178 citations · 1.1k across the 36 of their papers we have counts for
45 papers
Non-linear geometry of multiple zeta values
Francis Brown
Since their rediscovery in the 1990s, multiple zeta values have become ubiquitous in many areas of mathematics and physics. Their standard integral and sum representations can usua…
Mellin transforms, transfinite diameter and rational approximations of integrals
Francis Brown
We establish a higher-dimensional irrationality criterion for periods which are presented as Mellin integrals depending on many parameters. The criterion is stated as an upper boun…
On cellular rational approximations to
Francis Brown, Wadim Zudilin
We analyse a certain family of cellular integrals, which are period integrals on the moduli space of curves of genus zero with eight marked points, and give ris…
Generalised graph Laplacians and canonical Feynman integrals with kinematics
Francis Brown
To any graph with external half-edges and internal masses, we associate canonical integrals which depend non-trivially on particle masses and momenta, and are always finite. They a…
Invariant Differential Forms on Complexes of Graphs and Feynman Integrals
Francis Brown
We study differential forms on an algebraic compactification of a moduli space of metric graphs. Canonical examples of such forms are obtained by pulling back invariant differentia…
A double integral of dlog forms which is not polylogarithmic
Francis Brown, Claude Duhr
Feynman integrals are central to all calculations in perturbative Quantum Field Theory. They often give rise to iterated integrals of dlog-forms with algebraic arguments, which in…