Francis Brown
CNRS, IMJ
Institut de
Mathématiques de Jussieu
175, Rue du Chevaleret
75013 Paris
France
Tel: +33 (0) 1 44 27 53 56
Preprints:
Proof of the Zig-Zag conjecture (2012), 1-18 (with O. Schnetz)
Depth-graded motivic multiple zeta values (2012), 1-26 (based on a talk given at Cartier's 80th birthday conference)
Properties of c2 invariants of Feynman graphs (2012), 1-31 (with O. Schnetz, K. Yeats).
Multiple Elliptic Polylogarithms (2011), 1-40 (with A. Levin).
On
the periods of some Feynman integrals, arXiv:0910.0114v1,
(2009), 1-69.
Publications:
Dedekind
Zeta motives for totally real fields, to appear in Inventiones, 2013
Angles, Scales and Parametric Renormalization (2011), 1-58 (with D. Kreimer).
Decomposition of motivic multiple zeta values, to appear in `Galois-Teichmuller theory and Arithmetic Geometry', Advanced Studies in Pure Mathematics
A K3 in phi^4, to appear in Duke Math. Journal (with O. Schnetz)
Mixed Tate Motives over Spec(Z), to appear in Annals of Math., volume 175, no. 1 (2012).
Spanning forest
polynomials and the transcendental weight of Feynman graphs, Communications in Mathematical Physics (15 October 2010), pp. 1-26.
(with K. Yeats)
The
algebra of cell-zeta values, Compositio. Math. volume 146, issue 03, pp. 731-771 (2010) (with S. Carr, L.
Schneps)
Inversion
of series and the cohomology of the moduli spaces
$\mathcal{M}^{\delta}_{0,n}$, Clay Math Proceedings, Vol. 11, (2010) (with J. Bergström)
From
Moduli spaces to Feynman Integrals, To appear in proceedings of `Combinatorics and Physics', MPIM, March 19-23, 2007.
Multiple
Zeta Values and and periods of moduli spaces M_{0,n},
Annales scientifiques de l'ENS 42, fascicule 3 (2009), 371-489.
The
Massless higher-loop two point function, Comm. in Math.
Physics 287, Number 3, (2009), 925-958.
On
arithmetic and asymptotic properties of up-down numbers,
Discrete Math. 307 (2007), 1722-1736. (with T. Fink and K. Willbrand).
1-D random landscapes and non-random data series, EPL 79, (2007) 38006
(with T. Fink, K. Willbrand).
Unbiased pattern detection in microarray data series, Bioinformatics
22, (15 June 2006), 1471-1476 (with S. Ahnert, T. Fink, K. Willbrand).
Périodes des espaces des modules
$\overline{\mathfrak{M}}_{0,n}$ et multizêtas, C.R. Acad.
Sci. Paris, Ser. I 342 (2006), 949-954.
Li's
criterion and zero-free regions for L-functions,
Journal of Number theory 111, (2005), 1-32.
Single-valued
multiple polylogarithms in one variable, C.R. Acad. Sci.
Paris, Ser. I 338 (2004), 527-532.
Some talks given/Notes in preparation (caveat emptor):
Iterated integrals in quantum field theory.
Talk `On Multiple Zeta Values', Arbeitstagung 2011.
Talk `On MZV's and differential Galois Theory', Galois bicentenary conference at IHES, October 2011.
Talk `Amplitudes in phi^4', Amplitudes 2012, Hamburg, March 2012.
Lectures on Renormalization, Spring School in Bingen 2013.
Talk on Anatomy of Associators, Cambridge April 2013 (Printable).
(Page under construction)