## Status:

Professor of Mathematics

Senior Research Fellow at All Souls College

Israel Gelfand Chair of mathematics, IHES.

## Personal website:

## Research groups:

## Address

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

## Recent Publications:

From the Deligne-Ihara conjecture to multiple modular malues

RIMS Kôkyûroku
volume 2120
(31 July 2019)

A multi-variable version of the completed Riemann zeta function and other $L$-functions

Profinite Monodromy, Galois Representations and Complex Functions
(22 July 2019)

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

Research in the Mathematical Sciences
issue 5
volume 34
(13 August 2018)

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

Algebra and Number Theory
issue 3
volume 12
page 723–750-
(1 March 2018)

A class of non-holomorphic modular forms I

Research in the Mathematical Sciences
(1 January 2018)

## 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...