Andy Parrish andytparrish at gmail dot com

Alert! This page is frozen in time. In order to figure out what Andy is up to today, please take a course on Taylor Approximation and use the data from this webpage to project to the present.

Research
Through 2013, I was a PhD student in the Math department of UC San Diego. I worked in combinatorics, and specifically trying to discern necessary structures within large graphs, sets of integers, and anything else I can wrap my head around. This leads to some buzzwords like "extremal combinatorics," "Ramsey theory," and perhaps "the study of unreasonably large numbers." I worked with Ron Graham, with additional guidance from Fan Chung.

Papers

• Adventures in Graph Ramsey Theory This is my PhD dissertation. It mostly covers material from An additive version of Ramsey's theorem and Toward a graph version of Rado's theorem, with updated notation and a more unified framework.
• Toward a graph version of Rado's theorem (2013, Electronic Journal of Combinatorics). This is a follow-up to the previous paper. Call an equation graph-regular if every r-coloring of the complete graph on the natural numbers contains a monochromatic complete subgraph whose vertices solve the equation. This paper gives two Rado-like conditions for an equation which are respectively necessary and sufficient for graph-regularity.
• An additive version of Ramsey's theorem (2011, Journal of Combinatorics). This is a combination of the two flavors of Ramsey theory: additive and graph-theoretic. In short, Ramsey's theorem guarantees that any edge-coloring of a large complete graph will give large monochromatic complete subgraphs. In this paper, We show that we can get more: if the vertex set is the natural numbers up to n, we can guarantee some additive structure of the vertices in the monochromatic subgraph. Specifically, we prove that, for all r and k, there is an n = n(r, k) so that, for any r-coloring of the complete graph on vertex set {1, 2, ..., n}, there must be a solution to x₁ + ... + x_k = y₁ + ... + y_k by distinct numbers, so that all edges among those values have the same color.
• Three Proofs of the Hypergraph Ramsey Theorem (An Exposition) (2012, with William Gasarch and Sandow Sinai, submitted). This is an exposition of three proofs of the hypergraph version of Ramsey's theorem, giving successively better bounds.
• Van der Waerden's Theorem: Variants and Applications. I am working on this book with Bill Gasarch and Clyde Kruskal. It is a collection of combinatorial proofs of results in additive Ramsey theorey. This is built on my senior thesis at the University of Maryland. The original motivation for the book is its detailed combinatorial proofs of the Polynomial van der Waerden theorem and the Polynomial Hales-Jewett theorem, expanding on proofs in a short paper by Mark Walters.
• Efficient Computationally Private Information Retrieval from Anonymity or Trapdoor Groups (With Jonathan Trostle, appeared at ISC 2010). We describe a protocol for Private Information Retrieval, designed to be practical, in contrast with previous systems which have impressive communication bounds, but bad computational complexity.
• System and Method for Computationally Private Information Retrieval (With Jonathan Trostle, submitted to USPTO in 2009). Patent application for the above Private Information Retrieval protocol.
• There is no "large van der Waerden theorem" (2009). This is a minor negative result in Ramsey theory from a question of Bill Gasarch: the Large Ramsey theorem does not translate directly to a "Large van der Waerden theorem."
• Exploration of the three-person duel (2006). This was a toy problem I worked on as an undergrad at the University of Maryland. Under the guidance of Bill Gasarch, I formulated the equations governing the probabilities of winning in a three-person duel, and explored the conditions for the three players to be evenly matched.

Past teaching
I have a been teaching assistant for these courses:

• Math 183 (Spring 2012) — Statistical Methods
• Math 20A (Winter 2012) — Differential Calculus (evaluations)
• Math 186 (Winter 2012) — Probability and Statistics for Bioinformatics (evaluations)
• Math 10A (Fall 2011) — Differential Calculus. I was the instructor for this course.
• Math 152 (Spring 2011) — Game Theory (evaluations)
• Math 20B (Winter 2011) — Integral calculus (evaluations)
• Math 153 (Fall 2010) — Geometry for Secondary Education (evaluations)
• Math 202 (Winter/Spring 2010) — Applied Algebra
• Math 163 (Winter 2010) — History of Mathematics (evaluations)
• Math 20D (Fall 2009) — Differential equations (evaluations)
• Math 20C (Spring 2009) — Multivariable calculus and analytic geometry (evaluations)
• Math 20B (Winter 2009) — Integral calculus (evaluations)
• Math 20A (Fall 2008) — Differential calculus (evaluations)

Past course webpage
In summer 2009, I studied random geometric graphs with some other students and maintained the course website.

Jobs
Here are some jobs I have held outside of teaching. If you have any jobs you would like to see added to this list, the process begins with my résumé.

• Epic — Epic is a major force in the world of electronic medical records. As of August 2013, I am a full time software developer for its oncology application.
• Google — I worked in Google's Cambridge office in summer 2011. I attempted to optimize local storage for YouTube by understanding video request patterns.
• Johns Hopkins University Applied Physics Lab — I worked for two summers (2007-2008) investigating a new protocol for Private Information Retrieval, with the goal of attaining practical algorithms with low communication costs.

Some links
Here are some things which do not quite fit into other categories.

• Here is some advice for how to manage grad school applications. It is a detailed account of the specific things I did to avoid being overwhelmed by applications.
• Here is a list of every group of order up to 30. This list was created by John Pedersen at the University of South Florida, but has since been taken down. I still wanted to use it, and maybe you do, too.
• Here is a nicely-sorted list of binomial coefficient identities, which has been enormously helpful to me. The page was previously organized and maintained by Matthew Hubbard and Tom Roby, but has since been taken down. The link points to the most recent copy rescued by the "Wayback Machine" at Archive.org.
• Detexify is the best thing to happen to LaTeX since Donald Knuth and Leslie Lamport! Here's how it works: you draw a math symbol, and it tells you how to type it in LaTeX. It's far from perfect, but farther still from neutral.
• I spent Fall 2006 in Budapest, in the Budapest Semesters in Mathematics program. It was an incredible experience both culturally and academically, and I encourage all math majors to consider it. Feel free to contact me if you want to know more.
• I made a Dinosaur Comics Graphics Randomizer. For those unfamiliar, Dinosaur comics is a really wonderful webcomic, which happens to use the same six panels (of dinosaurs!) for every strip. The strip's creator Ryan North built in a way to replace the dinosaurs with other characters, and set up many different skins for the comic. My tiny contribution was to write a script which randomly generates one of these skins, for maximum enjoyment. Warning: one of the skins replaces the text in panel six. If you aren't careful, you could miss the intended punchline!
• I am a member of the National Bone Marrow Registry. You should be, too! Here's how it works: They mail you a packet, you swab the insides of your cheeks, and you mail them back. Then: probably nothing happens. But in the (individually) unlikely event that your bone marrow could save someone's life, they'll give you a call. Sweet!
• Here is Ian's Shoelace Site. Its methods are unscientifically proven to improve shoe appreciation.

Is Katie awesome?