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

**Office: ** Applied Physics & Mathematics 6446

**Mailing address:** 3869 Miramar St. PO Box #2130, La Jolla CA 92092

I am a second year graduate student at UCSD. My interests are in algebraic aspects of combinatorics, number theory, and geometry. Currently I am focusing on aspects of arithmetic statistics in both the number field setting and in the setting of algebraic geometry over finite fields. During the Winter Quarter I am TAing for MATH 190, Introduction to Knot Theory, and MATH 187A, Introduction to Cryptography. My office hours can be found below. This page was last updated on 2/5/2019.

In 2016 I won a Goldwater Scholarship for my undergraduate research.

Here is a (not necessarily updated) copy of my CV.

- With Anant Godbole, Bill Kay, and Paul Han. Threshold progressions in a variety of packing and covering contexts. Submitted to 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.

- 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 sit on UCSD's Graduate Student Association as a representative for the math department. I serve on the Academic and Judiciary committee. 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?

- I am currently TAing for MATH 190, Introduction to Knot Theory, and MATH 187, Introduction to Cryptography. My office hours for knot theory are Thursdays, 2-4 pm. My office hours for cryptography are Tuesdays, 2-4 pm.
- 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.