Kurusch
Ebrahimi-Fard Professor Department of Mathematical Sciences Norwegian University of Science and Technology Trondheim, Norway |
I am a member of the Differential Equations and Numerical Analysis (DNA) group at IMF-NTNU. |

• Research interests
• Biographical Review • Activities 2022 • Past activities 2021; 2020; 2019; 2018; 2017; 2016 - 2006 • Publications • Contact • News: TMS project "Pure Mathematics in Norway" Nasjonalt Matematikermøte i Trondheim, Sept. 3-4, 2020 Online seminar "Algebraic and Combinatorial Perspectives in the Mathematical Sciences (ACPMS)" FPSAC2020 poster session Lie-Størmer Center for Fundamental Structures in Computational and Pure Mathematics (video) |
Upcoming events/activities: • Lie-Størmer Colloquium: "Between Theoretical and Computational Mathematics", May 26-29, 2022, Barony Rosendal, Norway. • SciCADE 2022 (mini-symp.: Geometric and algebraic perspectives in numerical integration), University of Iceland, July 25-29, 2022, Reykjavik, Iceland. |
Teaching
Projects Group |

"There
is no branch of mathematics, however abstract, which may not someday be
applied to phenomena of the real world" Nikolai
Lobachevsky Research Interests: My work aims at developing mathematical methods useful to science and engineering. It is based on a surprising convergence of different areas of mathematical sciences. Indeed, fields ranging from geometric integration methods, to nonlinear control theory, to Lyons’ theory of rough paths, to Voiculescu’s free probability theory, to perturbative quantum field theory share common formalisms, where algebraic and combinatorial structures on graphs, partitions and other combinatorial objects are central. Currently, I am working on problems in nonlinear control theory, numerical analysis of ordinary and stochastic differential equations, and free probability theory. I am also keenly interested in various aspects of algebraic and combinatorial structures underlying multiple zeta values and related topics. |
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. ORCID ID: orcid.org/0000-0001-5180-5835 Scopus Author ID: 6603095842 ResearcherID: F-6672-2016 MathSciNet: Ebrahimi-Fard, Kurusch Google scholar |

___________________________________________
Biographical Review: I was born in Cologne, Germany, and 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 - IHES (Bures-sur-Yvette, France), Max Planck Institute for Mathematics - MPIM (Bonn, Germany), Universidad de Zaragoza (Zaragoza, Spain) and Instituto de Ciencias Matemáticas – ICMAT (Madrid, Spain). I held both a Juan de la Cierva as well as a Ramón y Cajal fellowship. 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). ___________________________________________ Activities 2022
Lie-Størmer Colloquium: "Between Theoretical and Computational Mathematics", May 26-29, 2022, Barony Rosendal, Norway.
SciCADE "International Conference on Scientific Computation and Differential Equations" (mini-symp.: Geometric and algebraic perspectives in numerical integration), University of Iceland, July 25-29, 2022, Reykjavik, Iceland. Workshop "Rough Paths, Algebraic Structures and Machine Learning" (RPASML22), Oct. 20-21, 2022, University of Agder, Kristiansand, Norway. GDR Renormalisation Annual Meeting 2022 "Hopf Algebras and Applications" (HAA2022), Nov. 14-18, 2022, Univ. du Littoral Cote d'Opale, Calais, France. ___________________________________________ Past activities 2021
• Mini-workshop "Cumulants in Stochastic Analysis" (online), Feb. 25-26, 2021.
• MFO Workshop "Geometric Numerical Integration" (online), Mathematical Research Institute of Oberwolfach, March 28 - April 3, 2021, Oberwolfach, Germany.
•
ACPMS special online seminar "The amplituhedron: algebra, combinatorics, and physics", April 8, 2021.
•
TMS-Pure Mathematics in Norway Colloquium "Fundamental interactions between algebra and computation" (hybrid), April 22-23, 2021, Department of Mathematics, University of Bergen, Bergen, Norway.
• SciCADE "International Conference on Scientific Computation and Differential Equations" (mini-symp.: Geometric and algebraic perspectives in numerical integration), University of Iceland, July 26-30, 2021,
Reykjavik, Iceland. (postponed)
•
ICERM Workshop "Applications of Rough Paths: Computational Signatures and Data Science" (online), 6-9 July, 2021, The Institute for Computational and Experimental Research in Mathematics, Brown University USA.
•
Workshop "Noncommutative geometry meets topological recursion" (hybrid), 16-20 Aug., 2021, Univ. of Münster, Germany.
•
International conference "Noncommutative algebra, probability and analysis in action" (hybrid), Sept. 20-25, 2021, Alfried Krupp Wissenschaftskolleg, Greifswald, Germany.
•
ACPMS Mini-workshop
"Topological Recursion and Combinatorics
" (online), Nov.5, 2021.
•
ESI Master class and workshop
"Higher Structures Emerging from Renormalisation", Nov. 8-19, 2021, Erwin Schrödinger Institute - ESI, Vienna, Austria.
•
TMS-Pure Mathematics in Norway Seminar "Rough path techniques in stochastic analysis and mathematical probability", Nov. 25-26, 2021, Department of Mathematics, University of Oslo, Oslo, Norway.
2020
• Workshop "Geometry & Algebra in Stochastic Dynamics" (poster), January 27-29, 2020, Department of Mathematics, University of Milan, Milan, Italy.
• "Free Probability", a conference on the occasion of Roland Speicher's 60th birthday, June 8-12, 2020, Saarland University, Saarbrücken, Germany. (postponed)
• Workshop “Rota-Baxter Algebras and Related Topics”, June 29 - July 3, 2020, Chern Institute of Mathematics, Nankai University, Tianjin, China. (postponed)
• FPSAC2020, 32nd Conference on Formal Power Series and Algebraic Combinatorics (online, poster/paper)
• Workshop "Geometry of curves in time series and shape analysis" (online), August 11-14, 2020, MPI für Mathematik in den Naturwissenschaften, Leipzig, Germany.
