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.
"On the cohomology of linear groups over imaginary quadratic fields"
(with M. Dutour Sikiric, P. Gunnells, J. Hanke, A. Schuermann, D. Yasaki), J Pure Appl Alg, 220 (2016), 2564--2589.
(with Ph. Elbaz-Vincent) Finite polylogarithms, their multiple analogues and the Shannon entropy, GSI 2015 (F. Nielsen and F. Barbaresco eds.), LNCS 9389 (2015) 1--9.
On the Broadhurst-Kreimer generating series for multiple zeta values (with S. Carr,
L. Schneps), in ``Feynman Amplitudes, Periods and Motives", (L. Alvarez-Consul, J.I. Burgos-Gil, K. Ebrahimi-Fard), Contemp. Math. 648, AMS (2015), 57--78.
"Functional equations and ladders for polylogarithms", Communications in Number Theory and Physics, 7, no.3 (2013), 397--410.
"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
Workshop on Bianchi Modularity, Luxembourg, 11.-15.7.2016. Slides of the talk.