**Email: ** tgrubb[at]ucsd[dot]edu

**Office: ** Applied Physics & Mathematics 5760

**Mailing address:** Please don't send me physical mail

I am a third year PhD student in the math department at UCSD. My interests are in algebraic aspects of geometry, number theory, and combinatorics. This page was last updated on 5/10/2020.

If you are looking for the webpage for the Tropical Reading Group, look here.

Here is a (not necessarily updated) copy of my CV. If you need a more recent one for some reason, please email me.

- With Fred Rajasekaran*. Set Partition Patterns and the Dimension Index. In Preparation.
- On smooth semiample complete intersections over finite fields. In Preparation.
- With Christian Woll*, Cyclotomic points and algebraic properties of polygon diagonals . Submitted, INTEGERS.
- With Anant Godbole, Bill Kay, and Paul Han*. Threshold progressions in a variety of packing and covering contexts. Submitted, Journal of Combinatorics.
- 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.

- 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 categoroy 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 am currently working with a UCSD undergrad, Fred Rajasekaran, on a research project involving set partition patterns and statistics. In particular, we are able to shed new light on questions of Dokos, Dwyer, Johnson, Sagan, and Selsor by connecting permutation patterns to set partition patterns, and then studying analogous questions in this new context.
- 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!

- 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)

- 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.

- I have been a representative on UCSD's Graduate Student Association for two years, and will serve as Vice President of Academic Affairs for the upcoming academic year. For information on what the GSA is currently working on or to get involved, feel free to contact me.
- Starting in 2018 I have 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. Hopefully there will be an article to point to soon!
- 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?

- 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.

- 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.