• Nasjonalt Matematikermøte i Trondheim, Sept. 3-4, 2020, NTNU, Trondheim, Norway. (postponed)
• BIRS workshops "Noncommutative Geometry meets Topological Recursion", Sept. 27 - Oct. 2, 2020, IAS Hangzhou, China. (postponed)
•
Workshop "Higher structures emerging from renormalisation" (online),
October 12-16, 2020. Erwin Schrödinger Institute - ESI, Vienna, Austria.
•
“Algebraic Structures in Perturbative Quantum Field
Theory”, a conference in honor of Dirk Kreimer’s 60th birthday, Nov. 16-20, 2020, IHES, Bures-sur-Yvette, France.
• Workshop "New Directions in Rough Path Theory", Mathematical Research Institute of Oberwolfach, December 6-12, 2020, Oberwolfach, Germany.
2019
• "Mørketidens Mattemøte", Department of Mathematics and Statistics, Universitetet i Tromsø UiT, January 10-11, 2019, Tromsø, Norway.
• Research seminar, Gruppe Prof. Kreimer, Humboldt-Universität zu Berlin - Institut für Mathematik, January 14, 2019, Berlin, Germany. • Arbeitsgruppenseminar Analysis, Mathematics Institute, Potsdam University, January 18, 2019, Golm, Germany. • Thematic one-month program "New Developments in Free Probability and Applications" (March 2019), Workshop "Free Probability: the theory, its extensions", March 4-8, 2019, CRM, Montréal, Canada. • Workshop "New Directions in Stochastic Analysis: Rough Paths, SPDEs and Related Topics" (Terry Lyons' 65th Birthday), March 18-22, 2019, Zuse Institute Berlin (ZIB), Berlin, Germany. • Algebra, Deformation and Quantization Conference (Bordemann's 60th birthday), IRIMAS - Mathematics Department, University of Haute Alsace UHA, May 2-4, 2019, Mulhouse, France. • Workshop on non-commutative stochastic analysis, Department of Mathematical Sciences, NTNU, May 8-10, 2019, Trondheim, Norway. • Isaac Newton Institute programme "Geometry, compatibility and structure preservation in computational differential equations", Tutorial workshop, 8-12 July 2019, Cambridge, UK. • SciCADE 2019, mini-symposium “Algebraic structures for numerical differential equations”, July 22 - 26, 2019, Innsbruck, Austria. • School+Workshop Quantum groups and their analysis, University of Oslo, July 29 - August 9, 2019, Oslo, Norway. • Rencontre du GDR Renormalisation "Equations de Dyson-Schwinger", Sept. 30 - Oct. 4, 2019, Lab. de Math. Pures et Appliquées Joseph Liouville, Univ. du Littoral Côte d’Opale, Calais, France. • BFS seminar "Deformation theory, Hopf algebras and mathematical physics", Oct. 11-12, 2019, Department of Mathematics, University of Bergen, Bergen, Norway. • BFS seminar "Algebraic and Analytic Perspectives in the Theory of Rough Paths and Signatures", Nov. 14-15, 2019, Department of Mathematics, University of Oslo, Oslo, Norway. • RWTH Aachen, Department of Mathematics, Nov. 25-29, 2019, Aachen, Germany. • Universität Greifswald, Institut für Mathematik und Informatik, Dec. 2-6, 2019, Greifswald, Germany. • The University of Edinburgh, School of Mathematics, Dec. 9-13, 2019, Edinburgh, Scotland, UK. 2018 • Stochastic
Analysis Seminar, Imperial College London, Department of
Mathematics, Mar. 20, 2018, London, UK. (title+abstract)
• "Symmetry and Computation/Symétries dans les méthodes de calcul", CIRM, April 3-7, 2018, Luminy, France. • C*-algebra seminar, Department of Mathematics, University of Oslo, May 3-4, 2018, Oslo, Norway. • ICIAM Workshop on Applied & Industrial Mathematics 2018, Drexel University, May 10-11, 2018, Philadelphia, Pennsylvania, USA. • Workshop "Modern Numerical Methods for Quantum Mechanics II", University of Gdańsk, June 27-29, 2018, Gdansk, Poland. • Conference "Algebraic and geometric aspects of numerical methods for differential equations", Institut Mittag-Leffler, July 2-7, 2018, Djursholm, Sweden. • BFS-TFS Colloquium-Seminar, Rough paths, regularity structures, and combinatorial Hopf algebras (poster), Univ. of Bergen, Aug. 31 + Sept. 1, 2018, Bergen, Norway. • Norwegian Nasjonalt matematikermøte (National Mathematicians meeting), University of Bergen, Sept. 13-14, 2018, Bergen, Norway. • CMI at 20, Andrew Wiles Building, University of Oxford, Sept. 24-26, 2018, Oxford, UK. • Rencontres du GDR Renormalisation, Laboratoire de Mathématiques Blaise Pascal, Nov. 12-16, 2018, Clermont-Ferrand, France. • Workshop "Free Probability Theory", Mathematical Research Institute of Oberwolfach, Dec. 2-8, 2018, Oberwolfach, Germany. 2017 • "Manifolds and
Geometric Integration Colloquia" (MaGIC2017), March 1-5, 2017, University of Bergen, Norway.
