Department of Mathematical Sciences
Norwegian University of Science and Technology
Tel.: +47 735 935-27 (office)
kurusch.ebrahimi-fard -at- ntnu.no
I am a member of the Differential Equations and Numerical Analysis (DNA) group at IMF-NTNU.
|• Research interests
• Biographical Review
• Activities 2018
• Past activities 2017; 2016; 2015; 2014; 2013; 2012; 2011; 2010; 2009; 2008; 2007; 2006
• Visits, talks and conferences
• News: BFS-TFS project "Pure Mathematics in Norway"
• Thematic one-month program "New Developments in Free Probability and Applications", (March 2019) CRM, Montréal, Canada. Workshop "Free Probability: the theory, its extension", March 4-8, 2019.
• Isaac Newton Institute programme "Geometry, compatibility and structure preservation in computational differential equations", Tutorial workshop, July 8-12, 2019, Cambridge, UK.
is no branch of mathematics, however abstract, which may not someday be
applied to phenomena of the real world" Nikolai
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
MathSciNet: Ebrahimi-Fard, Kurusch
Biographical Review: I was born in Germany, where 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 - 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 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).
"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 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.
• 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.
• "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)
• 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.
• "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.
• 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.
• 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.
• 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.
• 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.
• 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.
• School and Conference "Algebraic and Combinatorial Structures in Quantum Field Theory", March 23 – April 3, 2009, Institut d'Études Scientifiques de Cargèse, Corsica, France
• International~School-Conference "Hopf-in-Lux", Univ.~of Luxembourg, July 13-17, 2009, Luxembourg.
• Conference "Combinatorics and Physics", Poster, March 19-23, 2007, Max-Planck-Institut für Mathematik in Bonn, Germany.
• Mini-workshop "Renormalization", Poster, Dec. 15-16, 2006, Max-Planck-Institut für Mathematik in Bonn, Germany.___________________________________________
Visits, talks and conferences
• Univ. of Bergen, Department of Mathematics, Norway, January 11-31 + April 5-30, 2015.
• Univ. de Nice - Sophia Antipolis, Laboratoire J.-A. Dieudonné, Nice, France, June 3-20, 2015.
• Old Dominion Univ., Electrical & Computer Engineering, Norfolk, VA, USA, June 25 - July 11, 2015.
• Chern Institute of Mathematics, Nankai University, Tianjin 300071 China, August 3-5, 2015.
• City Univ. of Hong Kong, Department of Mathematics, Kowloon Tong, Hong Kong, August 17-19, 2015.
• Instituto de Ciências Matemáticas e de Computação da Univ. de São Paulo, São Carlos, Brazil, August 24 - Sept. 24, 2015.
• Computer Science and Artificial Intelligence Department, Univ. of the Basque Country, San Sebastian, Sept. 28 - Oct. 2, 2015.
• Univ. de Costa Rica, Escuela de Matematica, San Jose, Costa Rica.
Colloquium: "The Algebra of the Feedback Loop in Nonlinear Control Theory", August 14, 2014.
• 2014 European Mathematics Representatives Meeting, Academy of Finland, Helsinki, Finland, May 8-9, 2014.
• Scuola Internazionale Superiore di Studi Avanzati/International School for Advanced Studies (S.I.S.S.A.), Mathematical Physics sector, Non-commutative geometry seminar, Jan. 12-24, 2013, Trieste, Italy.
• Imperial College London, Department of Mathematics, Feb. 28 - March 5, 2013, London, UK.
• Univ. of Pennsylvania, Department of Mathematics, March 5-7, 2013, Philadelphia, USA.
• Univ. of Wisconsin-Madison, Department of Mathematics, March 10-16, 2013, Madison, USA.
• Kyoto Univ., Department of Mathematics, March 24-30, 2013, Kyoto, Japan.
• ADFA , Canberra, Australia.
• Heriot-Watt Univ., Edinburgh, Scotland.
• Univ. de Nice - Sophia Antipolis, Laboratoire J.-A. Dieudonné, Nice, France.
• Univ. de Zaragoza, Instituto Universitario de Matemáticas y Aplicaciones (IUMA), June 12-14, 2013, Zaragoza, Spain.
Title: "Time-ordered exponentials and pre-Lie algebras", June 14, Seminario de Álgebra.
• Univ. de La Laguna, Departamento de Matemática Fundamental, July 17-31, 2013, La Laguna, Tenerife, Spain.
Title: "Time-ordered exponentials and pre-Lie algebras", July 23, Seminario de Geometría y Topología.
• Heriot-Watt Univ., Edinburgh, Scotland, August 18-24, 2013.
• Univ. Blaise Pascal, Laboratoire de Mathématiques, Clermont-Ferrand, France, Sept. 9-13, 2013.
