Prof. Francis Brown
Professor of Mathematics
Senior Research Fellow at All Souls College
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
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…
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.
$\mathrm{GL}_n(\mathbb{Z})$, and $\mathrm{SL}_n(\mathbb{Z})$
$\mathrm{GL}_n(\mathbb{Z})$, canonical integrals and zeta values
varieties, and unstable cohomology of $\mathrm{GL}_g(\mathbb{Z})$ and
$\mathrm{SL}_g(\mathbb{Z})$