#### Research Interest

I am motivated by the belief that innovative mathematical reasoning may lead to new insights and applications in many areas of science. I am interested in algebraic and combinatorial structures in applied mathematics and theoretical physics. More precisely, I am studying applications of combinatorial Hopf algebras, pre-Lie algebras, and Rota-Baxter algebras to control theory, numerical analysis and quantum field theory. The goal is to develop new mathematical models and methods to facilitate work in these fields. Paramount is the use of advanced combinatorial and algebraic techniques, as they allow for greater transparency, eventually leading to insights and more information. I am also interested in various aspects of the theory of dynamical systems as well as algebro-combinatorial structures in the theory of multiple-zeta-values.

**Keywords**: Rota-Baxter algebras; combinatorial Hopf algebras; Lie and pre-Lie algebras, numerical integration methods; control theory; theory of noncommutative symmetric functions; Spitzer type identities; Baker-Campbell-Hausdorff formula; Magnus and Fer expansions; perturbative quantum field theory; renormalization theory; dynamical systems theory; algebraic structure of multiple zeta values; theory of operads.

• I am co-organizing the joint UAM-ICMAT Seminar "ALGEBRA AND COMBINATORICS"

• I am also co-organizing the joint UC3M-ICMAT Seminar "Applied Probability and Statistics"

• I am affiliated with the Mathematics department of Univ. Carlos III de Madrid.

• We are running the study group "Multiple Zeta Values - Geometric and Algebraic Structures" here at ICMAT; Luis Alvarez-Consul, Jose Burgos, KEF, Marina Logares. **Currently**, we have the MZV Trimester Research Seminar at ICMAT.

• I am part of the research project Discrete Mechanics, Geometric Integration and Lie-Butcher Series, supported by a grant from the Nils-Abel Mobility Project (2014-2015).

• 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.

** Upcoming events**:

ICMAT mini-course **Lie Group Integrators** (16hrs), María Barbero, KEF, David Martín de Diego & Hans Munthe-Kaas (Bergen, Norway), Summer 2016, ICMAT, Madrid, Spain.

**2016**:

• Abel Symposium 2016 "Computation and Combinatorics in Dynamics, Stochastics and Control", 16-19 August 2016, Barony Rosendal, Norway.

• Trends in Computational Mathematics, City University of Hong Kong, 18-20 January 2016, Hong Kong.

• Mathematical Perspectives in Biology, ICMAT, 3-5 February 2016, Madrid, Spain.

• Paths to, from and in renormalisation, 8-12 February 2016, UniversitÃ¤t Potsdam - Institut fÃ¼r Mathematik, Potsdam, Germany.

• UniversitÃ© de Nice Sophia-Antipolis, Laboratoire J.A.DieudonnÃ©, Parc Valrose, Nice, France, February - March, 2016.

• UniversitÃ¤t des Saarlandes, Fachrichtung Mathematik, "Research group in Free Probability", SaarbrÃ¼cken, Germany, March, 2016.

• Universidad de La Rioja, "Departamento de MatemÃ¡ticas y ComputaciÃ³n", LogroÃ±o, Spain, April 2016.

• European Research Centres on Mathematics (ERCOM) meeting, Euler International Mathematical Institute, St.Petersburg, Russia, April 15-16, 2016.

• Mathematics Department, The University of Warwick, Probability seminar, June 20-23, 2016, Warwick, UK.

• Escuela JAE de MatemÃ¡ticas 2016, ICMAT, Madrid, Spain. June 27 - July 15, 2016. POSTER

• Humboldt-UniversitÃ¤t zu Berlin, Mathematical Physics, research seminar, July 10-13, 2016, Berlin, Germany.

• Laboratoire de ProbabilitÃ©s et ModÃ¨les AlÃ©atoires (LPMA), UniversitÃ© Pierre et Marie Curie Paris, Paris, France, July 18-22, 2016.

• Computer Science and Artificial Intelligence Department, University 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.

**Activities 2015**

• Workshop on Hopf Algebras of Posets, January 15-16, 2015, Laboratoire 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), 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.

• New interactions of Combinatorics and Probability, August 24 - September 4, **2015**, Instituto de Ciências Matemáticas e de Computação (ICMC) Universidade de São Paulo, Brazil.

• 54th IEEE Conference on Decision and Control, December 15-18, 2015, Osaka, Japan. Session: Algebraic and Geometric Methods I

**Activities 2014**

• ICMAT Research Trimester on "Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory", Sept. 15 - Dec. 19, 2014. Orgs.: José I. Burgos Gil, KEF, Herbert Gangl, Ulf Kühn, Dominique Manchon.

