My work is concentrated around polylogarithms and variants thereof, in connection with algebraic K-theory, algebraic number theory and arithmetic algebraic geometry. The questions that I am interested in lead to a variety of rather disparate topics, comprising for instance the homology of the general linear group, configuration and moduli spaces, combinatorial Hopf algebras, multiple zeta values or (quasi-)modular forms and in recent years particle physics. A good chunk of my research has a computer-experimental flavour, using mostly the GP/PARI scripting language to try to detect patterns in piles of data, to find hitherto unknown objects or to formulate conjectures.
Selected Publications and Preprints
"Functional equations and ladders for polylogarithms" (to appear in Communications in Number Theory and Physics).
"On the cohomology of linear groups over imaginary quadratic fields"
(with M. Dutour Sikiri\v c, P. Gunnells, J. Hanke, A. Schuermann, D. Yasaki).
On the Broadhurst-Kreimer generating series for multiple zeta values (with S. Carr,
"Perfect forms, K-theory and the cohomology of modular groups" (with Ph. Elbaz-Vincent and C. Soulé), Adv. in Math. 245 (2013), 587-624.
"Tame kernels and second regulators
of number fields and their subfields" (with J. Browkin), Journal of K-Theory 12 (2013), 137-165.
"From polygons and symbols to polylogarithmic functions" (with C. Duhr and J. Rhodes), JHEP 10 (2012), 075.
"On special elements in higher algebraic K-theory and the Lichtenbaum-Gross Conjecture" (with D. Burns and R. de Jeu), Adv. in Math. 23 (2012), 1502-1529.
Arithmetic Study Group
Second conference on Geometric Science of Information,
October 28-30 2015.