Professor of Mathematics
Senior Research Fellow at All Souls College
Israel Gelfand Chair of mathematics, IHES.
+44 1865 283871
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
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)
Notes on motivic periods
Communications in Number Theory and Physics issue 3 volume 11 page 557-655 (2017)
Irrationality proofs for zeta values, moduli spaces and dinner parties
Moscow Journal of Combinatorics and Number Theory (10 December 2016)
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.