I am a fourth-year grad student at UCLA's Math department, working with Artem Chernikov. I'm interested in model theory as it relates to combinatorics and algebra. I graduated in 2018 with a B.S. in mathematics from Caltech.
I also teach at the Olga Radko Math Circle.
Feel free to email me at aaronanderson at math.ucla.edu
Research
- My graduate research so far has focused on the combinatorics of distal cell decompositions, resulting in this paper. I presented some of that research at the SMTH online conference.[pdf slides]
- In the summer of 2017, I worked with Martino Lupini on a Caltech SURF project. We have shown that a certain ring with metric, constructed by von Neumann as a limit of matrix rings endowed with a rank metric, is the metric Fraı̈ssé limit of said matrix rings, and given this, we have shown a few more facts about this structure, related to the Kechris-Pestov-Todorcevic correspondence. [arxiv][slides]
- In the summer of 2016, I worked with Alexander Kechris on a project in Descriptive Set Theory.
Teaching
Olga Radko Math Circle
Most Sundays, I teach high school students at the Olga Radko Math Circle, which I also attended in middle and high school. Here are some of the lessons I've written:
- Electrical circuits and random walks [pdf 1][pdf 2]
- The Cantor Set [pdf 1][pdf 2]
- Triangulated polygons and frieze patterns [pdf 1][pdf 2]
- Generating Functions [pdf]
- Graph Theory, Sperner's Lemma, Brouwer's Fixed Point Theorem [pdf 1][pdf 2]
- Game Theory [pdf]
- Cryptography [pdf]
- Dynamical Systems (mostly on the Logistic map and the Mandelbrot set) [pdf]
Email me at aaronanderson at math.ucla.edu for solutions.
Canada/USA Mathcamp
In Summer 2021, I taught at Canada/USA Mathcamp, which I also attended in high school. Here are problems and notes for some of the classes I taught
- Incidence Combinatorics [problems]
- Model Theory[notes]
- Surreal Numbers[problems][impartial games][partizan games]
- Sperner's Lemma and Brouwer's Fixed Point Theorem[problems]
Email me at aaronanderson at math.ucla.edu for solutions.
UCLA Teaching
I have been a teaching assistant for the following math classes at UCLA:
- 114L: Mathematical Logic
- 180: Graph Theory
- 170: Probability
- 106: History of Math
- 33A: Linear Algebra
In 2019, I assisted at the Curtis Center.
Caltech Teaching
At Caltech, I was a teaching assistant for Ma6a: Discrete Math.
Miscellaneous
- I am a contributor to mathlib, the main repository of math formalized in the Lean theorem prover. My contributions are visible on github.
- In summers 2011-2014, I attended Canada/USA Mathcamp, and I recommend it most strongly for high-schoolers interested in math.
- As an undergrad, I helped organize the Caltech Harvey Mudd Math Competition, a one-day, on-site math competition for high school students.
- Dabney Pumpkin Drop: Every Halloween, residents of Caltech's Dabney Hovse freeze pumpkins in liquid nitrogen and drop them off the tallest building on campus, Millikan Library. I was one of the pumpkin-droppers for several years, and was interviewed for this video.