## Fernando Xuancheng Shao

Graduate student

Stanford University

Department of Mathematics

381-N Sloan Hall

Stanford, CA 94305

Email address: xshao at math dot stanford dot edu

I am a fifth year math PhD student at Stanford University. My advisor is Prof. K. Soundararajan. My research interests include analytic number theory and additive combinatorics.

## Teaching

In Spring 2014, I am a teaching assistant for Math 21.
## Papers

On an inverse ternary Goldbach problem.

Finding linear patterns of complexity one. *Int. Math. Res. Notices.* To appear.

Carries, group theory, and additive combinatorics (with Persi Diaconis and Kannan Soundararajan). *Amer. Math. Monthly*

Large values of the additive energy in R^d and Z^d, *Math. Proc. Camb. Phil. Soc.* (2014) 156: 327–341.

A new proof of Vinogradov's three primes theorem.

Character sums over unions of intervals. *Forum Math.* To appear.

A density version of the Vinogradov three primes theorem, *Duke Math. J.* 163 (2014), no. 3, 489–512.

On character sums and exponential sums over generalized arithmetic progressions, *Bull. Lond. Math. Soc.* 45 (2013), no. 3, 541–550.