Status:
Senior Research Fellow Royal Society University Research Fellow Tutorial Fellow at St. Hugh's College
Personal website:
+44 1865 615163
ORCID iD:
https://orcid.org/0000-0003-1809-8248
Research groups:
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)
A quantitative version of the non-abelian idempotent theorem
Geom. Funct. Anal.
volume 21
page 141-221
(2011)
On Roth’s theorem on progressions
Ann. of Math. (2)
volume 174
page 619-636
(2011)
On a non-abelian Balog-Szemerédi-type lemma
Journal of the Australian Mathematical Society
volume 89
page 127-132
(2010)
On certain other sets of integers
(2010)
Recent Publications:
Boolean functions with small spectral norm, revisited
Mathematical Proceedings of the Cambridge Philosophical Society
page 1-10
(16 May 2018)
Approximate homomorphisms between the boolean cube and groups of prime order
Online Journal of Analytic Combinatorics
issue 13
page 1-7
(1 January 2018)
SOLVING xz = y(2) IN CERTAIN SUBSETS OF FINITE GROUPS
QUARTERLY JOURNAL OF MATHEMATICS
issue 1
volume 68
page 243-273
(March 2017)
Full text available
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)
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)