178 citations · 1.1k across the 36 of their papers we have counts for
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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…
Lauricella hypergeometric functions, unipotent fundamental groups of the punctured Riemann sphere, and their motivic coactions
Francis Brown, Clément Dupont
The goal of this paper is to raise the possibility that there exists a meaningful theory of `motives' associated to certain hypergeometric integrals, viewed as functions of their p…
From the Deligne-Ihara conjecture to Multiple Modular Values
Francis Brown
This is the write-up of a talk given in honour of Prof. Ihara's 80th Birthday conference in Kyoto in 2018. After briefly reviewing the work of Ihara on the projective line minus 3…
Modular forms in Quantum Field Theory
Francis Brown, Oliver Schnetz
The amplitude of a Feynman graph in Quantum Field Theory is related to the point-count over finite fields of the corresponding graph hypersurface. This article reports on an experi…
Framings for graph hypersurfaces
Francis Brown, Dzmitry Doryn
We present a method for computing the framing on the cohomology of graph hypersurfaces defined by the Feynman differential form. This answers a question of Bloch, Esnault and Kreim…
Properties of c_2 invariants of Feynman graphs
Francis Brown, Oliver Schnetz, Karen Yeats
The c_2 invariant of a Feynman graph is an arithmetic invariant which detects many properties of the corresponding Feynman integral. In this paper, we define the c_2 invariant in m…
Mixed Tate motives over
Francis Brown
We prove that the category of mixed Tate motives over is spanned by the motivic fundamental group of $\Pro^1$ minus three points. We prove a conjecture by M. Hoffman which sta…
A K3 in phi4
Francis Brown, Oliver Schnetz
Inspired by Feynman integral computations in quantum field theory, Kontsevich conjectured in 1997 that the number of points of graph hypersurfaces over a finite field $\F_q$ is a (…
Inversion of series and the cohomology of the moduli spaces
Francis Brown, Jonas Bergström
For , let denote the moduli space of genus 0 curves with marked points, and its smooth compactification. A theorem d…
On the periods of some Feynman integrals
Francis C. S. Brown
We study the related questions: (i) when Feynman amplitudes in massless theory evaluate to multiple zeta values, and (ii) when their underlying motives are mixed Tate. More g…
The massless higher-loop two-point function
Francis Brown
We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph t…
Dedekind Zeta motives for totally real fields
Francis Brown
Let be a totally real number field. For every odd , we construct a Dedekind zeta motive in the category $\MT(k)$ of mixed Tate motives over . By directly calculatin…
Multiple zeta values and periods of moduli spaces
Francis C. S. Brown
In this paper we prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces of Riemann spheres with marked points are…