Tom Grubb

Email: tgrubb[at]ucsd[dot]edu
Office: Applied Physics & Mathematics 5760
Mailing address: Please don't send me physical mail

I am a fourth year PhD student in the math department at UCSD working with Kiran Kedlaya. My interests are in algebraic and computational aspects of geometry, number theory, and combinatorics. I am currently looking for industry internships (and eventually, full time positions) in machine learning, data science, or software engineering. Please feel free to contact me with possible opportunities! This page was last updated on 10/7/2020.

Here is a copy of my Industry Resume. If you need an academic CV for some reason, please email me.

Papers and preprints:

An asterisk denotes undergraduate authorship; the first four articles were from my undergraduate work. Some preprints (listed and unlisted) available by email.

Pattern Matching in Set Partitions is NP-Complete. Submitted.
With Fred Rajasekaran*. Set Partition Patterns and the Dimension Index . Submitted.
On smooth semiample complete intersections over finite fields. In Preparation.
With Christian Woll*, Cyclotomic points and algebraic properties of polygon diagonals . Submitted.
With Anant Godbole, Bill Kay, and Paul Han*. Threshold progressions in a variety of packing and covering contexts. Responding to referee comments.
With Samantha Dahlberg, Robert Dorward*, Jonathan Gerhard*, Carlin Purcell*, Lindsey Reppuhn*, and Bruce Sagan. Restricted growth function patterns and statistics. Advances in Applied Mathematics, 100: 1-42, 2018.
With Samantha Dahlberg, Robert Dorward*, Jonathan Gerhard*, Carlin Purcell*, Lindsey Reppuhn*, and Bruce Sagan. Set partition patterns and statistics. Discrete Mathematics, 339(1):1-16, 2016.
With Chris Sullivan, Evan O'Connor, Remco Zegers, and Sam M. Austin. The sensitivity of core-collapse supernovae to nuclear electron capture. The Astrophysical Journal, 816(1):44, 2016.

Current Projects/Things I'm Thinking About (feel free to email with any questions):

I am currently trying to learn how to rollerblade.
It is well known that the (co)homology of configuration spaces can be controlled by the combinatorial category FI, and hence it exhibits representation stability. The homology of their Fulton-MacPherson compactifications is usually too big to use FI, so I am currently trying to control it with FSop. I have some partial results, and can (possibly) exhibit stability in certain cases, but nothing great yet. A more general long term question I have: suppose (X_n) is a sequence of topological spaces whose (co)homology can be controlled by FI. Can nice compactifications of the (X_n) be controlled with FSop? It seems unlikely for this to always be true, but possibly can work under certain assumptions. See, for instance, recent work of Phil Tosteson in which he studies the Deligne-Mumford compactification of the moduli space of marked stable curves.
I will be involved with David Zurieck-Brown's project on classical Chabauty at the 2020 Arizona Winter School. More news (hopefully) to come after the conference! (**Update**: This lead to an examination of uniform bounds for rational points on symmetric powers of curves, with Ashvin Swaminathan and Alex Smith. We are trying to solidify the details and write things up currently!)

Expository Writing

Here is a paper I wrote on the Golod Safarevic inequality with applications to the root discriminant problem for Benedict Gross's topics in algebra course, focusing on the structure of finite groups. (2018)
Here is a paper I wrote on p-adic L functions for Benedict Gross's topics in number theory course, focusing on the theory of L functions. (2017)
Here is a paper I wrote in which I give an econometric analysis on medical amnesty laws for Jeff Biddle's econ senior seminar class at Michigan State. (2017)

Here is a paper I wrote on list error correction of codes as part of a final project in Jon Hall's coding theory class during my sophomore year at Michigan State. (2015)

Expository Talks

Here are some slides for various expository talks I have given. Who knows how helpful the slides are without the accompanying discussion/hand drawn diagrams, but perhaps they are interesting to someone.

2017: Permutation Patterns and Schubert Varieties, based off of Hiraku Abe and Sara Billey's amazing article "Consequences of the Lakshmibai-Sandhya Theorem."
2016: The Robinson Schensted Correspondence.
2016: Pattern Avoidance in Derangements.

Outreach and Mentorship Activities:

In Spring 2020 I led an undergraduate reading group in Tropical Geometry as part of UCSD's RTG grant. The main focus was on tropical plane curves; in this setting we examined enumerative geometry, connections to arithmetic, combinatorial problems, and relations to classical algebraic geometry.
From 2017-2020 I was involved with the UCSD Graduate Student Association. I held various positions within the group, from everyday member to VP of academic affairs. I am no longer involved with the group, but if you have questions or want to get involved with it, send me an email.
From 2018 to 2020 I served as a graduate student mentor for Christian Woll, now a UCSD alum. With Kiran Kedlaya we have been studying applications and extensions of Conway Jones type results for trigonometric diophantine equations. You can see the results of the project in the articles section.
During Winter, 2017 I worked with the Pacific Trails Middle School Science Olympiad Team . Specifically, I coached their team for the Codebusters event, which involves encryption and decryption using several basic ciphers. Recently the Codebusters team took second place in their event at the statewide competition, and the team overall took fourth! If you are looking for someone to help out for an event similar to this, please feel free to contact me.
During Spring, 2018, Zach Higgins and I co-led an undergraduate reading group on error correction and coding theory, as part of UCSD's RTG grant. The main questions we examined with the students were twofold. First, how can we explicitly construct and implement "good" codes which are robust to noisy transmission, such as Generalized Reed-Soloman codes? Second, what are the theoretical limits to how "good" such a code can be?

Teaching/Grading Experience:

I am currently TAing for MATH 100A: Abstract Algebra.
In Winter, 2020 at UCSD I TA'd for MATH 157: Introduction to Mathematical Software.
In Summer, 2019 at UCSD I TA'd for MATH 109: Introduction to Proofs.
In Spring, 2019 at UCSD I TA'd for MATH 202: Applied Algebra.
In Winter, 2019 at UCSD I TA'd for MATH 190: Introduction to Knot Theory, and Math 187: Introduction to Cryptography.
In Fall, 2018 at UCSD I TA'd for MATH 157: Introduction to Mathematical Software.
In Summer, 2018 at UCSD I TA'd for MATH 184: Combinatorics.
In Spring, 2018 at UCSD I TA'd for MATH 187: The Mathematics of Modern Cryptography.
In Winter, 2018 at UCSD I TA'd for MATH 157: Introduction to Mathematical Software.
In Fall, 2017 at UCSD I TA'd for MATH 20B: Integral Calculus.
In Fall, 2016 at MSU I was a course grader for MTH 418H: Honors Abstract Algebra.
In Fall, 2015 at MSU I TA'd for MTH 299: Transitions, an introductory proofs course.

Useful/Interesting Links, Articles, References, etc:

Here is an English translation of Serre's "Faisceaux algebriques coherents," translated by Piotr Achinger and Lukasz Krupa.
I have written several (shoddy, not optimal) programs using the Cocalc computation platform which allows one to study combinatorial pattern avoidance and statistic distributions in the setting of set partitions, RGFs, and permutations. If you would like access to some of these, feel free to send me an email.