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Prof. Francis Brown

Status
Academic Faculty

Professor of Mathematics

Senior Research Fellow at All Souls College

 

+44 1865 283871
Contact form
ORCID iD
https://orcid.org/0000-0002-9295-2572
Research groups
  • Number Theory
  • Mathematical Physics
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
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-partic…

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.

Recent publications
LAURICELLA HYPERGEOMETRIC FUNCTIONS, UNIPOTENT FUNDAMENTAL GROUPS OF THE PUNCTURED RIEMANN SPHERE, AND THEIR MOTIVIC COACTIONS
Brown, F Dupont, C Nagoya Mathematical Journal volume 249 148-220 (26 Mar 2023)
Generalised graph Laplacians and canonical Feynman integrals with
kinematics
Brown, F (20 May 2022) http://arxiv.org/abs/2205.10094v1
A double integral of d log forms which is not polylogarithmic
Brown, F Duhr, C Proceedings of Science (15 Feb 2022)
Invariant differential forms on complexes of graphs and Feynman integrals
Brown, F Symmetry, Integrability and Geometry: Methods and Applications volume 17 (23 Nov 2021)
Depth-graded motivic multiple zeta values
Brown, F Compositio Mathematica volume 157 issue 3 529-572 (22 Mar 2021)
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Stonewall Silver Employer 2022 Athena SWAN Silver Award (ECU Gender Charter) London Mathematical Society Good Practice Scheme
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