• Workshop on "Algebraic Renormalisation of Regularity Structures", April 3-7, 2017, Department of Mathematics, University of Bergen, Norway. • Conference "Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA), June 26 - 30, 2017, CIRM, Luminy, France. • 18th Santaló Summer School "Algebraic and Combinatorial Methods in Stochastic Calculus", July 17-21, 2017, Palacio de La Magdalena, Santander, Spain. (Poster) • Workshop "Homotopy Probability Theory", September 4-8, 2017, Saarbrücken, Germany. • International Conference on "Scientific Computation and Differential Equations" (SciCADE2017), September 11-15, 2017, Bath, UK. • "European Conference on Numerical Mathematics and Advanced Applications" (ENUMATH), Minisymposia MS18 - Noncommutative stochastic differential equations: Analysis and simulation (Orgs.: K. Ebrahimi-Fard, S.J.A. Malham, A. Wiese), September 25-29, 2017, Voss, Norway. • "Symmetry and Computation", LMS-IMA Joint Meeting, October 12, 2017, De Morgan House, Russell Square, London, UK. • Centre de Recerca Matemàtica (CRM), Campus UAB, Nov. 6-10, 2017, Barcelona, Spain. • Stochastic Analysis Seminar, Mathematical Institute, University of Oxford, Nov. 13, 2017, Oxford, UK. (title+abstract) 2016 • Abel Symposium 2016
"Computation
and Combinatorics in Dynamics, Stochastics and Control", Poster,
16-19 August 2016, Barony Rosendal, Norway.
• "Trends in Computational Mathematics", City Univ. of Hong Kong, 18-20 January 2016, Hong Kong. • "Mathematical Perspectives in Biology", Poster, ICMAT, 3-5 February 2016, Madrid, Spain. • "Paths to, from and in renormalisation", 8-12 February 2016, Univ. Potsdam - Institut für Mathematik, Potsdam, Germany. • Univ. de Nice Sophia-Antipolis, Lab. J.A.Dieudonné, Parc Valrose, Nice, France, February - March, 2016. • Univ. des Saarlandes, Fachrichtung Mathematik, "Research group in Free Probability", Saarbrücken, Germany, March, 2016. • Univ. de La Rioja, "Departamento de Matemáticas y Computación", Logroño, Spain, April 2016. • European Research Centres on Mathematics (ERCOM) meeting, Euler International Mathematical Institute, St.Petersburg, Russia, April 15-16, 2016. • Mathematics Department, The Univ. of Warwick, Probability seminar, June 20-23, 2016, Warwick, UK. • Escuela JAE de Matemáticas 2016, Poster, ICMAT, Madrid, Spain. June 27 - July 15, 2016. POSTER • Humboldt-Univ. zu Berlin, Mathematical Physics, research seminar, July 10-13, 2016, Berlin, Germany. • Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Univ. Pierre et Marie Curie Paris, Paris, France, July 18-22, 2016. • Computer Science and Artificial Intelligence Department, Univ. of the Basque Country, San Sebastian, Oct. 10-14, 2016. • Analytic versus Combinatorial in Free Probability, 4-9 December 2016, Banff International Research Station (BIRS), Alberta, Canada. 2015 • "Workshop on Hopf
Algebras of
Posets", January 15-16, 2015, Lab. de Mathématiques Pures et
Appliquées Joseph Liouville, Univ. du Littoral Côted'Opale, France.
• "4th Winter Workshop in non-perturbative Quantum Field Theory", Univ. of Nice, 2-5 February, 2015, Nice, France. • ESI Program - "The interrelation between mathematical physics, number theory and non-commutative geometry", Erwin Schrödinger Institute, Vienna, March 2-13, 2015. • "Stochastic Systems Simulations and Control 2015 Workshop" (SSSC2015), Poster, March 9-13, 2015, International Centre for Mathematical Sciences (ICMS), Edinburgh, Scotland. • "Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spain. • "ICIAM2015 Eighth International Congress of Industrial and Applied Mathematics": embedded conference DART-VI "Sixth International Workshop on Differential Algebra and Related Topics", August 10-14,2015, Beijing, China. • CIMPA research school "New interactions of Combinatorics and Probability" (poster), August 24 - September 4, 2015, Instituto de Ciências Matemáticas e de Computação (ICMC) Univ. de São Paulo, Brazil. • "54th IEEE Conference on Decision and Control", December 15-18, 2015, Osaka, Japan. Session: Algebraic and Geometric Methods I • Research grant: Ayudas Fundación BBVA a Investigadores, Innovadores y Creadores Culturales 2014. Research Project "Mathematical Methods for Ecology and Industrial Management", ICMAT, Madrid, 01/12/2014 - 30/11/2015. 2014 •
ICMAT Research Trimester on
"Multiple
Zeta Values, Multiple Polylogarithms, and Quantum Field
Theory", Poster 1,
Poster 2,
Sept. 15 - Dec. 19, 2014.
• "ICMAT-China Exploratory Workshop", ICMAT, Madrid, Nov. 17-21, 2014. • Workshop "Dyson-Schwinger Equations in Modern Mathematics & Physics" (DSEMP2014), ECT*, Trento, Sept. 22-26, 2014. • Clay Mathematics Institute Summer School 2014 "Periods and Motives: Feynman amplitudes in the 21st century", Poster, ICMAT, Madrid, June 30 - July 25, 2014. • "Homotopical Algebra Summer Days", Poster, Univ. de Barcelona, Barcelona, Spain, July 14+15, 2014. • Department of Mathematical Sciences, The Norwegian Univ. of Science and Technology (NTNU), Trondheim, Norway, Feb. 28, 2014. • "Manifolds and Geometric Integration Colloquium 2014" (MAGIC2014), Meraker (Norway), Feb. 24-27, 2014. • "Approaches to Quantum Gravity", Clermont-Ferrand, France, Jan. 6-10, 2014. 2013 • Workshop "Combinatoire
des systèmes dynamiques", Nov. 18-22, 2013, CIRM, Luminy, France.
