photo

Robert Marsh

Teaching:

Research interests

Cluster algebras, Representation theory of finite dimensional algebras, Homological algebra, Tilting theory, Quantum groups, Algebraic groups, Lie algebras, Coxeter groups.

Fast Breaking Comments: an interview with Thomson Scientific on the article Tilting theory and cluster combinatorics (joint with A. Buan, M. Reineke, I. Reiten and G. Todorov; see published article (8) below).

Preprints

List of publications

    List of publications on MathSciNet (subscription required).

  1. A. B. Buan, R. J. Marsh and I. Reiten. Denominators of cluster variables.
    Journal of the London Mathematical Society 2009; doi: 10.1112/jlms/jdn082. Published article (free reprint).
  2. K. Baur and R. J. Marsh. Frieze patterns for punctured discs.
    Journal of Algebraic Combinatorics 30, Issue 3 (2009), Pages 349-379, doi: 10.1007/s10801-008-0161-0. Preprint. Published article.
  3. K. Baur and R. J. Marsh. A geometric description of m-cluster categories.
    Trans. Amer. Math. Soc. 360 (2008), 5789-5803. Preprint. Published article.
  4. A. B. Buan, R. J. Marsh and I. Reiten. Cluster mutation via quiver representations.
    Commentarii Mathematici Helvetici 83 Issue 1 (2008), 143-177. Preprint. Published article.
  5. K. Baur and R. J. Marsh. A geometric description of the m-cluster categories of type D_n.
    International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm011, 19 pages, doi:10.1093/imrn/rnm011. Preprint. Published article.
  6. A. B. Buan, R. J. Marsh, I. Reiten and G. Todorov. Clusters and seeds in acyclic cluster algebras.
    Includes appendix co-authored in addition with P. Caldero and B. Keller.
    Proc. Amer. Math. Soc. 135, No. 10 (2007), 3049-3060. Preprint. Published article.
  7. A. B. Buan, R. J. Marsh and I. Reiten. Cluster-tilted algebras.
    Trans. Amer. Math. Soc. 359, No. 1 (2007), 323-332. Preprint. Published article.
  8. A. B. Buan, R. J. Marsh and I. Reiten. Cluster-tilted algebras of finite representation type.
    Journal of Algebra 306, No. 2, (2006), 412-431. Preprint. Published article.
  9. A. B. Buan and R. J. Marsh. Cluster-tilting theory.
    Pages 1-30 in Trends in Representation Theory of Algebras and Related Topics, Workshop August 11-14, 2004, Queretaro, Mexico. Editors J. A. de la Pena and R. Bautista, Contemporary Mathematics 406 (2006), 1-30. Preprint.
  10. A. B. Buan, R. J. Marsh, M. Reineke, I. Reiten and G. Todorov. Tilting theory and cluster combinatorics.
    Adv. Math. 204 (2006), 572-618. Preprint. Published article.
  11. P. Caldero, R. J. Marsh and S. Morier-Genoud. Realisation of Lusztig cones.
    Representation Theory 8 (2004), 458-478. Preprint. Published article.
  12. R. J. Marsh and K. Rietsch. Parametrizations of flag varieties.
    Representation Theory 8 (2004), 212-242. Preprint. Published article.
  13. P. Caldero and R. J. Marsh. A multiplicative property of quantum flag minors II.
    Journal of the L.M.S. 69 no.3 (2004), 608-622. Preprint. Published article.
  14. R. J. Marsh and M. Reineke. Canonical basis linearity regions arising from quiver representations.
    J. Algebra 270 no.2 (2003), 696-727. Preprint. Published article.
  15. R. J. Marsh, M. Reineke and A. Zelevinsky. Generalized associahedra via quiver representations.
    Trans. Amer. Math. Soc. 355 no.10 (2003), 4171-4186. Preprint. Published article.
  16. R. J. Marsh and K. Rietsch. The intersection of opposed big cells in the real flag variety of type G_2.
    Proc L.M.S 85 no.1 (2002), 22-42. Preprint. Published article.
  17. R. W. Carter and R. J. Marsh. Regions of linearity, Lusztig cones and canonical basis elements for the quantized enveloping algebra of type A_4.
    J. Algebra 234 no.2 (2000), 545-603. Preprint. Published article.
  18. R. W. Carter and R. J. Marsh. Canonical bases and piecewise-linear combinatorics.
    Pages 33-47 in Quantum Groups and Lie Theory, edited by Andre w Pressley, LMS Lecture Note Series 290, C.U.P., 2001. Preprint.
  19. R. J. Marsh. Rectangle diagrams for the Lusztig cones of quantized enveloping algebras of type A.
    J. Algebra 249 no.2 (2002), 377-401. Preprint. Published article.
  20. R. J. Marsh. The Lusztig cones of a quantized enveloping algebra of type A.
    J. Algebra 244 no.1 (2001), 59-75. Preprint. Published article.
  21. R. J. Marsh. More tight monomials for quantized enveloping algebras.
    J. Algebra 204 no.2 (1998), 711-732. Preprint. Published article.
  22. R. J. Marsh. Canonical bases and standard monomials.
    Proc. E. M. S. 41 no.3 (1998), 611-623. Published article (free).
  23. R. M. Green and R. J. Marsh. Quantized symmetric powers.
    Quart. J. Math. 48 (1997), 479-492. Preprint. Published article.
  24. R. J. Marsh. Canonical bases for fundamental modules of quantized enveloping algebras of type A.
    Comm. Algebra 25 no.5 (1997), 1365-1386. Preprint. Published article.
  25. R. J. Marsh. Canonical bases for the miniscule modules of the quantized enveloping algebras of types B and D.
    Comm. Algebra 25 no.5 (1997), 1387-1411. Preprint. Published article.
  26. R. J. Marsh. Algorithms to obtain the canonical basis in some fundamental modules of quantum groups.
    J. Algebra 186 no.3 (1996), 831-860. Preprint. Published article.

    27. Preprints are available above in pdf format, readable with Acrobat Reader.

Research Fellows

  • Yann Palu, Research Fellow on EPSRC-funded project Cluster-tilting theory, starting September 2009.
  • Jeanne Scott, Research Fellow and Co-Investigator on EPSRC-funded project Cluster algebras and applications, May 2006 - May 2009.
  • Karin Baur, Research Associate on EPSRC-funded project Braid actions on derived categories of representations of simple Lie algebras, July 2005 - August 2007.
  • Intan Muchtadi-Alamsyah, Research Associate on EPSRC-funded project Braid actions on derived categories of representations of simple Lie algebras, June 2004 - June 2005.
  • Ruth Corran, Research Associate on EPSRC-funded project Canonical bases, reduced expressions and normal forms, January 2001 to September 2003.

Research Students

  • Raquel Simoes, started April 2008.
  • Mark Parsons, PhD University of Leicester, 2008.

Engineering and Physical Sciences Research Council Funded Projects