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Kurusch Ebrahimi-Fard

Kurusch Ebrahimi-Fard

Professor
Department of Mathematical Sciences

kurusch.ebrahimi-fard@ntnu.no
+4773593527 Sentralbygg 2, 1342, Gløshaugen, Alfred Getz' vei 1
Personal website arXiv publications
About Publications Media

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

  • Chronological
  • By category
  • See all publications in Cristin

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 lecture
    Ebrahimi-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

  • Documentary
    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 [Tidsskrift]. 2019-11-06.

2017

  • Academic lecture
    Berlin, 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 lecture
    Curry, 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.
  • Lecture
    Gray, 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.
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