• Workshop "Recent Trends in Algebraic and Geometric Combinatorics" (AlGeCo2013), Nov. 27-29, 2013, ICMAT, Madrid, Spain. • ICMAT Fall School "Multiple Zeta Values, Multiple Polylogarithms and Quantum Field Theory", Oct. 7-11, 2013, ICMAT, Madrid, Spain. • European Science Foundation (ESF) - Exploratory Workshop "New Approaches to Multiple Zeta Values", Sept. 30 - Oct. 2, 2013, ICMAT, Madrid, Spain. • "SciCADE 2013 International Conference on Scientific Computation and Differential Equations", Sept. 16-20, 2013, Valladolid, Spain. Minisymposium Geometric and Algebraic Methods for Differential Equations, talk:"Algebraic structures related to stochastic differential equations", Sept. 19, 2013. • Workshop "Topics in Numerical Analysis for Differential Equations" (TNADE2013), July 8-12, 2013, ICMAT, Madrid, Spain. 2012 •
ICMAT workshop "Periods and
Motives, A Modern Perspective on Renormalization", Poster, July 2-6, 2012,
Madrid, Spain.
• Workshop "Mathematical Aspects of Hadron Physics", Poster, European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Oct. 8-12, 2012, Trento, Italy. • ICMAT workshop "Stochastic Systems Simulation and Control" (SSSC2012), Nov. 5-9, 2012, Madrid, Spain. • Workshop "Algebraic Combinatorics and Numerical Analysis", 6-12th Dec. 2012, Institutt for matematiske fag, Norges teknisk-naturvitenskapelige universitet (NTNU) , Trondheim, Norway. • 7th International Young Researchers Workshop on Geometry, Mechanics and Control, Dec. 17-19, 2012, ICMAT, Madrid, Spain. 2011 • Congreso
de la Real
Sociedad de Matemática Española (RSME’11), Feb. 1-5, 2011, Avila,
Spain.
• "Nikolai Neumaier Gedenk-Kolloquium" (NNGK2011), June 16-18, 2011, LMIA, Univ. de Haute Alsace, Mulhouse, France. • "Conference Dyson-Schwinger Equations and Faà di Bruno Hopf Algebras in Physics and Combinatorics", Poster, June 27 - July 1, 2011, IRMA, Strasbourg, France. • "Congress on Industrial and Applied Mathematics" (ICIAM’11), Session Part I + Part II, July 18-22, 2011, Vancouver, Canada. • "Workshop on Rough Paths and Combinatorics in Control Theory" (RPCCT2011), July 25-27, 2011, Univ. of California, San Diego, USA. • "XX Fall Workshop on Geometry and Physics", Aug. 31 - Sept. 3, 2011, ICMAT, Madrid, Spain. • Lecture series by F. Lizzi on "Physical applications of Noncommutative Geometry" at Univ. Politècnica de Catalunya (Sept. 20-22, 2011, Barcelona), and ICMAT-Instituto de Ciencias Matemáticas (Sept. 27-29, 2011, Madrid). • Workshop: "Stochastic Differential Equations, Rough Paths, and Hopf Algebras", Nov. 30 - Dec. 1, 2011, ICMAT-Instituto de Ciencias Matemáticas. Speakers: M. Gubinelli, S. Malham, D. Manchon. 2010 • Research Trimester
"Combinatorics and Control" (COCO2010), Poster 1, Poster 2, Poster 3, Closing Conference, April-June
2010, CSIC, Madrid,
Spain.
• School on "Combinatorics and Control", April 11-17, 2010, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain. • Seminar Sophus Lie XXXIX, April 22-24, 2010, Univ. de Haute Alsace, Mulhouse, France. 2009 •
School and Conference "Algebraic and Combinatorial Structures in
Quantum Field Theory", March 23 – April 3, 2009, Institut d'Études
Scientifiques de Cargèse, Corsica, France.
• SIAM Conference ''Control & Its Applications" (Minisymposium Algebraic Tools for Nonlinear Control), July 6-8, 2009, Colorado Covention Center, Denver Colorado, USA. • International~School-Conference "Hopf-in-Lux", Univ.~of Luxembourg, July 13-17, 2009, Luxembourg. 2008 • Oberwolfach-Seminar:
Geometric Numerical Integration, Mathematisches
Forschungsinstitut Oberwolfach, 23-29 Nov. 2008, Oberwolfach,
Germany.
2007 • Conference
"Combinatorics and Physics", Poster, March
19-23, 2007, Max-Planck-Institut
für Mathematik in Bonn,
Germany.
2006 • Mini-workshop
"Renormalization", Poster, Dec. 15-16, 2006, Max-Planck-Institut
für Mathematik in Bonn,
Germany.
___________________________________________Publications (arXiv)
97.
