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Robert Marsh - Personal Home Page

Teaching, 2015/2016:

Research interests

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

Preprints

List of publications


  1. R. J. Marsh and Y. Palu. Nearly Morita equivalences and rigid objects. Nagoya Mathematical Journal, FirstView Article, August 2016, pp 1 - 36. DOI: 10.1017/nmj.2016.27. Preprint version (2/2016).
  2. R. J. Marsh and I. Reiten. Rigid and Schurian modules over cluster-tilted algebras of tame type. Mathematische Zeitschrift, 2016. Online First; DOI: 10.1007/s00209-016-1668-z. Preprint version.
  3. R. J. Marsh and J. S. Scott. Twists of Plücker coordinates as dimer partition functions. Comm. Math. Phys. 341 Issue 3 (2016), 821-884. Preprint version
  4. M. Barot and R. J. Marsh. Reflection group presentations arising from cluster algebras. Trans. Amer. Math. Soc. 367 (2015), 1945-1967. Preprint version.
  5. R. J. Marsh and S. Schroll. The geometry of Brauer graph algebras and cluster mutations. J. Algebra 419, (2014), 141-166. Preprint version.
  6. R. J. Marsh and S. Schroll. A circular order on edge-coloured trees and RNA m-diagrams. Adv Appl. Math. 54 (2014), 11-26. Adv. Appl. Math 54 (2014), 11-26. Preprint version.
  7. R. J. Marsh, Lecture Notes on Cluster Algebras. Zurich lectures in Advanced Mathematics. European Mathematical Society, 2014.
  8. R. J. Marsh and Y. Palu. Coloured quivers for rigid objects and partial triangulations: The unpunctured case. Proceedings of the London Mathematical Society (2014) 108 (2), 411-440. Preprint version. Free-access link.
  9. K. Baur, A. B. Buan and R. J. Marsh. Torsion pairs and rigid objects in tubes.
    Algebras and Representation Theory (2014) 17(2): 565-591. Preprint. The final publication is available at link.springer.com.
  10. A. B. Buan and R. J. Marsh. From triangulated categories to module categories via localization II: Calculus of fractions.
    J. London Math. Soc. (2012) 86 (1): 152-170. OPEN ACCESS
  11. A. B. Buan and R. J. Marsh. From triangulated categories to module categories via localisation.
    Trans. Amer. Math. Soc. 365, no. 6 (2013), 2845--2861. Preprint.
  12. K. Baur and R. J. Marsh. A geometric model of tube categories.
    J. Algebra 362 (2012), 178--191. Preprint.
  13. K. Baur and R. J. Marsh. Categorification of a frieze pattern determinant.
    Journal of Combinatorial Theory, Series A 119 (2012), 1110-1122. Preprint.
  14. A. P. Fordy and R. J. Marsh. Cluster mutation-periodic quivers and associated Laurent sequences.
    Journal of Algebraic Combinatorics, 34, no. 1 (2011), 19-66. Preprint.
  15. R. J. Marsh and P. P. Martin. Tiling bijections between paths and Brauer diagrams.
    Journal of Algebraic Combinatorics, 33, no. 3 (2011), 427-453. Preprint.
  16. K. A. Brown, P. A. Guil Asensio and R. J. Marsh (editors),
    Proceedings of the Rings and Modules Conference, Lisbon, Portugal, September 2008, in honour of Patrick F. Smith's 65th Birthday.
    Volume 52A of the Glasgow Mathematical Journal (Chief Editor, Ian Strachan), July 2010.
  17. A. B. Buan and R. J. Marsh. Denominators in cluster algebras of affine type.
    Journal of Algebra, 323 no. 8, (2010), pages 2083-2102. Preprint.
  18. A. B. Buan, R. J. Marsh and D. F. Vatne. Cluster structures from 2-Calabi-Yau categories with loops.
    Mathematische Zeitschrift 265 no. 4 (2010), pages 951-970. Preprint.
  19. A. B. Buan, R. J. Marsh and I. Reiten. Denominators of cluster variables.
    Journal of the London Mathematical Society 79, no. 3 (2009), pages 589-611. Preprint.
  20. K. Baur and R. J. Marsh. Frieze patterns for punctured discs.
    Journal of Algebraic Combinatorics 30, Issue 3 (2009), Pages 349-379. Preprint.
  21. K. Baur and R. J. Marsh. A geometric description of m-cluster categories.
    Trans. Amer. Math. Soc. 360 (2008), 5789-5803. Preprint.
  22. A. B. Buan, R. J. Marsh and I. Reiten. Cluster mutation via quiver representations.
    Commentarii Mathematici Helvetici 83 Issue 1 (2008), 143-177. Preprint.
  23. 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.
  24. 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.
  25. A. B. Buan, R. J. Marsh and I. Reiten. Cluster-tilted algebras.
    Trans. Amer. Math. Soc. 359, no. 1 (2007), 323-332. Preprint.
  26. 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.
  27. 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.
  28. 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.
  29. P. Caldero, R. J. Marsh and S. Morier-Genoud. Realisation of Lusztig cones.
    Representation Theory 8 (2004), 458-478. Preprint.
  30. R. J. Marsh and K. Rietsch. Parametrizations of flag varieties.
    Representation Theory 8 (2004), 212-242. Preprint.
  31. 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.
  32. R. J. Marsh and M. Reineke. Canonical basis linearity regions arising from quiver representations.
    J. Algebra 270 no.2 (2003), 696-727. Preprint.
  33. R. J. Marsh, M. Reineke and A. Zelevinsky. Generalized associahedra via quiver representations.
    Trans. Amer. Math. Soc. 355 no.10 (2003), 4171-4186. Preprint.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. R. J. Marsh. The Lusztig cones of a quantized enveloping algebra of type A.
    J. Algebra 244 no.1 (2001), 59-75. Preprint.
  39. R. J. Marsh. More tight monomials for quantized enveloping algebras.
    J. Algebra 204 no.2 (1998), 711-732. Preprint.
  40. R. J. Marsh. Canonical bases and standard monomials.
    Proc. E. M. S. 41 no.3 (1998), 611-623. Preprint.
  41. R. M. Green and R. J. Marsh. Quantized symmetric powers.
    Quart. J. Math. 48 (1997), 479-492. Preprint.
  42. R. J. Marsh. Canonical bases for fundamental modules of quantized enveloping algebras of type A.
    Comm. Algebra 25 no.5 (1997), 1365-1386. Preprint.
  43. 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.
  44. 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.

  45. Preprints are available above in pdf format, readable with Acrobat Reader.
  • 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 publication above).
  • Working seminar in 2009/10 on tilting theory.

Research Fellows

  • Joseph Grant, Research Fellow on EPSRC-funded project Cluster-tilting theory, February 2012 - Present.
  • Yann Palu, Research Fellow on EPSRC-funded project Cluster-tilting theory, September 2009 - August 2011.
  • 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.

Webpages of recent meetings (co)-organised

Research Students

  • Raquel Simoes, April 2008 - March 2012.
  • Mark Parsons, PhD University of Leicester, 2008.

Engineering and Physical Sciences Research Council Funded Projects