Professor of Mathematics

Senior Research Fellow at All Souls College

Israel Gelfand Chair of mathematics, IHES.

## Personal website:

+44 1865 283871

## Research groups:

## Address

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

## Recent Publications:

A class of non-holomorphic modular forms III: real analytic cusp forms for $\mathrm{SL}_2(\mathbb{Z})$

Research in the Mathematical Sciences
(13 August 2018)

Algebraic de Rham theory for weakly holomorphic modular forms of level one

Algebra & Number Theory
(1 March 2018)

A class of non-holomorphic modular forms I

Research in the Mathematical Sciences
(6 February 2018)

ZETA ELEMENTS IN DEPTH 3 AND THE FUNDAMENTAL LIE ALGEBRA OF THE INFINITESIMAL TATE CURVE

Forum of Mathematics, Sigma
volume 5
(5 January 2017)

Feynman amplitudes, coaction principle, and cosmic Galois group

Communications in Number Theory and Physics
issue 3
volume 11
page 453-556
(2017)

## Research interests:

Arithmetic algebraic geometry and quantum field theory.

I am currently working on a `Galois theory of periods' and its applications. Periods are a class of transcendental numbers defined by integrals which includi pi and values of the Riemann zeta function at positive integers. A deep conjecture of Grothendieck predicts the existence of a linear algebraic group acting on such numbers.

Applications include: the study of mixed modular motives (iterated extensions of motives of modular forms) coming from the fundamental group of the moduli space of elliptic curves, and a new Galois group of symmetries of particle-scattering amplitudes in high-energy physics.

## Major / recent publications:

Deligne, Pierre:`Multizêtas, d'après Francis Brown', Séminaire Bourbaki, Astérisque No. 352 (2013), Exp. No. 1048, viii, 161–185.

https://www.quantamagazine.org/20161115-strange-numbers-found-in-particl...