Tropical time series, iterated-sums signatures and quasisymmetric functions (with J. Diehl, N. Tapia),
accepted for publication in SIAM Journal on Applied Algebra and Geometry, June 2022. arXiv:2009.08443 96. Post-Lie-Magnus expansion and BCH-recursion (with M. J. H. Al-Kaabi, D. Manchon), SIGMA 18 (2022), 023, 16 pages, March 2022. arXiv:2108.11103 95. Wick polynomials in non-commutative probability (with F. Patras, N. Tapia, L. Zambotti), to appear in Canadian Journal of Mathematics (online), Aug. 2021. arXiv:2001.03808 94. Relations between infinitesimal non-commutative cumulants (with A. Celestino, D. Perales), Documenta Mathematica 26, (2021), 1145-1185 (online). arXiv:1912.0493 93. Additive Networks of Chen-Fliess Series: Local Convergence and Relative Degree (with W.S. Gray and L. A. Duffaut Espinosa), Proc. 60th IEEE Conference on Decision and Control, Austin, Texas, 2021, to appear. arXiv:2104.08950 92. Universal Zero Dynamics: SISO Case (with W.S. Gray and A. Schmeding), Proc. 55th Conference on Information Sciences and Systems (CISS) (online), Baltimore, Maryland, 2021 91. From iterated integrals and chronological calculus to Hopf and Rota-Baxter algebras (with F. Patras), in the series Algebra and Applications 2: Combinatorial Algebra and Hopf Algebras, ISTE Ltd-Wiley 2021. arXiv:1911.08766 90. Cumulant-cumulant relations in free probability theory from Magnus' expansion (with A. Celestino, F. Patras, D. Perales), accepted for publication in Foundations of Computational Mathematics, (online), March 2021, arXiv:2004.10152 89. Generating Series for Networks of Chen-Fliess Series (with W.S. Gray) Systems & Control Letters, 147, (2021), 104827. arXiv:2007.00743 88. Quasi-shuffle algebras in non-commutative stochastic calculus (with F. Patras), in proceedings volume "Geometry and Invariance in Stochastic Dynamics", Springer Proceedings in Mathematics & Statistics Vol. 378, 89-112. arXiv:2004.06945 87. Planarly branched rough paths and rough differential equations on homogeneous spaces (with C. Curry, D. Manchon, H. Munthe-Kaas), Journal of Differential Equations, 269, (2020) 9740-9782. arXiv:1804.08515 86. Time warping invariants of multidimensional time series (with J. Diehl, N. Tapia), Acta Applicandae Mathematicae, 170, (2020) 265-290. arXiv:1906.05823 85. Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations (with L. Foissy, J. Kock, F. Patras), Advances in Mathematics, 369, (2020) 107170. arXiv:1907.01190 84. Iterated-sums signature, quasi-symmetric functions and time series analysis (with J. Diehl, N. Tapia) Proceedings of the 32nd Conference on Formal Power Series and Algebraic Combinatorics FPSAC2020 (paper, poster). 83. The Magnus expansion and Post-Lie algebras (with C. Curry, B. Owren), Mathematics of Computation, 89, (2020) 2785-2799. arXiv:1808.04156 82. Evaluating Generating Functions for Periodic Multiple Polylogarithms (with W. S. Gray, D. Manchon), Periods in Quantum Field Theory and Arithmetic, Springer Proceedings in Mathematics & Statistics Vol. 314, March 2020, arXiv:1603.05948 81. Quasi-shuffle algebras and renormalisation of rough differential equations (with Y. Bruned, C. Curry), Bull. London Math. Soc., 52 (2020) 43-63 (online). arXiv:1801.02964 80. A group-theoretical approach to conditionally free cumulants (with F. Patras), IRMA Lectures in Mathematics and Theoretical Physics Vol. 31, 2020, "Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Vol. 1" (online). arXiv:1806.06287 79. Shuffle group laws. Applications in free probability (with F. Patras), Proc. London Math. Soc.(3) 119 (2019) 814–840 (online), March 2019. arXiv:1704.04942 78. Algebraic Structures and Stochastic Differential Equations driven by Levy processes (with C. Curry, S.J.A. Malham, A. Wiese), Proc. R. Soc. A, 2019, issue 475: 20180567. arXiv:1601.04880 77. Hopf-algebraic deformations of products and Wick polynomials (with F. Patras, N. Tapia, L. Zambotti), International Mathematics Research Notices, 2020, issue 24 (2020), 10064-10099. (online), arXiv:1710.00735 76. Monotone, free, and boolean cumulants: a shuffle algebra approach (with F. Patras), Advances in Mathematics, 328, (2018) 112-132. arXiv:1701.06152 75. On non-commutative stochastic exponentials (with C. Curry, F. Patras), proceedings volume ENUMATH2017 conference, Springer's Lecture Notes in Computational Science and Engineering, volume 126, 2018. 74. What is a post-Lie algebra and why is it useful in geometric integration (with C. Curry, H. Munthe-Kaas), proceedings volume ENUMATH2017 conference, Springer's Lecture Notes in Computational Science and Engineering, volume 126, 2018. arXiv:1712.09415 73. Renormalisation group for multiple zeta values (with D. Manchon, J. Singer, J. Zhao), Communications in Number Theory and Physics, 12, No. 1 (2018), 75-96. arXiv:1511.06720v1 72. Combinatorial Hopf algebra for interconnected nonlinear input-output systems – with a view towards discretization (with L. Duffaut Espinosa, W. S. Gray), proceedings volume of the conference DMGILBS2015, Springer Proceedings in Mathematics & Statistics, vol. 267, Dec. 2018. arXiv:1805.02954 71. Post-Lie Algebras, Factorization Theorems and Isospectral Flows (with I. Mencattini), proceedings volume of the conference DMGILBS2015, Springer Proceedings in Mathematics & Statistics, vol. 267, Dec. 2018. arXiv:1711.02694 70. The Faa di Bruno Hopf algebra for multivariable feedback recursions in the center problem for higher order Abel equations (with W. S. Gray), Springer's Abel Symposia, Vol. 13, 2019. arXiv:1703.05372 69. A comodule-bialgebra structure for word-series substitution and mould composition (with F. Fauvet, D. Manchon), Journal of Algebra, 489, (2017) 552-581. arXiv:1609.03549 