I am an analytic number theorist, and have just completed my D. Phil under the supervision of Prof. Ben J. Green. In October 2018 I will be taking up a Junior Research Fellowship at Trinity College Cambridge. What follows is a broad explanation of the sort of mathematics that I do; for a more detailed overview, my thesis is available here.

Addition and multiplication are seemingly straightforward arithmetical operations, but the way in which they interact with each other is complicated and mysterious. Though this interaction has been the subject of mathematical research for over two thousand years, the study of such number-theoretic notions remains an extremely active area of research today, and a huge variety of advanced mathematical tools -- ranging from the continuous methods of mathematical calculus, through the structure of networks, through abstract algebra and geometry -- may be applied within it. Indeed, it is the variety of methods used which makes number theory such a fascinating and important area.

By considering problems in number theory, new connections can be discovered between apparently disparate areas of mathematics. Most recently, connections between Fourier analysis (a technique from calculus), ergodic theory (the study of dynamics), and combinatorics (the manipulation of unstructured mathematical objects), were all found to be connected to each other, via a seemingly innocuous problem on equally spaced whole numbers. Through working on specific questions in number theory, I try to develop these connections, and to understand each area more clearly.

## Personal Website:

+44 1865 283875

## Address

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

## Research Interests:

Analytic Number Theory: Diophantine inequalities, circle method, mean values of multiplicative functions, sieve theory, Diophantine approximation.

Additive Combinatorics: Gowers norms, discrete Fourier analysis, Chang's lemma and refinements, regularity methods.

## Teaching:

Michaelmas 2014: Analytic Number Theory (TA)

Hilary 2015: Graphy Theory (TA)

Michaelmas 2015: Analytic Number Theory (Tutor), Banach Spaces (Tutor)

Hilary 2016: Probabilistic Combinatorics (Tutor)

Trinity 2016: Analytic Number Theory (Consultation class tutor)

Michaelmas 2016: Analytic Number Theory (Tutor)

Trinity 2017: Statistics and Data Analysis (Tutor), Number Theory (Tutor), Analytic Number Theory (Consulation class tutor).

Michaelmas 2017: Introduction to Complex Numbers (Tutor), Analysis I (Tutor), Linear Algebra A0 (Tutor),

Hilary 2018: Analysis II (tutor)

Trinity 2018: Groups and group actions (tutor)

## Prizes, Awards, and Scholarships:

Edward Gibbon Prize, Magdalen College, 2016.

Awarded for research communication.

Italian Scholarship award, Magdalen College, 2016.

Funded study at British Institute, Florence.

Heilbronn Prize, University of Cambridge, Trinity College, 2013.

Award from Gulbenkian Foundation, Gulbenkian foundation, Portugal, 2012. Funded attendance at Lisbon Combinatorics Summer School.

Senior Scholar, University of Cambridge, Trinity College, 2011-2014.

OCR Bursary, Cambridge Assessment, 2010-2013.

UK IMO Team, International Mathematical Olympiad, 2010.

## Major / Recent Publications:

GCD sums and sum-product estimates

arXiv:1806.07849

Additive energy and the metric Poissonian property

Mathematika, 64(3):679–700, 2018.

Joint with Sam Chow, Ayla Gafni, and Thomas Bloom.

The primes are not metric Poissonian

Mathematika, 64(1), 230-236, 2018

A footnote in parity breaking

J. Théor. Nombres Bordeaux, 30(1):219–225, 2018.

Joint with Olivier Ramaré.

Gowers norms control Diophantine inequalities

arXiv:1703.00885

A multiplicative analogue of Schnirelmann’s theorem

Bull. London Math. Soc. 48 (6): 1018-1028, 2016.