ABOUT ME
My name is Catherine Ray (they/them), and I’m a mathematician and artist. My current math research is on arithmetic patterns in homotopy theory and physics.
Before I was in math, I worked mostly in scientific simulation, autonomous robotics, and medical technology. I continue to work in chronic pain research, which you can read about here.
Here for the math? Skip to the research ↓
THE PATH
I am currently a postdoc at Uni-Münster in the Arithmetic and Homotopy Theory Working Group led by Thomas Nikolaus and Christopher Deninger.
Before that, I graduated from George Mason University at 16 with a B.S. in Computational Physics, and accepted the Thiel Fellowship in 2014 to develop medical technology and study mathematics under my mentor, Edward Frenkel. I graduated with my Master’s degree from UChicago working with Peter May and Kazuya Kato (加藤 和也), and with my PhD from Northwestern working with Paul Goerss and Yifeng Liu.
THE OTHER STUDIO
I primarily work with pastels, acrylic, spray paint and polaroids. When I spray I make colorful street murals of creatures. Please enjoy this small collection of my art.
Away from the desk I rock climb, write short stories, speak intermediate German, beginners Russian and Spanish, embarrassingly “robotic” American Sign Language, read braille, and play trombone and ukulele.
pastels acrylic spray paint polaroids tattoo design
SEE THE GALLERY →BEFORE MATH
tl;dr my technical background is mainly in robotics (machine learning and SLAM), and computational physics. In autumn 2014 I began teaching myself algebraic topology full time, and did not stop.
Robotics and autonomous systems
A hexapod that followed people around, and a Rubik’s cube solving robot2011
Positronics Division, George Washington University Robotics LabSummer 2012
SLAM and motion planning on the ARDroneFall 2013
Polyglass — a Google Glass app that computes a human pulse from the video feedHackMIT 2013
Simulation and computational physics
Resistive switching behaviour of flexible TiO2Spring 2012
Modes of conductive polyhedra2012
Predicting the material properties of compound materialsFall 2012
The rookie mistake of trying to prove the Collatz conjectureNov 2013
Machine learning and language
CAMEL — learning the grammar rules of compressed Braille from partially translated textSpring 2013
Software Engineering Intern, ClouderaSummer 2013
Automating the collection and classification of lab-animal vocalizationslate 2013 – mid 2014
Medical and assistive technology
Improving mobility devicesSummer 2013 – Spring 2014
A keychain-sized food scanner for gluten and other common food allergen proteinsEarly 2014
NeuroprostheticsSummer 2014
Mentored Ada Rosa on mobility assistance for people with ALS and spinal cord injuriesEarly 2015
Complex systems
Visiting Researcher, Santa Fe InstituteJan 2015
CONTACT ME
- Curiosity is welcome
- fractalcows@gmail.com
- My work email
- cray@uni-muenster.de
You will find the name Catherine Ray on my old research papers and Rin Ray on my newer works — these both refer to the same person. I prefer Rin nowadays.
PUBLISHED
PREPRINTS
IN PROGRESS
Zeta Functions in Homotopy Theory
Syntomic cohomology of ring spectra and a T(h)-local zeta function
Toward Categorifying the relationship of Symplectic L-functions and Reidemeister Torsion
L-genera and Localizations in K-theory
All Bernoulli Numbers in Homotopy Theory Are Shiftson hiatus
Moduli Stacks of Curves in Homotopy Theory
The group cohomology of the maximal finite subgroups of the Lubin–Tate action is the E2 page needed to capture all p-torsion information in the stable homotopy groups of spheres. My thesis (2023) attempts to resolve the 40-year-old open problem of describing the Lubin–Tate action for all maximal finite subgroups.
It does so by outlining a universal way to build a geometric model using a moduli stack of G-curves given a subgroup G. A key insight is to replace the role of level structures with higher ramification information. To make the thesis more digestible, I have broken it up into three parts, the last of which is forthcoming. The only nontrivial p-torsion for odd primes is found at heights pk−1(p−1).
Writhing Jewels: A Conjectural Description of the Lubin–Tate Action via Moduli Stacks of G-Curves for h = pk−1(p−1)
The Eigenvalues of Frobenius of Artin–Schreier–Witt Curves are Gauss Sums
EXPOSITORY
Zeta Functions and THH
Using Automorphism Groups of Curves to Control the Slopes of their Jacobians
K-theoretic Tate–Poitou Duality Seminarcoming soon
A 4-page summary of my graduate work for a general audience
Geometry for Prime Addicts
The Hecke Orbit Conjecture and Homotopy Theory
An Overview of the Classic Theory of p-Divisible Groups
Fiber Bundles of Formal Disks
A Complete Proof of the Polynomial Ham Sandwich Theorem
My two Master’s theses
