My name is Catherine Ray, and I’m a mathematician. My current research is namely in understanding the interplay of Galois theory and Galois representations with homotopy theory. Before I was in math, I worked mostly in scientific simulation, autonomous robotics, and medical technology.

### 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 in progress)
- 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)

### Contact me

Curiosity is welcome: fractalcows@gmail.com