## Research Information

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.

## Recent Publications

"On the topological computation of K_4 of the Gaussian and Eisenstein integers"
(with M. Dutour Sikiric, P. Gunnells, J. Hanke, A. Schuermann, D. Yasaki), J of Homotopy and Related Structures, 14 (2019), 281-291.
"Homophonic Quotients of Linguistic Free Groups: German, Korean, and Turkish"
(with G. Kiraali, W. Lee), Involve 12:3 (2019), 463-474.
"The Grassmannian complex and Goncharov's motivic complex in weight 4", Preprint.
"Multiple polylogarithms in weight 4", Preprint.
"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.
"Finite polylogarithms, their multiple analogues and the Shannon entropy", (with Ph. Elbaz-Vincent) 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.

### Further publications

## Seminars:

Arithmetic Study Group

### Upcoming Activities

Aug 2019: Research stay at MPIM, Bonn

Workshop on "Interactions between Hyperbolic Geometry and Number Theory", Luxembourg, 4-5 Jul 2019.

21-25 Jan 2019 "Arithmetic and Algebraic Geometry", in honour of Tomohide Terasoma's 60th birthday,

May --Dec 2018: Research stay at MPIM, Bonn

Jan -- Apr 2018: Co-organiser of a Special programme on "Periods in Number Theory, Algebraic Geometry and Physics".