a.debray@math.utexas.edu

Hello! I am a Ph.D. student in UT Austin's department of mathematics; my advisor is Dan Freed. I'm interested in algebraic topology with an eye towards quantum field theory and condensed-matter physics. Previously, I was at Stanford University as an undergraduate; I graduated with a math major and CS minor in June 2015.

I find mathematics so fascinating partly because different subfields and concepts are very interconnected,
reinforcing and influencing each other.

*“Good mathematicians see analogies between theorems or
theories; the very best ones see analogies between analogies.” – Stefan Banach *

I am graduating in Spring 2021, and I am applying for postdoc positions this cycle.

**Lecture notes**: course notes I typed up for my classes and learning seminars.**Seminars**I'm organizing: none in Fall 2020.## Past seminars

Spring 2019: 10/8 theorem learning seminar (with Riccardo Pedrotti).

Fall 2018: homotopy theory learning seminar (with Richard Wong).

Spring 2018: Gromov-Witten theory learning seminar (with Jonathan Lai).

Fall 2017: Quantum topology and categorification learning seminar (with Richard Wong).

**Classifying crystalline invertible phases of matter using homotopy theory**, coming soon!**The low-energy TQFT of the generalized double semion model**. Comm. Math. Phys. volume 375, issue 2, pp. 1079–1115. 2020. arXiv:1811:03583.**The Arf-Brown TQFT of Pin**, joint with Sam Gunningham. In^{−}Surfaces*Topology and Quantum Theory in Interaction*, Contemp. Math. volume 718, pp. 49–87. 2018. arXiv:1803.11183.

These projects are a mix of math and computer science, and include a few side projects. A few of these will migrate to my GitHub soon.

**Dropbox API Explorer**, Summer 2015: my summer internship project at Dropbox. The API Explorer is a tool to learn the Dropbox v2 API and quickly test examples, and is generated from the API spec. The project uses React and was written in TypeScript. See also the associated blog post.**Modular Representation Theory and the CDE Triangle**, 2014-15: my senior thesis, written under the direction of Akshay Venkatesh as part of the honors major in mathematics. I discussed modular representation theory and a collection of results on modular representations encapsulated in a diagram called the CDE triangle, presenting the background theory of modular representations needed to state and prove these results and using these results in several explicit examples.**AT&T Foundry**, Summer 2014: In this internship, I applied techniques from abstract algebra and statistics to problems within network theory, including understanding conditions on a network for a linear code to exist and implementing probabilistic power conservation techniques within sensor networks.**Sleep Data Tracker**, Summer 2014. In order to better understand my sleep schedule (to the degree that “sleep schedule” isn't an oxymoron), I wrote a script to track my sleep habits and collate statistics on them. The statistics side was written in Haskell, and the data plotting in Python (using Matplotlib for the plotting). The results are automatically written up; here is my data from over the summer. At some point, I intend to clean this program up to the point where other people can use it.**Astronomical Implications of Machine Learning**, Fall 2013: Working with Raymond Wu, we used supervised learning to develop a classifier for stellar lightcurves to detect whether they indicated the presence of exosolar planets. We achieved 82% classification accuracy. This project was for Stanford's CS 229 (machine learning) class.**Quick Error Detection in LLVM**, Summer 2013: I worked in a team, under direction of David Lin and Sundaram Anthanarayanan, to implement and improve Quick Error Detection, a technique to insert error-checking routines for hardware errors into software with the LLVM compiler infrastructure. This project was for Stanford's Computer Science Undergraduate Research Internship (CURIS) research program.**Class Numbers of Binary Quadratic Forms**, Summer 2012: As part of this program, I did research on class numbers of binary quadratic forms, investigating their maxima and the structure of the class groups. The program included weekly presentations and writing a concluding paper. This project was part of the Stanford Research Institute in Mathematics (SURIM).

Surprising Manifestations of Incompleteness: An essay I wrote in Spring 2012 for a class on the philosophy of science about incompleteness as a commonality across the formal sciences. This essay won a Boothe prize for excellence in first-year writing at Stanford.

I've played bassoon for about half my life. Most recently, I was in UT Austin's Engineering Chamber Orchestra.

A calculator for the size of unoriented cobordism group.

Dough pear wonton sauce Foodtongue?

This sentence has thirty-one letters.

This sentence has thirty-two letters.

This sentence has thirty-three letters.