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)