68. Post-Lie algebras and factorization theorems (with I. Mencattini, H. Munthe-Kaas), Journal of Geometry and Physics, 119, (2017) 19-33. arXiv:1701.07786 67. Epsilon-noncrossing partitions and cumulants in free probability (with F. Patras, R. Speicher), Int. Math. Res. Notices (2018), 2018, Issue 23, 2018, 7156-7170. arXiv:1612.02671 66. Discrete-Time Approximations of Fliess Operators (with W. S. Gray, L. A. Duffaut Espinosa), Numerische Mathematik (2017) 137:35-62. arXiv:1510.07901v1 65. Sensitivity of the Left Inverse of a SISO Analytic Nonlinear System (with W. S. Gray, L. A. Duffaut Espinosa), The 51st Annual Conference on Information Systems and Sciences (CISS), March 22-24, 2017, Johns Hopkins University, Baltimore, Maryland, USA. 64. On the Performance of Antipode Algorithms for the Multivariable Output Feedback Hopf Algebra (with L. Berlin, W. S. Gray, L. A. Duffaut Espinosa), The 51st Annual Conference on Information Systems and Sciences (CISS), March 22-24, 2017, Johns Hopkins University, Baltimore, Maryland, USA. 63. SISO Output Affine Feedback Transformation Group and Its Faa di Bruno Hopf Algebra (with S. Gray), SIAM Journal on Control and Optimization, 55, No. 2, (2017) 885-912. arXiv:1411.0222 62. Center problem, Abel equation and the Faa di Bruno Hopf algebra for output feedback (with W. S. Gray), IMRN, 2017, Issue 17, (2017), 5415-5450. arXiv:1507.06939 [math.RA] 61. The Hopf algebra of (q)multiple polylogarithms with non-positive arguments (with D. Manchon, J. Singer), IMRN, 2017, Issue 16, (2017) 4882-4922. arXiv:1503.02977 60. Dendriform-Tree Setting for Fully Non-commutative Fliess Operators (with W. S. Gray, L. A. Duffaut Espinosa), IMA Journal of Mathematical Control and Information, 32, (2016) 1-31. (online) 59. Duality and (q-)multiple zeta values (with D. Manchon, J. Singer), Advances in Mathematics, 298, (2016) 254-285. arXiv:1512.00753 58. The combinatorics of Green's functions in planar field theories (with F. Patras), Springer's Frontiers of Physics, 11(6), (2016) 110310. arXiv:1509.08678v1 57. Renormalisation of q-regularised multiple zeta values (with D. Manchon, J. Singer), Letters in Mathematical Physics, 106(3), (2016) 365-380. arXiv:1508.02144v2 56. Post-Lie Algebras and Isospectral Flows (with A. Lundervold, I. Mencattini, H. Z. Munthe-Kaas), SIGMA 11 (2015), 093, 16 pages. arXiv:1505.02436 55. A combinatorial Hopf algebra for nonlinear output feedback control systems (with L. A. Duffaut Espinosa, W. S. Gray), Journal of Algebra 453, (2016) 609-643. arXiv:1406.5396 54. The exponential Lie series for continuous semimartingales (with S.J.A. Malham, F. Patras, A. Wiese), Proc. R. Soc. A: 2015, 471, Issue: 2184. arXiv:1506.07686 53. Flows and stochastic Taylor series in Ito calculus (with S.J.A. Malham, F. Patras, A. Wiese), J. Phys. A: Math. Theor., 48, (2015) 495202. arXiv:1504.07226 52. The splitting process in free probability (with F. Patras), Int. Math. Res. Notices (2016) 2016 (9): 2647-2676. arXiv:1502.02748v1 51. On the Lie enveloping algebra of a post-Lie algebra (with A. Lundervold, H. Munthe-Kaas), Journal of Lie Theory, 25, No. 4, (2015) 1139-1165. arXiv:1410.6350 50. Cumulants, free cumulants and half-shuffles (with F. Patras), Proc. R. Soc. A: 2015, 471, Issue: 2176. arXiv:1409.5664 49. Analytic Left Inversion of Multivariable Lotka-Volterra Models (with W. S. Gray, L. A. Duffaut Espinosa) Proc. 54nd IEEE Conference on Decision and Control, Osaka, Japan, 2015. 48. Analytic Left Inversion of SISO Lotka-Volterra Models (with S. Gray, L. A. Duffaut Espinosa), Proc. 49th Conference on Information Sciences and Systems, Baltimore, Maryland, 2015. 47. Unfolding the double shuffle structure of q-multiple zeta values (with J. Castillo Medina, D. Manchon), Bulletin of the Australian Mathematical Society, 91, issue 03, (2015) 368-388. arXiv:1310.1330 46. On Euler's decomposition formula for qMZVs (with J. Castillo Medina, D. Manchon), The Ramanujan Journal, 37, Issue 2, (2015) 365-389. arXiv:1309.2759 45. Faà di Bruno Hopf algebra of the Output Feedback Group for Multivariable Operators (with L. A. Duffaut Espinosa, W. S. Gray), Systems & Control Letters, 74, (2014) 64-73. arXiv:1406.5378 44. Dendriform-Tree Setting for Fully Non-commutative Fliess Operators (with W. S. Gray, L. A. Duffaut Espinosa), Proc. 53rd IEEE Conference on Decision and Control, Los Angeles, USA, Dec. 15-17, 2014, pp. 4814-4819. 43. Noncommutative Bell polynomials, quasideterminants and incidence Hopf algebras (with A. Lundervold and D. Manchon), International Journal of Algebra and Computation, 24, no 5 (2014), 671-705. arXiv:1402.4761 42. Recursive Algorithm for the Antipode in the SISO Feedback Product (with W. S. Gray, L. A. Duffaut Espinosa), Proc. 21st International Symposium on the Mathematical Theory of Networks and Systems, Groningen, The Netherlands 2014, pp. 1088-1093. 41. The pre-Lie structure of the time-ordered exponential (with F. Patras), Letters in Mathematical Physics, 104, no. 10 (2014), 1281-1302. arXiv:1305.3856 40. Lévy processes and quasi-shuffle algebras (with C. Curry, S. Malham, A. Wiese), Stochastics, 86, (2014), 632-642. arXiv:1311.1683v1 39. La structure combinatoire du calcul intégral (with F. Patras), Gazette des Mathématiciens 138, Oct. 2013, Société Mathématique de France (SMF). English translation: Rota-Baxter Algebra. The Combinatorial Structure of Integral Calculus, arXiv:1304.1204v1 [math.RA]. 