Professor of Mathematics
Senior Research Fellow at All Souls College
+44 1865 283871
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Depth-graded motivic multiple zeta values
Compositio Mathematica issue 3 volume 157 page 529-572 (22 March 2021)
Single-valued integration and super-string amplitudes in genus zero
Communications in Mathematical Physics issue 2 volume 382 page 815-874 (24 February 2021)
Invariant differential forms on complexes of graphs and Feynman
(12 January 2021) Full text available
Single-valued integration and double copy
Journal für die reine und angewandte Mathematik (15 December 2020)
A class of nonholomorphic modular forms II: equivariant iterated Eisenstein integrals
Forum of Mathematics, Sigma volume 8 (28 May 2020)
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.