**•** 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* at ICMAT, Madrid, Spain. Org. by: J.I. Burgos Gil, KEF, D. Ellwood, D. Manchon, J. Rué Perna, N. Woodhouse. June 30 - July 25, 2014.

• Homotopical Algebra Summer Days, Univ. de Barcelona, Spain, July 14+15, 2014.

• Department of Mathematical Sciences, The Norwegian University 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.

**Activities 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: "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.

**Activities 2012**

• ICMAT workshop "Periods and Motives, A Modern Perspective on Renormalization", July 2-6, 2012, Madrid, Spain. Orgs.: L. Álvarez-Cónsul, J. Burgos, KEF, D. A. Ellwood, D. Manchon, S.Weinzierl.

• Workshop "**Mathematical Aspects of Hadron Physics"** at the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Oct. 8-12, 2012, Trento, Italy. Orgs.: KEF, F. Patras, C. Roberts.

• ICMAT workshop "Stochastic Systems Simulation and Control" (SSSC2012), Nov. 5-9, 2012, Madrid, Spain. Orgs.: M. Barbero Linan, KEF, S. Gray, M. Kawski, S. Malham, H. Munthe-Kaas, A. Wiese.

• Workshop "Algebraic Combinatorics and Numerical Analysis", 6-12th Dec. 2012, Institutt for matematiske fag, Norges teknisk-naturvitenskapelige universitet (NTNU) , Trondheim, Norway. Orgs.: Elena Celledoni, Brynjulf Owren.

• 7th International Young Researchers Workshop on Geometry, Mechanics and Control, Dec. 17-19, 2012, ICMAT, Madrid, Spain.

**Activities 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, 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, University 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 Universitat Politècnica de Catalunya (Sept. 20-22, 2011, Barcelona), and ICMAT-Instituto de Ciencias Matemáticas (Sept. 27-29, 2011, Madrid). Orgs.: KEF (ICMAT, Madrid), Miguel Rodriguez-Olmos (UPC, Barcelona).

• **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. Org. KEF (ICMAT, Madrid).

**Activities 2010
**

• Research Trimester "Combinatorics and Control" (COCO2010), April-June 2010, CSIC, Madrid, Spain.

**Visits, Talks and Conferences**

**2015**

• Univ. of Bergen, Department of Mathematics, Norway, January 11-31 + April 5-30, 2015.

• Université 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 University of Hong Kong, Department of Mathematics, Kowloon Tong, Hong Kong, August 17-19, 2015.

• Instituto de CiÃªncias MatemÃ¡ticas e de ComputaÃ§Ã£o da Universidade de SÃ£o Paulo, SÃ£o Carlos, Brazil, August 24 - Sept. 24, 2015.

• Computer Science and Artificial Intelligence Department, University of the Basque Country, San Sebastian, Sept. 28 - Oct. 2, 2015.

**2014**

• 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.

**2013**

• 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 University, Department of Mathematics, March 24-30, 2013, Kyoto, Japan.

• ADFA , Canberra, Australia.

• Heriot-Watt University, Edinburgh, Scotland.

• Université de Nice - Sophia Antipolis, Laboratoire J.-A. Dieudonné, Nice, France.

• Universidad 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.

• Universidad 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 University, Edinburgh, Scotland, August 18-24, 2013.

• Université Blaise Pascal, Laboratoire de Mathématiques, Clermont-Ferrand, France, Sept. 9-13, 2013.

• Université Paris 13, Institut Galilée, journee spéciale "Trees and graphs (from algebraic combinatorics to topology and random tensor models)", Villetaneuse, France, Sept. 24, 2013.

**2012**

• 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 University, July 16-27, 2012, Edinburgh, Scotland.

• Mini-course: *Algebraic structures in stochastic expansions* (Estructuras algebraicas de desarrollos estocásticos), August 10-21, 2012, Escuela de Matematica, Universidad de Costa Rica, San Jose, Costa Rica.

• 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 University of Science and Technology, Trondheim, Norway, December 6-13, 2012.

#### Publications

**arXiv.org** / **SPIRES** / **MathSciNet**

62.* Dendriform-Tree Setting for Fully Non-commutative Fliess Operators* (with W. S. Gray, L. A. Duffaut Espinosa), accepted for publication in IMA Journal of Mathematical Control and Information.

