## Fernando Xuancheng Shao

Mathematical Institute

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

Email address: Xuancheng dot Shao at maths dot ox dot ac dot uk

I am a postdoctoral research fellow at University of Oxford and a member of Magdalen College. My research is supported by a Glasstone Research Fellowship. My CV is available.

I am interested in analytic number theory and arithmetic combinatorics in general, and more specifically I like topics regarding character and exponential sums, sieve theory, Szemeredi's theorem in the integers and in the primes, structures in sumsets, etc.

Previously I was a PhD student at Stanford University under the supervision of Prof. K. Soundararajan.

Contact details can be found here.

## Papers

My papers can be found on Arxiv and MathSciNet. Please note that the arxiv version may be a bit different from the published version.

Vinogradov's theorem with almost equal summands (with Kaisa Matomaki and James Maynard). Submitted.

Gowers norms of multiplicative functions in progressions on average. Submitted.

Upper tails for arithmetic progressions in a random set (with Bhaswar Bhattacharya, Shirshendu Ganguly, and Yufei Zhao). Submitted.

Weyl sums, mean value estimates, and Waring's problem with friable numbers (with Sary Drappeau). *Acta Arith.* To appear.

Vinogradov's three primes theorem with almost twin primes (with Kaisa Matomaki). Submitted.

Narrow arithmetic progressions in the primes. *Int. Math. Res. Not.* (IMRN). To appear.

When the sieve works II (with Kaisa Matomaki). Submitted.

Polynomial values modulo primes on average and sharpness of the larger sieve. * Algebra Number Theory* 9 (2015), no. 10, 2325-2346.

On an inverse ternary Goldbach problem. *Amer. J. Math.* 138 (2016), no. 5, 1167-1191.

Finding linear patterns of complexity one. *Int. Math. Res. Not.* IMRN 2015, no. 9, 2311-2327.

Carries, group theory, and additive combinatorics (with Persi Diaconis and Kannan Soundararajan). *Amer. Math. Monthly* 121 (2014), no. 8, 674-688.

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

A L-function-free proof of Vinogradov's three primes theorem. *Forum Math. Sigma 2* (2014), e27, 26 pp.

Character sums over unions of intervals. *Forum Math.* 27 (2015), no. 5, 3017-3026.

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.

*Last updated*: 14 October, 2016.