Libby Taylor

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.

My CV

Recent papers


  1. Derived equivalences of gerbey fourfolds. In preparation.

  2. On the arithmetic of a twisted constant family of superelliptic curves. Joint with Arpin, Griffon, and Triantafillou. In preparation.

  3. Derived equivalences of stacky curves. Joint with Soumya Sankar. arXiv version.

  4. An arithmetic variant of Raynaud's theorem. Joint with Jonathan Love. arXiv version.

  5. A^1 local degree via stacks. Joint with Andrew Kobin. arXiv version.

  6. 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


  1. On the regularity of orientable matroids. Discrete Mathematics Vol. 342, Issue 9, 2733-2737. arXiv version.

  2. 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.

  3. Kasteleyn cokernels and perfect matchings on planar bipartite graphs. arXiv version.

  4. 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.


  5. Comparing Dushnik-Miller dimension, boolean dimension and local dimension. Joint with Barrera-Cruz, Prag, Smith, and Trotter. Order, to appear. arXiv version.

  6. The graph of critical pairs of a crown. Joint with Barrera-Cruz, Garcia, Harris, Kubik, Smith, Talbott, and Trotter.Order, to appear. arXiv version.

Teaching

  1. Summer 2019: Assisting with SURIM (Stanford undergraduate research in mathematics).

  2. Fall 2019-present: Mentor for the Stanford directed reading program.

  3. Spring 2018: TA for Algebra 2 (Georgia Tech).

  4. Spring 2018: TA for elementary number theory (Georgia Tech).

  5. Fall 2017: TA for algebra 1 (Georgia Tech)

  6. Spring 2017: TA for number theory and cryptography.

Other

Contact Info:


Recent and upcoming travel

  1. Joint Math Meetings, January 15-18. Invited speaker.

  2. Arizona Winter School, March 7-11. Participant.

  3. AMS Spring sectional meeting, Charlottesville, Virgina, March 13-15. Invited speaker.

  4. Madison Moduli Weekend, March 27-29. Invited speaker.

  5. University of Georgia number theory seminar, April 22.
  6. 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.


    Expository writing