Francis Brown  



All Souls College  
Oxford,
OX1 4AL,
United Kingdom.

Institut des Hautes Etudes Scientifiques  
Le Bois-Marie, 35 Route de Chartres
91440 Bures-sur-Yvette
France
Tel: +33 (0) 1 60 92 66 34





Selected publications:


Dedekind Zeta motives for totally real fields, Inventiones, January (2013)

A K3 in phi^4, Duke Math. Journal, Vol. 161, No. 10 (2012), 1817-1862 (with O. Schnetz)  

Mixed Tate Motives over Spec(Z), Annals of Math., volume 175, no. 1 (2012). 

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.





Some recent preprints:


Zeta elements in depth 3 and the fundamental Lie algebra of a punctured elliptic curve (2015), 1-33  

Irrationality proofs for zeta values, moduli spaces and dinner parties (2014), 1-39  (Slides)

Multiple Modular Values for SL_2(Z) (2014), 1-50  

Motivic periods and P^1 minus 3 points (ICM proceedings) (2014), 1-25  (Slides)

Proof of the Zig-Zag conjecture (2012), 1-18 (with O. Schnetz)  

Depth-graded motivic multiple zeta values (2012), 1-26  

Framings for graph hypersurfaces (2013), 1-31 (with D. Doryn).  

Modular forms in quantum field theory (2013), 1-31 (with O. Schnetz).  

Single-valued periods and multiple zeta values (2013), 1-24.  

Multiple Elliptic Polylogarithms (2011), 1-40 (with A. Levin).  

On the periods of some Feynman integrals, arXiv:0910.0114v1, (2009), 1-69.





Some talks given/Notes in preparation (caveat emptor):


Some old (unchecked) notes on single-valued hyperlogarithms (2004)

Iterated integrals in quantum field theory

Talk `On Multiple Zeta Values', Arbeitstagung 2011, (video of a talk given at Clay Research conference 2012). 

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)

Talk on Quantum Field Theory and Arithmetic, Journées Arithmétiques, Grenoble, July 2013. 

Talks at summer school at Les Houches (Lecture 1 : algebraic c invariants), (Lecture 2 : proof of coaction conjecture), June 2014. 

Talk on coaction structure for amplitudes and a small graphs principle (Oxford September 2014)





Slides of recent talks:


Talk on zeta elements, Michel Waldschmidt's 70th Birthday conference, June 2016 

Talk on Periods and Cosmic Galois Group, SMF inaugural meeting, June 2016 

Talk on modular forms in high-energy physics, Abel Symposium, May 2016  

Gergen Lecture I, Duke University, March 2016

Gergen Lecture II

Gergen Lecture III

Gergen Lecture IV


Former Ph.D students (financed by ERC grant 257638)

Clément Dupont

Claire Glanois

David Jarossay