Calculating pi_*(tmf) at the prime 2 (An Illustrated Guide to the May Spectral Sequence)
- A Complete Proof of the Polynomial Ham Sandwich Theorem, Based on Gromov’s Proof
- Fiber Bundles of Formal Disks (with A. Holeman)
- An Overview of the Classic Theory of P-Divisible Groups (Published in Oberwolfach Proceedings)