• Univ. Paris 13, Institut Galilée, journee spéciale "Trees and graphs (from algebraic combinatorics to topology and random tensor models)", Villetaneuse, France, Sept. 24, 2013.
• Visit to CEREMADE, Univ. Paris Dauphine, Jan. 9-13, 2012, Paris, France.___________________________________________
• Visit to Univ. Blaise Pascal, Feb. 27 - March 4, 2012, Clermont-Ferrand, France.
• Workshop "Mathematical Aspects of Quantum Mechanics and Quantum Transport Theory", ZiF Research Group Quantumscience. Convenors: J. Froehlich, Ph. Blanchard, April 23-28, 2012, Bielfeld, Germany.
• Seminar talk Combinatorial Hopf Algebras and Applications, at Univ. de Almería, Algebra and Analysis Dept., May 2012.
• Visit to IMAC (Univ. Jaume I, Castellón), "Special Session on Algebraic Structures in the Numerical Analysis of Differential Equations" (Org.: F. Casas), May 31, 2012.
Talk: "The Magnus expansion, trees, and Knuth's rotation correspondence".
• 1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Liège, Belgium, June 6-8, 2012. Program - Algebra Session.
• Groupe de travail Calcul moulien et algèbres de Hopf combinatoire June 18-22, 2012, Besse, France.
• 6th International Summer School on Geometry, Mechanics, and Control (ICMAT school), June 22-26, 2012, La Cristalera, Miraflores de la Sierra, Spain.
• Visit to Heriot-Watt Univ., July 16-27, 2012, Edinburgh, Scotland.
• Escuela de Matematica, Univ. de Costa Rica, August 10-21, 2012, San Jose, Costa Rica.
Mini-course: Algebraic structures in stochastic expansions (Estructuras algebraicas de desarrollos estocásticos).
• Conference on Renormalization at the confluence of analysis, algebra and geometry. September 17-21, 2012 at the CIRM, Luminy (Marseille, France).
• Visit to Univ. of Sevilla, Faculty of Mathematics, Algebra Deptartment. October 22-23, 2012, Sevilla, Spain.
Talk: "From Magnus' expansion to Butcher's B-series".
• Meeting on Algebra and Numerical Analysis, Department of Mathematical Sciences, The Norwegian Univ. of Science and Technology, Trondheim, Norway, December 6-13, 2012.
78. Algebraic Structures and Stochastic Differential Equations driven by Levy processes (with C. Curry, S. J.A. Malham, A. Wiese),
accepted for publication in Proc. R. Soc. A, Dec. 2018. arXiv:1601.04880
77. Hopf-algebraic deformations of products and Wick polynomials (with F. Patras, N. Tapia, L. Zambotti),
accepted for publication in IMRN (online), Oct. 2018. 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),
accepted for publication in Springer's Abel Symposia. 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 (conference publication 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 (conference publication 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 (conference publication 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 (conference publication 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 (conference publication 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 (conference publication 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 in 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 (conference publication 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 (conference publication with D. Manchon),
European Mathematical Society, IRMA Lectures in Mathematics & Theoretical Physics, CIRM 2006 workshop "Renormalization and Galois Theory", Orgs. F. Fauvet, J.-P. Ramis.
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 (conference publication 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.
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, August 16-19, 2016, Barony Rosendal, Norway.
Discrete Mechanics, Geometric Integration and Lie–Butcher Series, Springer Proceedings in Mathematics & Statistics, vol. 267, Dec. 2018. Eds. KEF, M. Barbero Liñan. Proceedings of the Brainstorming Workshop on New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", ICMAT, Madrid May 25-28, 2015.
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.
Shuffle groups in free probability (with F. Patras),
Oberwolfach Workshop Free Probability Theory, Dec. 2018, Oberwolfach Report no. 53
The Magnus expansion and Post-Lie algebras (with C. Curry and B. Owren),
August 2018, arXiv:1808.04156
A group-theoretical approach to conditionally free cumulants (with F. Patras),
June 2018, arXiv:1806.06287
Planarly branched rough paths and rough differential equations on homogeneous spaces (C. Curry, D. Manchon, H. Munthe-Kaas),
April 2018, arXiv:1804.08515
Quasi-shuffle algebras and renormalisation of rough differential equations (with Y. Bruned, C. Curry),
Jan. 2018, arXiv:1801.02964
Shuffle group laws. Applications in free probability (with F. Patras)
April 2017, arXiv:1704.04942
Evaluating Generating Functions for Periodic Multiple Polylogarithms (with W. S. Gray, D. Manchon),
March 2016, arXiv:1603.05948
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:hep-th/0508155v1
Last updated: 04/02/2019