## Papers

- Derived structures in the Langlands correspondence, with Michael Harris. (Survey article)
- Modularity of higher theta series II: Chow group of the generic fiber, with Adeel Khan.
- Geometric Langlands duality for periods, with Jonathan Wang.
- Modular functoriality in the Local Langlands Correspondence.
- Mirror symmetry and the Breuil-Mezard Conjecture, with Bao Le Hung.
- Modularity of higher theta series I: cohomology of the generic fiber, with Zhiwei Yun and Wei Zhang.
- G-spectra of cyclic defect, with David Treumann and Allen Yuan.
- 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*. - 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*. - 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. - Smith theory and cyclic base change functoriality, joint appendix with Gus Lonergan.
*Forum Math. Pi*12 (2024), Paper No. e1. - The Galois action on symplectic K-theory, with Soren Galatius and Akshay Venkatesh.
*Invent. Math.*230 (2022), no. 1, 225--319. - 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. - The Spectral Hecke algebra.
- 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.
- 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.
- 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. - 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. - 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:**

*Math. Comp. 83*(2014), 2925-2951.

*Ram. Journal*31, Issue 3 (2013), 435-459.

*Trans. Amer. Math. Soc.*364 (2012), 2703-2721.