Kurusch Ebrahimi-Fard
About
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.
Courses
MA2501 Numerical Methods
Publications
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
-
Diehl, Joscha;
Ebrahimi-Fard, Kurusch;
Tapia, Nikolas.
(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/Conference paper
-
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).
Academic anthology/Conference proceedings
-
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).
Academic anthology/Conference proceedings
-
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).
Academic anthology/Conference proceedings
-
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).
Academic anthology/Conference proceedings
Journal publications
-
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
-
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
-
Diehl, Joscha;
Ebrahimi-Fard, Kurusch;
Tapia, Nikolas.
(2022)
Tropical Time Series, Iterated-Sums Signatures, and Quasisymmetric Functions.
SIAM Journal on applied algebra and geometry.
volum 6 (4).
Academic article
-
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;
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
-
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
-
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
-
Curry, Charles Henry Alexander;
Ebrahimi-Fard, Kurusch;
Owren, Brynjulf.
(2018)
The Magnus expansion and Post-Lie algebras.
arXiv.org.
Academic article
-
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
-
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
-
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
-
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
Books
-
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).
Academic anthology/Conference proceedings
-
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).
Academic anthology/Conference proceedings
-
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).
Academic anthology/Conference proceedings
-
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).
Academic anthology/Conference proceedings
Part of book/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/Conference paper
Report
-
Ebrahimi-Fard, Kurusch;
Gray, W. Steven;
Schmeding, Alexander.
(2021)
Universal Zero Dynamics: The SISO Case.
IEEE. 2021. ISBN 9781665412681.
Report
Media
2021
-
Academic lectureEbrahimi-Fard, Kurusch; Gray, W. Steven; Duffaut Espinosa, Luis A.. (2021) Additive Networks of Chen-Fliess Series: Local Convergence and Relative Degree. 60th IEEE Conference on Decision and Control (CDC) . IEEE; Austin, Texas. 2021-12-13 - 2021-12-15.
2019
-
DocumentaryBruned, Yvain; Curry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch. (2019) Quasi-shuffle algebras and renormalisation of rough differential equations. Bulletin of the London Mathematical Society [Tidsskrift]. 2019-11-06.
2017
-
Academic lectureBerlin, Lance; Gray, Steven; Ebrahimi-Fard, Kurusch; Duffaut Espinosa, Luis A.. (2017) On the Performance of Antipode Algorithms for the Multivariable Output Feedback Hopf Algebra. 2017 51st Annual Conference on Information Sciences and Systems (CISS) ; 2017-03-22 - 2017-03-24.
-
Academic lectureCurry, Charles Henry Alexander; Ebrahimi-Fard, Kurusch; Patras, Frederic. (2017) On non-commutative stochastic exponentials. European Conference on Numerical Mathematics and Advanced Applications . minisymposium; Voss. 2017-09-25 - 2017-09-29.
-
LectureGray, Steven; Duffaut Espinosa, Luis A.; Ebrahimi-Fard, Kurusch. (2017) Sensitivity of the left inverse of a SISO analytic nonlinear system. 2017 51st Annual Conference on Information Sciences and Systems (CISS) ; 2017-03-22 - 2017-03-24.