I am currently a third-year graduate student in mathematics at Stanford, advised by Ravi Vakil. My primary interests are in algebraic and arithmetic geometry.
I think a lot about derived equivalences of varieties and their relation to moduli problems, and am especially interested in studying the derived categories of stacks and equivalences thereof.
I have also recently worked in arithmetic enumerative geometry and combinatorial aspects of algebraic geometry.
As an undergraduate, I worked mostly in combinatorics, advised by Matt Baker and Tom Trotter.
My Erdos number is 2.
- Derived equivalences of gerbey fourfolds. In preparation.
- On the arithmetic of a twisted constant family of superelliptic curves. Joint with Arpin, Griffon, and Triantafillou. In preparation.
- Derived equivalences of stacky curves. Joint with Soumya Sankar. arXiv version.
- An arithmetic variant of Raynaud's theorem. Joint with Jonathan Love. arXiv version.
- A^1 local degree via stacks. Joint with Andrew Kobin. arXiv version.
- An arithmetic count of the lines meeting 4 lines in P^3 (appendix). Joint with Kadets, Srinivasan, Swaminathan, and Tseng. arXiv version.
Undergrad papers in combinatorics
- On the regularity of orientable matroids. Discrete Mathematics Vol. 342, Issue 9, 2733-2737. arXiv version.
- The k-planar crossing number of random graphs and random regular graphs. Joint with Asplund, Do, Hamm, Szekely, and Wang. Discrete Applied Math, Vol. 247, 419-422. arXiv version.
- Kasteleyn cokernels and perfect matchings on planar bipartite graphs. arXiv version.
- The separation of tree-chromatic number from path-chromatic number. Joint with Barrera-Cruz, Felsner, Meszaros, Micek, Smith, and Trotter. Journal of Combinatorial Theory, Series B, to appear. arXiv version.
- Comparing Dushnik-Miller dimension, boolean dimension and local dimension. Joint with Barrera-Cruz, Prag, Smith, and Trotter. Order, to appear. arXiv version.
- The graph of critical pairs of a crown. Joint with Barrera-Cruz, Garcia, Harris, Kubik, Smith, Talbott, and Trotter.Order, to appear. arXiv version.
- Summer 2019: Assisting with SURIM (Stanford undergraduate research in mathematics).
- Fall 2019-present: Mentor for the Stanford directed reading program.
- Spring 2018: TA for Algebra 2 (Georgia Tech).
- Spring 2018: TA for elementary number theory (Georgia Tech).
- Fall 2017: TA for algebra 1 (Georgia Tech)
- Spring 2017: TA for number theory and cryptography.
- My office is Sloan Hall 381B.
- My email address is lt691 at stanford.edu.
- Bonus points for recognizing the numerology involved in my email address.
Recent and upcoming travel
- Joint Math Meetings, January 15-18. Invited speaker.
- Arizona Winter School, March 7-11. Participant.
- AMS Spring sectional meeting, Charlottesville, Virgina, March 13-15. Invited speaker.
- Madison Moduli Weekend, March 27-29. Invited speaker.
- University of Georgia number theory seminar, April 22.
Organization and activities
During the 2018-2019 and 2019-2020 school years, I am organizing Stanford's student algebraic geometry seminar (SAGS). SAGS meets Tuesdays 4-5pm in Sloan Hall, 384I.
In fall 2019, I am attending the learning seminar at Berkeley on arithmetic statistics of function fields via Hurwitz spaces. Notes are available here and will be updated weekly: Learning seminar notes. Any errors in the notes are entirely mine; if you find any, whether mathematical or typographical, please email and let me know.
- The Hodge theory of Soergel Bimodules, joint with Minh-Tam Trinh. To appear as a chapter in “Soergel Bimodules”, Springer RSME series, edited by Ben Elias and Geordie Williamson. (Draft available upon request.)