Senior Research Fellow Royal Society University Research Fellow Tutorial Fellow at St. Hugh's College
Personal Website:
+44 1865 615163
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Publications:
On the Bogolyubov–Ruzsa lemma
Analysis & PDE
issue 3
volume 5
page 627-655
(15 October 2012)
On Roth’s theorem on progressions
Ann. of Math. (2)
volume 174
page 619-636
(2011)
A quantitative version of the non-abelian idempotent theorem
Geom. Funct. Anal.
volume 21
page 141-221
(2011)
On certain other sets of integers
(2010)
On a non-abelian Balog-Szemerédi-type lemma
Journal of the Australian Mathematical Society
volume 89
page 127-132
(2010)
Recent Publications:
Solving xz = y in certain subsets of finite groups
Quarterly Journal of Mathematics
issue 1
volume 68
page 243-273
(1 January 2017)
A statistical approach to covering lemmas
EUROPEAN JOURNAL OF COMBINATORICS
volume 48
page 19-33
(August 2015)
Full text available
The structure theory of set addition revisited
Bulletin of the American Mathematical Society
issue 1
volume 50
page 93-127
(5 March 2013)
Green’s sumset problem at density one half
Acta Arith.
volume 146
page 91-101
(2011)
On a theorem of Shkredov
Online Journal of Analytic Combinatorics
page Art. 6-4
(2010)
Research Group:
Research Interests:
I am a research mathematician interested in aspects of algebra, analysis, combinatorics, geometry and number theory, with particular emphasis on using tools from the former to address problems in the latter. I completed my PhD in additive combinatorics and since then my research has primarily focused on additive combinatorics and the allied areas of harmonic analysis and analytic number theory.
Preferred Address:
Prizes, Awards, and Scholarships:
Adams Prize (2011), European Mathematical Society Prize (2012), Whitehead Prize (2013), European Prize in Combinatorics (2013), ICM Section Lecture (2014)