38. The Magnus expansion, trees and Knuth's rotation correspondence (with D. Manchon), Foundations of Computational Mathematics, 14, (2014) 1-25. arXiv:1203.2878v1 37. The tridendriform structure of a discrete Magnus expansion (with D. Manchon), AI65 special issue in Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 34, Number 3, (2014), 1021-1040. arXiv:1306.6439v2 [math.CO] 36. Time-ordering and a generalized Magnus expansion (with M. Bauer, R. Chetrite, F. Patras), Letters in Mathematical Physics, 103, (2013), 331-350. arXiv:1206.3990v1 35. On an extension of Knuth's rotation correspondence to reduced planar trees (with D. Manchon), Journal of Noncommutative Geometry, 8, (2014), 303-320. arXiv:1203.0425v1 34. Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes (with F. Patras), J. Math. Phys., 53, (2012) 083505. arXiv:1104.3415v2 33. Algebraic structure of stochastic expansions and efficient simulation (with A. Lundervold, S.J.A. Malham, H. Munthe-Kaas, A. Wiese), Proc. R. Soc. A, August 8, 2012, vol. 468 no. 2144, 2361-2382. arXiv:1112.5571v1 32. Harmonium as a laboratory for mathematical chemistry (with J.M. Gracia-Bondía), Journal of Mathematical Chemistry, 50, (2012), 440-454. 31. Twisted dendriform algebras and the pre-Lie Magnus expansion (with D. Manchon), Journal of Pure and Applied Algebra, 215, (2011), 2615-2627. 30. Two interacting Hopf algebras of trees: A Hopf-algebraic approach to composition and substitution of B-series (with D. Calaque, D. Manchon), Advances in Applied Mathematics,47, (2011) 282-308. 29. Exponential Renormalization (with F. Patras), Annales Henri Poincaré, 11, (2010), 943-971. 28. Dendriform Equations (with D. Manchon), Journal of Algebra, 322, (2009), 4053-4079. 27. Generalized shuffles related to Nijenhuis and TD-algebras (with P. Leroux), Communications in Algebra, 37, (2009), 3064-3094 . 26. A Magnus- and Fer-type formula in dendriform algebras (with D. Manchon), Foundations of Computational Mathematics, 9, (2009), 295-316. 25. A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's counterterm recursion (with D. Manchon and F. Patras), Journal of Noncommutative Geometry, 3, Issue 2 (2009), 181-222. 24. Free Rota-Baxter algebras and rooted trees (with L. Guo), Journal of Algebra and Its Applications, 7, (2008), 167-194. 23. Multiple-zeta-values and Rota-Baxter algebras (with L. Guo), Integers, 8, (2008) (http://www.integers-ejcnt.org/) 22. New identities in dendriform algebras (with D. Manchon and F. Patras), Journal of Algebra, 320, (2008), 708-727. 21. Rota-Baxter Algebras and Dendriform Algebras (with L. Guo), Journal of Pure and Applied Algebra, 212, (2008), 320-339. 20. A Zassenhaus-type algorithm solves the Bogoliubov recursion (with F. Patras), Proceedings of the VII. International workshop Lie Theory and Its Applications in Physics, (Varna, June 2007), eds. H.-D. Doebner and V. K. Dobrev, Heron Press, Sofia, 2008. 19. Rota-Baxter algebras in renormalization of perturbative quantum field theory (with L. Guo), Fields Inst. Communications, 50, (2007), 47-105. 18. Rota-Baxter algebras and new combinatorial identities (with J. M. Gracia-Bondía and F. Patras), Letters in Mathematical Physics, 81, (2007), 61-75. 17. Coherent Unit Actions on Operads and Hopf Algebras (with L. Guo), Theory and Applications of Categories, 18, (2007), 348-371. 16. A Lie theoretic approach to renormalization (with J. M. Gracia-Bondía and F. Patras), Commun. Math. Phys., 276, (2007), 519-549. 15. Hopf algebras in dynamical systems theory (with J. F. Cariñena, H. Figueroa and J. M. Gracia-Bondía), Int. J. of Geom. Meth. in Mod. Physics, 4, (2007), 577-646. 14. The combinatorics of Bogoliubov's recursion in renormalization (with D. Manchon), IRMA Lectures in Mathematics and Theoretical Physics Vol. 15, 2009, "Renormalization and Galois Theories" (online). arXiv:0710.3675 13. On matrix differential equations in the Hopf algebra of renormalization (with D. Manchon), Adv. Theor. Math. Phys., 10, (2006), 879-913. 12. Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion (with L. Guo and D. Manchon), Commun. Math. Phys., 267, (2006), 821-845. 11. Combinatorics of renormalization as matrix calculus (with J. M. Gracia-Bondía, L. Guo and J. C. Varilly), Phys. Lett. B, 632, (2006), 552-558. 10. Quasi-shuffles, Mixable Shuffles, and Hopf Algebras (with L. Guo), Journal of Algebraic Combinatorics, 24, no.1 (2006), 83-101. 9. Hopf algebra approach to Feynman diagram calculations (with D. Kreimer), J. Phys. A: Math. Gen., 38, (2005), R385-R406. 8. On Products and Duality of Binary, Quadratic, Regular Operads (with L. Guo), Journal of Pure and Applied Algebra, 200, (2005), 293-317. 7. Integrable Renormalization II: the General case (with L. Guo and D. Kreimer), Ann. Inst. Henri Poincaré, 6, (2005), 369-395. 6. Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT (with L. Guo and D. Kreimer), J. Phys. A: Math. Gen., 37, (2004), 11037-11052. 5. Integrable Renormalization I: the Ladder case (with L. Guo and D. Kreimer), J. Math. Phys., 45, (2004), 3758-3769. 4. On the associative Nijenhuis Relation, The Electronic Journal of Combinatorics, 11(1), (2004), R38. 3. On the Insertion-Elimination Lie algebra of Feynman graphs (with D. Kreimer and I. Mencattini), Proceedings of the V. International workshop Lie Theory and Its Applications in Physics, (Varna, June 2003), eds. H.-D. Doebner and V. K. Dobrev, World Sci., Singapore, 2004. 2. Loday-type Algebras and the Rota-Baxter Relation, Letters in Mathematical Physics, 61, (2002), 139-147. 1. On the relation between modular theory and geometry, J. Phys. A: Math. Gen., 35, (2002), 6319-6328. Editorial publications
Special Issue on Non-Commutative Algebra, Probability and Analysis in Action. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) . Eds. J. Diehl, KEF, U. Franz, M. Gerhold, N. Tapia. Talks presented at the international conference Noncommutative algebra, probability and analysis in action”, Sept. 20-25, 2021, Alfried Krupp Kolleg, Greifswald, Germany.
