ICMAT Member
- Data
Institution: Consejo Superior de Investigaciones Científicas
Position: Ramón y Cajal
Office: 416 Phone: 796
E-mail: kurusch()icmat.es
Theory Department, Physics Inst., Univ. Bonn, Germany
- Personal webpage
- http://www.icmat.es/kurusch
- 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.
Recent and upcoming events:
Congreso de la Real Sociedad de Matemática Española (RSME’11), February 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).Upcoming events in 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*), October 8-12, 2012, Trento, Italy. Orgs.: KEF, F. Patras, C. Roberts.
Visits, Talks and Conferences
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.
1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Liège, Belgium, June 6-8, 2012. Program - Algebra Session.
- Publications
arXiv.org / SPIRES / MathSciNet
29. Algebraic structure of stochastic expansions and efficient simulation (with A. Lundervold, S.J.A. Malham, H. Munthe-Kaas, A. Wiese), accepted for publication in Proceedings of the Royal Society A. arXiv:1112.5571v1 [math.NA]
28. Harmonium as a laboratory for mathematical chemistry (with J.M. Gracia-Bondía), Journal of Mathematical Chemistry, 50, (2012), 440-454.
27. Twisted dendriform algebras and the pre-Lie Magnus expansion (with D. Manchon), Journal of Pure and Applied Algebra, 215, (2011), 2615-2627.
26. Exponential Renormalization (with F. Patras), Annales Henri Poincaré, 11, (2011), 943-971.
25. Two interacting Hopf algebras of trees (with D. Calaque and D. Manchon), Advances in Applied Mathematics, 47, (2011) 282-308.
24. Dendriform Equations (with D. Manchon), Journal of Algebra, 322, (2009), 4053-4079.
23. Generalized shuffles related to Nijenhuis and TD-algebras (with P. Leroux), Communications in Algebra, 37, (2009), 3064-3094 .
22. A Magnus- and Fer-type formula in dendriform algebras (with D. Manchon), Foundations of Computational Mathematics, 9, (2009), 295-316.
21. 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.
20. Free Rota-Baxter algebras and rooted trees (with L. Guo), Journal of Algebra and Its Applications, 7, (2008), 167-194.
19. Multiple-zeta-values and Rota-Baxter algebras (with L. Guo), Integers, 8, (2008) (http://www.integers-ejcnt.org/)
18. New identities in dendriform algebras (with D. Manchon and F. Patras), Journal of Algebra, 320, (2008), 708-727.
17. Rota-Baxter Algebras and Dendriform Algebras (with L. Guo), Journal of Pure and Applied Algebra, 212, (2008), 320-339.
16. Rota-Baxter algebras and new combinatorial identities (with J. M. Gracia-Bondía and F. Patras), Letters in Mathematical Physics, 81, (2007), 61-75.
15. Coherent Unit Actions on Operads and Hopf Algebras (with L. Guo), Theory and Applications of Categories, 18, (2007), 348-371.
14. A Lie theoretic approach to renormalization (with J. M. Gracia-Bondía and F. Patras), Commun. Math. Phys., 276, (2007), 821-845.
13. 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.
12. On matrix differential equations in the Hopf algebra of renormalization (with D. Manchon), Adv. Theor. Math. Phys., 10, (2006), 879-913.
11. Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion (with L. Guo and D. Manchon), Commun. Math. Phys., 267, (2006), 821-845.
10. Combinatorics of renormalization as matrix calculus (with J. M. Gracia-Bondía, L. Guo and J. C. Varilly), Phys. Lett. B, 632, (2006), 552-558.
9. Quasi-shuffles, Mixable Shuffles, and Hopf Algebras (with L. Guo), Journal of Algebraic Combinatorics, 24, no.1 (2006), 83-101.
8. Hopf algebra approach to Feynman diagram calculations (with D. Kreimer), J. Phys. A: Math. Gen., 38, (2005), R385-R406.
7. On Products and Duality of Binary, Quadratic, Regular Operads (with L. Guo), Journal of Pure and Applied Algebra, 200, (2005), 293-317.
6. Integrable Renormalization II: the General case (with L. Guo and D. Kreimer), Ann. Inst. Henri Poincaré, 6, (2005), 369-395.
5. 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.
4. Integrable Renormalization I: the Ladder case (with L. Guo and D. Kreimer), J. Math. Phys., 45, (2004), 3758-3769.
3. On the associative Nijenhuis Relation, The Electronic Journal of Combinatorics, 11(1), (2004), R38.
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.
Publications in peer-reviewed conference proceedings and book contributions:
5. 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.
4. The Spitzer Identity (with L. Guo), to appear in Encyclopaedia of Mathematics, Springer, M. Hazewinkel ed.
3. 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.
2. Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory (with L. Guo), Fields Institute Communications, 50, (2007), 47-105.
1. 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.
Editorial-publications:
Combinatorics and Physics, Contemporary Mathematics 539, American Mathematical Society, 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.
Pre-publications:
The Magnus expansion, trees and Knuth's rotation correspondence (with D. Manchon), March 2012. arXiv:1203.2878v1 [math.CO]
On an extension of Knuth's rotation correspondence to reduced planar trees (with D. Manchon), March 2012. arXiv:1203.0425v1 [math.CO]
Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes (with F. Patras), April 2011. arXiv:1104.3415v1 [math-ph]
Unpublished work:
Matrix Representation of Renormalization in Perturbative Quantum Field Theory (with L. Guo), August 2005. arXiv:hep-th/0508155v1
