2023

• Ebrahimi-Fard, Kurusch; Celestino, Adrián; Witzman, Leon; Perales, Daniel; Nica, Alexandru. (2023) Multiplicative and semi-multiplicative functions on non-crossing partitions, and relations to cumulants. Advances in Applied Mathematics. volum 145.
  Academic article

2022

• Al-Kaabi, Mahdi J. Hasan; Ebrahimi-Fard, Kurusch; Manchon, Dominique. (2022) Post-Lie Magnus Expansion and BCH-Recursion. SIGMA. Symmetry, Integrability and Geometry. volum 18.
  Academic article
• Caudillo, Diego; Diehl, Joscha; Ebrahimi-Fard, Kurusch; Verri, Emanuele. (2022) Graph counting signatures and bicommutative Hopf algebras. arXiv.
  Academic article
• Ebrahimi-Fard, Kurusch; Tapia, Nikolas; Diehl, Joscha. (2022) Tropical Time Series, Iterated-Sums Signatures, and Quasisymmetric Functions. SIAM Journal on applied algebra and geometry. volum 6 (4).
  Academic article

2021

• Celestino Rodriguez, Adrian de Jesus; Ebrahimi-Fard, Kurusch; Patras, Frédéric; Perales, Daniel. (2021) Cumulant–Cumulant Relations in Free Probability Theory from Magnus’ Expansion. Foundations of Computational Mathematics.
  Academic article
• Ebrahimi-Fard, Kurusch; Celestino Rodriguez, Adrian de Jesus; Perales Anaya, Daniel. (2021) Relations between Infinitesimal Non-Commutative Cumulants. Documenta Mathematica. volum 26.
  Academic article
• Ebrahimi-Fard, Kurusch; Gray, W. Steven; Schmeding, Alexander. (2021) Universal Zero Dynamics: The SISO Case. IEEE. 2021. ISBN 9781665412681.
  Report
• Ebrahimi-Fard, Kurusch; Patras, Frederic. (2021) From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras. Algebra and Applications 2: Combinatorial Algebra and Hopf Algebras.
  Academic chapter/article
• Ebrahimi-Fard, Kurusch; Patras, Frédéric; Tapia, Nikolas; Zambotti, Lorenzo. (2021) Wick polynomials in non-commutative probability: A group-theoretical approach. Canadian Journal of Mathematics (CJM). volum 74 (6).
  Academic article
• Gray, W. Steven; Ebrahimi-Fard, Kurusch. (2021) Generating series for networks of Chen–Fliess series. Systems & control letters (Print). volum 147.
  Academic article

2020

• Curry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch; Manchon, Dominique; Munthe-Kaas, Hans Zanna. (2020) Planarly branched rough paths and rough differential equations on homogeneous spaces. Journal of Differential Equations. volum 269 (11).
  Academic article
• Curry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch; Owren, Brynjulf. (2020) The Magnus expansion and post-Lie algebras. Mathematics of Computation. volum 89 (326).
  Academic article
• Diehl, Joscha; Ebrahimi-Fard, Kurusch; Tapia, Nikolas. (2020) Time-warping invariants of multidimensional time series. Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. volum 170 (1).
  Academic article
• Ebrahimi-Fard, Kurusch; Foissy, Loïc; Kock, Joachim; Patras, Frédéric. (2020) Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations. Advances in Mathematics. volum 369.
  Academic article
• Ebrahimi-Fard, Kurusch; Gray, W. Steven; Manchon, Dominique. (2020) Evaluating Generating Functions for Periodic Multiple Polylogarithms via Rational Chen–Fliess Series. Springer Proceedings in Mathematics & Statistics. volum 314.
  Academic article
• Ebrahimi-Fard, Kurusch; Patras, Frédéric; Tapia, Nikolas; Zambotti, Lorenzo. (2020) Hopf-algebraic deformations of products and Wick polynomials. International mathematics research notices. volum 2020 (24).
  Academic article

