Kurusch Ebrahimi-Fard
Background and activities
Biographical review: I obtained my Ph.D. in Theoretical Physics from Bonn University (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.
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
Journal publications
- (2020) Planarly branched rough paths and rough differential equations on homogeneous spaces. Journal of Differential Equations. vol. 269 (11).
- (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.
- (2018) Hopf-algebraic Deformations of Products and Wick Polynomials. International mathematics research notices.
- (2017) A comodule-bialgebra structure for word-series substitution and mould composition. Journal of Algebra. vol. 489.
- (2017) Center problem, Abel equation and the Faa di Bruno Hopf algebra for output feedback. International mathematics research notices. vol. 2017 (17).
- (2017) Post-Lie algebras and factorization theorems. Journal of Geometry and Physics. vol. 119.
- (2017) ϵ-Noncrossing Partitions and Cumulants in Free Probability. International mathematics research notices.
- (2017) SISO Output Affine Feedback Transformation Group and Its Faa di Bruno Hopf Algebra. SIAM Journal of Control and Optimization. vol. 55 (2).
- (2017) Discrete-Time Approximations of Fliess Operators. Numerische Mathematik. vol. 137 (1).
- (2016) Dendriform–Tree Setting for Fliess Operators. IMA Journal of Mathematical Control and Information. vol. 32.
Books
- (2018) Computation and Combinatorics in Dynamics, Stochastics and Control. Springer. 2018. ISBN 978-3-030-01592-3. Abel Symposia (1).