## Papers

- Higher theta series for unitary groups over function fields, with Zhiwei Yun and Wei Zhang
- Higher Siegel--Weil formula for unitary groups: the non-singular terms, with Zhiwei Yun and Wei Zhang.
- Equivariant localization, parity sheaves, and cyclic base change functoriality, joint appendix with Gus Lonergan.
- The Galois action on symplectic K-theory, with Soren Galatius and Akshay Venkatesh.
- The geometric distribution of Selmer groups of elliptic curves over function fields, with Aaron Landesman and Eric Rains.
- 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.
*Journal of the Institute of Mathematics of Jussieu*, 1-46. - Privately Evaluating Decision Trees and Random Forests, with D. Wu, M. Naehrig, and K. Lauter.
*Proceedings on Privacy Enhancing Technologies*4 (2016), 1-21. - (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.

**Old REU (undergraduate) work:**