Francis Brown (mathematician)

Francis Brown is a British mathematician specializing in number theory and algebraic geometry, particularly in the areas of motivic periods, multiple zeta values, and Feynman amplitudes.

Brown received his PhD from the University of Bordeaux in 2007 under the supervision of Pierre Cartier. His thesis was titled "Mixed Tate Motives over Spec(Z)."

He has made significant contributions to the understanding of the structure and properties of multiple zeta values (MZVs), which are generalizations of the Riemann zeta function and appear in various contexts in mathematics and physics. Brown proved that all MZVs are linear combinations of MZVs with odd arguments, a significant result in the field. His work also connects MZVs to the theory of mixed Tate motives over the integers.

Brown's research also explores the connection between motivic periods and Feynman amplitudes, which are integrals that arise in perturbative quantum field theory. He has investigated the motivic nature of these amplitudes and their relationship to number theory.

He has held positions at the Institut des Hautes Études Scientifiques (IHES) and the Max Planck Institute for Mathematics (MPIM) in Bonn. He is currently a professor at the University of Oxford.

His work has been recognized with several awards, including the Whitehead Prize in 2012.