Background and activities
Biographical review: I obtained my Ph.D. in Theoretical Physics from the University of Bonn (supervisors: D. Kreimer, R. Flume). I also obtained a Maîtrise de Mathématiques from Université Joseph Fourier in Grenoble, France. I have covered postdoctoral positions at: Institut des Hautes Études Scientifiques (Bures-sur-Yvette, France), Max Planck Institute for Mathematics (Bonn, Germany), Universidad de Zaragoza (Zaragoza, Spain) and Instituto de Ciencias Matemáticas – ICMAT (Madrid, Spain). I was a fellow of the Studienstiftung des Deutschen Volkes, the Evangelisches Studienwerk e.V., the German Academic Exchange Service (DAAD), and the European Post-Doctoral Institute (EPDI).
Research keywords: numerical integration methods; nonlinear control theory; stochastic calculus; free probability theory; quantum field theory; renormalization theory; dynamical systems theory; Rota-Baxter algebras; combinatorial Hopf algebras; pre- and post-Lie algebras, Spitzer-type identities; Poincaré's center-focus problem; Baker-Campbell-Hausdorff formula; Magnus and Fer-type expansions; theory of multiple zeta values.
MA2501 Numerical Methods
Scientific, academic and artistic work
A selection of recent journal publications, artistic productions, books, including book and report excerpts. See all publications in the database
- (2022) Post-Lie Magnus Expansion and BCH-Recursion. SIGMA. Symmetry, Integrability and Geometry. vol. 18.
- (2021) Cumulant–Cumulant Relations in Free Probability Theory from Magnus’ Expansion. Foundations of Computational Mathematics.
- (2021) Relations between infinitesimal non-commutative cumulants. Documenta Mathematica. vol. 26.
- (2021) Wick polynomials in non-commutative probability: A group-theoretical approach. Canadian Journal of Mathematics (CJM).
- (2021) Generating series for networks of Chen–Fliess series. Systems & control letters (Print). vol. 147.
- (2020) Planarly branched rough paths and rough differential equations on homogeneous spaces. Journal of Differential Equations. vol. 269 (11).
- (2020) The Magnus expansion and post-Lie algebras. Mathematics of Computation. vol. 89 (326).
- (2020) Time-warping invariants of multidimensional time series. Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. vol. 170 (1).
- (2020) Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations. Advances in Mathematics. vol. 369.
- (2020) Evaluating Generating Functions for Periodic Multiple Polylogarithms via Rational Chen–Fliess Series. Springer Proceedings in Mathematics & Statistics. vol. 314.
- (2020) Hopf-algebraic deformations of products and Wick polynomials. International mathematics research notices. vol. 2020 (24).
- (2019) Quasi-shuffle algebras and renormalisation of rough differential equations. Bulletin of the London Mathematical Society.
- (2019) Algebraic structures and stochastic differential equations driven by Levy processes. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. vol. 475 (2221).
- (2019) What is a post-Lie algebra and why is it useful in geometric integration. Lecture Notes in Computational Science and Engineering. vol. 126.
- (2019) On non-commutative stochastic exponentials. Lecture Notes in Computational Science and Engineering. vol. 126.
- (2019) The Faá di Bruno Hopf algebra for multivariable feedback recursions in the center problem for higher order Abel equations. Abel Symposia. vol. 13.
- (2019) Shuffle group laws: applications in free probability. Proceedings of the London Mathematical Society. vol. 119 (3).
- (2018) The Magnus expansion and Post-Lie algebras. arXiv.org.
- (2018) Renormalisation group for multiple zeta values. Communications in Number Theory and Physics. vol. 12 (1).
- (2018) Monotone, free, and boolean cumulants: a shuffle algebra approach. Advances in Mathematics. vol. 328.