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Prof. Francis Brown

Status
Academic Faculty

Professor of Mathematics

Senior Research Fellow at All Souls College

 

Contact form
+44 1865 283871
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

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)
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-partic…

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