2019

• Bruned, Yvain; Curry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch. (2019) Quasi-shuffle algebras and renormalisation of rough differential equations. Bulletin of the London Mathematical Society.
  Academic article
• Curry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch; Malham, Simon J. A.; Wiese, Anke. (2019) Algebraic structures and stochastic differential equations driven by Levy processes. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. volum 475 (2221).
  Academic article
• Curry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch; Munthe-Kaas, Hans. (2019) What is a post-Lie algebra and why is it useful in geometric integration. Lecture Notes in Computational Science and Engineering. volum 126.
  Academic article
• Curry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch; Patras, Frederic. (2019) On non-commutative stochastic exponentials. Lecture Notes in Computational Science and Engineering. volum 126.
  Academic article
• Ebrahimi-Fard, Kurusch; Gray, W. Steven. (2019) The Faá di Bruno Hopf algebra for multivariable feedback recursions in the center problem for higher order Abel equations. Abel Symposia. volum 13.
  Academic article
• Ebrahimi-Fard, Kurusch; Patras, Frederic. (2019) Shuffle group laws: applications in free probability. Proceedings of the London Mathematical Society. volum 119 (3).
  Academic article

2018

• Celledoni, Elena; Di Nunno, Giulia; Ebrahimi-Fard, Kurusch; Munthe-Kaas, Hans. (2018) Computation and Combinatorics in Dynamics, Stochastics and Control. Springer. 2018. ISBN 978-3-030-01592-3. Abel Symposia (1).
  Scientific anthology
• Curry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch; Owren, Brynjulf. (2018) The Magnus expansion and Post-Lie algebras. arXiv.org.
  Academic article
• Ebrahimi-Fard, Kurusch; Barbero Liñan, Maria. (2018) Discrete Mechanics, Geometric Integration and Lie–Butcher Series. Springer Publishing Company. 2018. ISBN 978-3-030-01396-7. Springer Proceedings in Mathematics & Statistics (1).
  Scientific anthology
• Ebrahimi-Fard, Kurusch; Manchon, Dominique; Singer, Johannes; Zhao, Jianqang. (2018) Renormalisation group for multiple zeta values. Communications in Number Theory and Physics. volum 12 (1).
  Academic article
• Ebrahimi-Fard, Kurusch; Patras, Frederic. (2018) Monotone, free, and boolean cumulants: a shuffle algebra approach. Advances in Mathematics. volum 328.
  Academic article

2017

• Ebrahimi-Fard, Kurusch; Fauvet, Frederic; Manchon, Dominique. (2017) A comodule-bialgebra structure for word-series substitution and mould composition. Journal of Algebra. volum 489.
  Academic article
• Ebrahimi-Fard, Kurusch; Gray, Steven. (2017) Center problem, Abel equation and the Faa di Bruno Hopf algebra for output feedback. International mathematics research notices. volum 2017 (17).
  Academic article
• Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans. (2017) Post-Lie algebras and factorization theorems. Journal of Geometry and Physics. volum 119.
  Academic article
• Ebrahimi-Fard, Kurusch; Patras, Frederic; Speicher, Roland. (2017) ϵ-Noncrossing Partitions and Cumulants in Free Probability. International mathematics research notices.
  Academic article
• Gray, Steven; Ebrahimi-Fard, Kurusch. (2017) SISO Output Affine Feedback Transformation Group and Its Faa di Bruno Hopf Algebra. SIAM Journal of Control and Optimization. volum 55 (2).
  Academic article
• Gray, W Steven; Duffaut Espinosa, Luis A.; Ebrahimi-Fard, Kurusch. (2017) Discrete-Time Approximations of Fliess Operators. Numerische Mathematik. volum 137 (1).
  Academic article

2016

• Duffaut-Espinosa, Luis; Gray, Steven; Ebrahimi-Fard, Kurusch. (2016) Dendriform–Tree Setting for Fliess Operators. IMA Journal of Mathematical Control and Information. volum 32.
  Academic article

2015

• Ebrahimi-Fard, Kurusch; Alvarez-Consul, Luis; Burgos Gil, Jose Ignacio. (2015) Feynman Amplitudes, Periods and Motives. American Mathematical Society (AMS). 2015. ISBN 978-1-4704-2247-9. Contemporary Mathematics (1).
  Scientific anthology
• Ebrahimi-Fard, Kurusch; Patras, Frederic. (2015) Cumulants, free cumulants and half-shuffles. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. volum 471 (2176).
  Academic article

2011

• Ebrahimi-Fard, Kurusch; Marcolli, Matilde; van Suijlek, Walter D.. (2011) Combinatorics and Physics. American Mathematical Society (AMS). 2011. ISBN 978-0-8218-5329-0. Contemporary Mathematics (1).
  Scientific anthology