Special Issue on Algebraic Structures in Perturbative Quantum Field Theory in honor of Dirk Kreimer for his 60th birthday. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) . Eds. KEF, E. Panzer, K. Yeats. Talks presented at Algebraic Structures in Perturbative Quantum Field Theory”, a conference in honor of Dirk Kreimer’s 60th birthday, Nov. 16-20, 2020, IHES, Bures-sur-Yvette, France. Amplitudes, Hodge Theory and Ramification: From Periods and Motives to Feynman Amplitudes, CMI/AMS Vol. 21, 2020 (AMS bookstore). Eds. KEF, J. Burgos Gil, D. Manchon. Volume 1 of the lectures presented at the Clay Mathematics Institute 2014 Summer School, “Periods and Motives: Feynman amplitudes in the 21st century”, June 30 - July 25, 2014, ICMAT, Madrid. Periods in Quantum Field Theory and Arithmetic, Springer Proceedings in Mathematics & Statistics, vol. 314, 2020. Eds. J. Burgos Gil, KEF, H. Gangl. Proceedings of the ICMAT Research Trimester on "Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory", Sept. 15 - Dec. 19, 2014., Madrid, Spain. Computation and Combinatorics in Dynamics, Stochastics and Control, Abel Symposia, Springer, Jan. 2019. Eds. E. Celledoni, G. Di Nunno, KEF, H. Munthe-Kaas. Proceedings of the Abel Symposium 2016, Aug. 16-19, 2016, Barony Rosendal, Norway. Discrete Mechanics, Geometric Integration and Lie–Butcher Series, Springer Proceedings in Mathematics & Statistics, vol. 267, 2018. Eds. KEF, M. Barbero Liñan. Proceedings of the Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid. Feynman Amplitudes, Periods and Motives, Contemporary Mathematics, vol. 648 , American Mathematical Society (AMS), 2015. Eds. L. Alvarez-Consul, J. Burgos Gil, KEF. Proceedings of the workshop Periods and Motives - A Modern Perspective on Renormalization, July 2-6, 2012, ICMAT, Spain.. Faà di Bruno Hopf Algebras, Dyson-Schwinger Equations, and Lie-Butcher Series, European Mathematical Society, IRMA Lectures in Mathematics and Theoretical Physics, Volume: 21, 2015. Eds. KEF, F. Fauvet. Proceedings of the conference "Dyson-Schwinger Equations and Faà di Bruno Hopf Algebras in Physics and Combinatorics", June 27 – July 1, 2011, IRMA, Strasbourg, France. Special issue: Selected papers based on the presentations at the commemorative colloquium dedicated to Nikolai Neumaier (June 16-18, 2011), Travaux Mathématiques 20. Univ. of Luxembourg, Faculty of Science, Technology and Communication, 2012. Eds. M. Bordemann, KEF, A. Makhlouf, M. Schlichenmaier, S. Waldmann. LMIA, Université de Haute-Alsace, Mulhouse, France. Combinatorics and Physics, Contemporary Mathematics, vol. 539, American Mathematical Society (AMS), 2011. Eds. KEF, M. Marcolli, W. D. van Suijlekom. Proceedings of the mini-workshop "Renormalization", held in December 2006, and the conference "Combinatorics and Physics", held in March 2007. Both meetings took place at the Max-Planck-Institut für Mathematik in Bonn, Germany. Other publications Towards Lie-Butcher Theory for geodesic flows (with H. Munthe-Kaas, D. Manchon),
Oberwolfach Workshop Numerical Geometric Integration, March 28 - April 3, 2021, Oberwolfach Report 2021 no. 17 Generalized iterated-sums signatures (with J. Diehl, N. Tapia),
Oberwolfach Workshop New Directions in Rough Path Theory, Dec. 2020, Oberwolfach Report 2020 no. 40 Shuffle groups in free probability (with F. Patras),
Oberwolfach Workshop Free Probability Theory, Dec. 2018, Oberwolfach Report 2018 no. 53 Pre-publications (arXiv) Algebraic groups in non-commutative probability theory revisited (with I. Chevyrev, F. Patras) August 2022, arXiv:2208.02585 Graph counting signatures and bicommutative Hopf algebras (with D. Caudillo, J. Diehl, E. Verri) June 2022, arXiv:2206.08323 Algebraic aspects of connections: from torsion, curvature, and post-Lie algebras to Gavrilov's double exponential and special polynomials (with M. J. H. Al-Kaabi, D. Manchon, H. Z. Munthe-Kaas) May 2022, arXiv:2205.04381 Shifted substitution in non-commutative multivariate power series with a view toward free probability (with F. Patras, N. Tapia, L. Zambotti) April 2022, arXiv:2204.01445 Multiplicative and semi-multiplicative functions on non-crossing partitions, and relations to cumulants (with A. Celestino, A. Nica, D. Perales, L. Witzman) June 2021, arXiv:2106.16072 On the twisted factorization of the T-transform (with N. Gilliers) May 2021, arXiv:2105.096397 Generalized iterated-sums signatures (with J. Diehl, N. Tapia) Dec. 2020, arXiv:2012.04597 Bogoliubov type recursions for renormalisation in regularity structures (with Y. Bruned) June 2020, arXiv:2006.05284 Unpublished work:
Transfer group for renormalized multiple zeta values (with D. Manchon, J. Singer, J. Zhao),
Oct. 2015, arXiv:1510.09159v1 (abbreviated version of 1511.06720v1) Matrix Representation of Renormalization in Perturbative Quantum Field Theory (with L. Guo), August 2005, arXiv:0508155v1 Last updated: 13/08/2022 |