I’m Catherine Ray, a researcher training to be 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.
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. I am currently at Northwestern for my PhD working under Paul Goerss.
Here is my CV.
Here is a summary of my pre-math research.
tl;dr My technical background is mainly in robotics (machine learning/SLAM), and computational physics.
My first projects in robotics were in 2011: a dinky hexapod that autonomously followed people around, and Rubik’s cube solving robot.
In Spring 2012, I became interested in physical examples of nonlinear systems due to a research project at the Chemistry and Physics Department of Mary Baldwin College, and modeled the resistant switching behavior of flexible TiO2.
Summer 2012, the Positronics Division of the George Washington University Robotics Lab took me under their wing as an intern. Our team smoothed joint movement of the Willow Garage Personal Robot 2 (PR2), alongside improving load equalization (below). I programmed the PR2 to autonomously “learn” to place objects in holes with the corresponding shape (using only past motor position commands and the finger gripper sensors).
Spring 2013, an interest in contextual machine learning led me to write an automated contextual analysis program that learned the grammar rules of compressed Braille from partially translated text. I used Braille as a test language, but this is a framework to automate the decoding of any partially understood (ancient) language by creating probabilistic dictionaries.
Summer 2013, I interned as a software engineer at Cloudera. During my time there, I developed a consumer download metrics tracking system for internal purposes.
Fall 2013, I played with SLAM and motion planning on the ARDrone. For HackMIT 2013, I collaborated with Kartik Talwar and Spencer Hewett to create a Google Glass application that calculates the human pulse from the video feed.
In late November 2013, I made the rookie mistake of trying to prove the Collatz conjecture (mainly using the prime factor relations within the number sequences and finding a few neat recurrence relations).
Early 2014, I briefly devoted my time to designing a keychain-sized food scanner that detects gluten and other common food allergen proteins. From late 2013 to mid 2014, I dipped my toes into audio processing by automating the collection and classification of lab-animal vocalizations.
Summer 2013-Spring 2014, I explored the improvement of mobility devices. A nonprovisional patent was submitted in Dec 2014 for the 5 pressure sore relief mechanisms that grew out of this.
Summer 2014, I became interested in neuroprosthetics. I started with the software side (convergence analysis of common decoder algorithms), and transitioned into playing with the hardware side (optical recording methods).
In autumn 2014, I began to teach myself algebraic topology full-time.
Early 2015, I began mentoring Paul Rosa on mobility assistance for those with ALS and spinal chord injuries. Here is a video of him showing off the eye control feature.
In January 2015, I was a visiting researcher at the Santa Fe Institute, and gave a seminar on Simplifying Multiscale Modeling. I still think about applications of topology to multi-scale modeling, and occasionally venture to consider modeling complex systems of a biological nature with an eye toward immunotherapy and neuroscience.
I have mentored Tali Khan, Molly Wolfson, and Charlie Hudgins in the UChicago REU, on fractal geometry, general relativity, and Noether’s theorem, respectively.
- Automorphisms of Abelian Varieties and Principal Polarizations joint with D. Lee
- Towards Directed Collapsibility joint with R. Belton, R. Brooks, S. Ebli, L. Fajstrup, B. T. Fasy, N. Sanderson, E. Vidaurre
- A Global Crystalline Period Map joint with M. Neaton and A. Pieper
- Curves with Prescribed Automorphisms
- 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)
Very Rough Exposition (notes for my talks):
- Geometry for Prime Addicts (On Scholze’s proof of the monodromy weight conjecture)
[so rough that it isn’t online, email me for notes]
(On the Tamagawa Conjecture for Function Fields proof)
Curiosity is welcome: email@example.com,
my university email is cray at math.northwestern.edu.