Papers

  1. Derived structures in the Langlands correspondence, with Michael Harris. (Survey article)
  2. Modularity of higher theta series II: Chow group of the generic fiber, with Adeel Khan.
  3. Geometric Langlands duality for periods, with Jonathan Wang.
  4. Modular functoriality in the Local Langlands Correspondence.
  5. Mirror symmetry and the Breuil-Mezard Conjecture, with Bao Le Hung.
  6. Modularity of higher theta series I: cohomology of the generic fiber, with Zhiwei Yun and Wei Zhang.
  7. G-spectra of cyclic defect, with David Treumann and Allen Yuan.
  8. Cyclic base change of cuspidal automorphic representations over function fields, with Gebhard Böckle, Michael Harris, Chandrashekhar Khare, Jack A. Thorne. To appear in Compositio Mathematica.
  9. Higher theta series for unitary groups over function fields, with Zhiwei Yun and Wei Zhang. To appear in Annales scientifiques de l'École normale supérieure.
  10. Higher Siegel--Weil formula for unitary groups: the non-singular terms, with Zhiwei Yun and Wei Zhang. Invent. Math. 235 (2024), no. 2, 569--668.
  11. Smith theory and cyclic base change functoriality, joint appendix with Gus Lonergan. Forum Math. Pi 12 (2024), Paper No. e1.
  12. The Galois action on symplectic K-theory, with Soren Galatius and Akshay Venkatesh. Invent. Math. 230 (2022), no. 1, 225--319.
  13. The geometric distribution of Selmer groups of elliptic curves over function fields, with Aaron Landesman and Eric Rains. Math. Ann. 387 (2023), no. 1-2, 615--687.
  14. The Spectral Hecke algebra.
  15. Etale Steenrod operations and the Artin-Tate pairing. Compos. Math. 156 (2020), no. 7, 1476--1515.
    • Here are some notes for a talk on this paper.
  16. Nearby cycles of parahoric shtukas, and a fundamental lemma for base change. Selecta Math. (N.S.) 26 (2020), no. 2, Paper No. 21, 59 pp.
    • Here are some notes for a talk on this paper.
  17. Epipelagic Langlands parameters and L-packets for unitary groups, with Niccolo Ronchetti and Cheng-Chiang Tsai. Int. J. Number Theory 16 (2020), no. 7, 1449--1491.
  18. Extensions of vector bundles on the Fargues-Fontaine curve, with C. Birkbeck, D. Hansen, S. Hong, Q. Li, A. Wang, and L. Ye. J. Inst. Math. Jussieu 21 (2022), no. 2, 487--532.
  19. Privately Evaluating Decision Trees and Random Forests, with D. Wu, M. Naehrig, and K. Lauter. Proceedings on Privacy Enhancing Technologies 4 (2016), 1-21.
Old REU (undergraduate) work:

  • (with Z. Li, S. Trebat-Leder, D. Corwin) Elliptic Curves with Full Two-Torsion and Maximal Adelic Galois Representations, Math. Comp. 83 (2014), 2925-2951.
  • (with K. James, C. Kim, E. Ramos, C. Trentacoste, H. Xue) Three Selmer Groups for Elliptic Curves with 3-torsion, Ram. Journal 31, Issue 3 (2013), 435-459.
  • (with M. Wage, R. Kirsch, E. McCall) Birth-death Processes and $q$-Continued Fractions, Trans. Amer. Math. Soc. 364 (2012), 2703-2721.