61.* Center problem, Abel equation and the Faa di Bruno Hopf algebra for output feedback* (with W. S. Gray), accepted for publication in IMRN, July 2016, arXiv:1507.06939 [math.RA]

60.* The Hopf algebra of (q)multiple polylogarithms with non-positive arguments* (with D. Manchon, J. Singer), IMRN online, May 2016, arXiv:1503.02977

59.* Duality and (q-)multiple zeta values* (with D. Manchon, J. Singer), Advances in Mathematics, **298** (2016) 254-285 online. arXiv:1512.00753

58.* The combinatorics of Green's functions in planar field theories* (with F. Patras), Springer's Frontiers of Physics, 11(6), 110310 (2016). arXiv:1509.08678v1 [math-ph]

57.* Renormalisation of q-regularised multiple zeta values* (with D. Manchon, J. Singer), Letters in Mathematical Physics, **106**(3), 365-380, 2016 (online). 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 [math.RA]

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 [math.CO]

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 [math.PR]

53.* Flows and stochastic Taylor series in Ito calculus* (with S.J.A. Malham, F. Patras, A. Wiese), J. Phys. A: Math. Theor. **48** 495202 (2015). arXiv:1504.07226 [math.PR]

52.* The splitting process in free probability* (with F. Patras), Int Math Res Notices (2016) 2016 (9): 2647-2676, IMRN online. arXiv:1502.02748v1 [math.CO].

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 [math.CO].

50. *Cumulants, free cumulants and half-shuffles* (with F. Patras), Proc. R. Soc. A: 2015, **471**, Issue: 2176. arXiv:1409.5664 [math.CO].

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 [math.NT].

46. *On Euler's decomposition formula for qMZVs* (with J. Castillo Medina, D. Manchon), The Ramanujan Journal, **37**, Issue 2, (2015) 365-389 (online first), November 2014, arXiv:1309.2759 [math.NT].

45. *Faa 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 [math.OC].

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 [math.CO]

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 [math.RA]

40. *Lévy processes and quasi-shuffle algebras* (with C. Curry, S. Malham, A. Wiese), Stochastics, **86**, (2014), 632-642. arXiv:1311.1683v1 [math.PR]

39. *La structure combinatoire du calcul intégral* (with F. Patras), February 2013, 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 [math.CO]

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. Online LMP. arXiv:1206.3990v1 [math-ph]

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 [math.CO]

34. *Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes* (with F. Patras), J. Math. Phys., **53**, 083505 (2012) Online. arXiv:1104.3415v2 [math-ph]

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 Online. arXiv:1112.5571v1 [math.NA]

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), 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* (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__:

**Combinatorics and Physics**, Contemporary Mathematics Vol. **539**, American Mathematical Society (AMS), 2011. Eds. KEF, M. Marcolli and 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.

**Special issue: Selected papers based on the presentations at the commemorative colloquium dedicated to Nikolai Neumaier**, 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, June 16-18, 2011.

**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 (Strasbourg, France). 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.

**Feynman Amplitudes, Periods and Motives**, Contemporary Mathematics Vol. **648** , American Mathematical Society (AMS), 2015. Eds. L. Alvarez-Consul (ICMAT-CSIC), J. Burgos Gil (ICMAT-CSIC), KEF. Proceedings of the workshop Periods and Motives - A Modern Perspective on Renormalization, July 2-6, 2012, ICMAT, Spain.

__Pre-publications__:

*A comodule-bialgebra structure for word-series substitution and mould composition*
(with F. Fauvet, D. Manchon), Sept. 2016, arXiv:1609.03549 [math.CO]

*Post-Lie Algebras, R-Matrices and Factorization theorems* (with I. Mencattini, H. Munthe-Kaas), Sept. 2016, submitted.

*Evaluating Generating Functions for Periodic Multiple Polylogarithms*
(with W. S. Gray, D. Manchon), March 2016, arXiv:1603.05948 [math.NT]

*Algebraic Structures and Stochastic Differential Equations driven by Levy processes* (with C. Curry, S. J.A. Malham, A. Wiese), Jan. 2016, arXiv:1601.04880 [math.PR]

*Renormalisation group for multiple zeta values* (with D. Manchon, J. Singer, J. Zhao), Nov. 2015, arXiv:1511.06720v1

*Transfer group for renormalized multiple zeta values* (with D. Manchon, J. Singer, J. Zhao), Oct. 2015, arXiv:1510.09159v1 (abbreviated version of 1511.06720v1)

*Discrete-Time Approximations of Fliess Operators* (with W. S. Gray, L. A. Duffaut Espinosa), Oct. 2015, under revision arXiv:1510.07901v1

*Affine SISO Feedback Transformation Group and Its Faà di Bruno Hopf Algebra* (with S. Gray), November 2014, arXiv:1411.0222 [math.OC]

__Unpublished work__:

*Matrix Representation of Renormalization in Perturbative Quantum Field Theory* (with L. Guo), August 2005. arXiv:hep-th/0508155v1