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Topics in Modern Geometry, 2014.

Number Theory and Group Theory, 2012.

Galois Theory, 2012.

Papers.

Quantitative bounds for sets lacking homogeneous polynomial progressions

**Improvements
in Birch's theorem on forms in many variables**

with T.D.
Browning

*Journal reine angew. Math.*, to appear, 31pp. Video lecture.

**Matrix
****progressions in multidimensional sets of
integers**

*Mathematika*,** to appear, 28pp.**

__Near-optimal
mean value estimates for multidimensional Weyl
sums__

with S.T.
Parsell and T.D. Wooley

*Geom.
Funct. Anal.* 23 (2013), 1962–2024.

**Solution-free
sets for sums of binary forms**

** ***Proc. Lond. Math.
Soc.* (3) 107 (2013), no. 2, 267–302.

**PhD
thesis**

Completed under the supervision of Prof. Trevor D.
Wooley

**My ****old
band.**

http://cymbalsmusic.com