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

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).

R. J. Marsh
and
I. Reiten.
Rigid and Schurian modules over clustertilted algebras of tame type.
Mathematische Zeitschrift, 2016.
Online First; DOI: 10.1007/s002090161668z.
Preprint version.

R. J. Marsh and
J. S. Scott.
Twists of Plücker coordinates as dimer partition functions.
Comm. Math. Phys. 341 Issue 3 (2016), 821884.
Preprint version

M. Barot and
R. J. Marsh.
Reflection group presentations arising from cluster algebras.
Trans. Amer. Math. Soc. 367 (2015), 19451967.
Preprint version.

R. J. Marsh and
S. Schroll.
The geometry of Brauer graph algebras and cluster mutations.
J. Algebra 419, (2014), 141166.
Preprint version.

R. J. Marsh and
S. Schroll.
A circular order on edgecoloured trees and RNA mdiagrams.
Adv Appl. Math. 54 (2014), 1126.
Adv. Appl. Math 54 (2014), 1126.
Preprint version.

R. J. Marsh,
Lecture Notes on Cluster Algebras.
Zurich lectures in Advanced Mathematics. European Mathematical Society,
2014.

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), 411440.
Preprint version.
Freeaccess link.

K. Baur,
A. B. Buan and
R. J. Marsh.
Torsion pairs and rigid objects in tubes.
Algebras and Representation Theory (2014) 17(2): 565591.
Preprint. The final publication is available at link.springer.com.

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): 152170.
OPEN ACCESS

A. B. Buan and
R. J. Marsh.
From triangulated categories to module categories via localisation.
Trans. Amer. Math. Soc. 365, no. 6 (2013), 28452861.
Preprint.

K. Baur and
R. J. Marsh.
A geometric model of tube categories.
J. Algebra 362 (2012), 178191.
Preprint.

K. Baur and
R. J. Marsh.
Categorification of a frieze pattern determinant.
Journal of Combinatorial Theory, Series A 119 (2012), 11101122.
Preprint.

A. P. Fordy and
R. J. Marsh.
Cluster mutationperiodic quivers and associated Laurent sequences.
Journal of Algebraic Combinatorics, 34, no. 1 (2011), 1966.
Preprint.

R. J. Marsh and
P. P. Martin.
Tiling bijections between paths and Brauer diagrams.
Journal of Algebraic Combinatorics,
33, no. 3 (2011), 427453.
Preprint.

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.

A. B. Buan and
R. J. Marsh.
Denominators in cluster algebras of affine type.
Journal of Algebra, 323 no. 8, (2010), pages 20832102.
Preprint.

A. B. Buan,
R. J. Marsh and
D. F. Vatne.
Cluster structures from 2CalabiYau categories with loops.
Mathematische Zeitschrift 265 no. 4 (2010), pages 951970.
Preprint.

A. B. Buan,
R. J. Marsh and
I. Reiten.
Denominators of cluster variables.
Journal of the London Mathematical Society 79, no. 3 (2009),
pages 589611.
Preprint.

K. Baur and
R. J. Marsh.
Frieze patterns for punctured discs.
Journal of Algebraic Combinatorics 30, Issue 3 (2009),
Pages 349379.
Preprint.

K. Baur and
R. J. Marsh.
A geometric description of mcluster categories.
Trans. Amer. Math. Soc. 360 (2008), 57895803.
Preprint.

A. B. Buan,
R. J. Marsh and
I. Reiten.
Cluster mutation via quiver representations.
Commentarii Mathematici Helvetici 83 Issue 1 (2008), 143177.
Preprint.

K. Baur and
R. J. Marsh.
A geometric description of the mcluster categories of type D_n.
International Mathematics Research Notices (2007) Vol. 2007 :
article ID rnm011, 19 pages, doi:10.1093/imrn/rnm011.
Preprint.

A. B. Buan,
R. J. Marsh,
I. Reiten and
G. Todorov.
Clusters and seeds in acyclic cluster algebras.
Includes appendix coauthored in addition with
P. Caldero and
B. Keller.
Proc. Amer. Math. Soc. 135, no. 10 (2007), 30493060.
Preprint.

A. B. Buan,
R. J. Marsh and
I. Reiten.
Clustertilted algebras.
Trans. Amer. Math. Soc. 359, no. 1 (2007), 323332.
Preprint.

A. B. Buan,
R. J. Marsh and
I. Reiten.
Clustertilted algebras of finite representation type.
Journal of Algebra 306, no. 2, (2006), 412431.
Preprint.

A. B. Buan and
R. J. Marsh.
Clustertilting theory.
Pages 130 in Trends in Representation Theory of Algebras and Related
Topics, Workshop August 1114, 2004, Queretaro, Mexico.
Editors J. A. de la Pena and
R. Bautista, Contemporary Mathematics 406 (2006), 130.
Preprint.

A. B. Buan,
R. J. Marsh,
M. Reineke,
I. Reiten and
G. Todorov.
Tilting theory and cluster combinatorics.
Adv. Math. 204 (2006), 572618.
Preprint.

P. Caldero,
R. J. Marsh and
S. MorierGenoud.
Realisation of Lusztig cones.
Representation Theory 8 (2004), 458478.
Preprint.

R. J. Marsh and
K. Rietsch.
Parametrizations of flag varieties.
Representation Theory 8 (2004), 212242.
Preprint.

P. Caldero and
R. J. Marsh.
A multiplicative property of quantum flag minors II.
Journal of the L.M.S. 69 no.3 (2004), 608622.
Preprint.

R. J. Marsh and
M. Reineke.
Canonical basis linearity regions arising from quiver representations.
J. Algebra 270 no.2 (2003), 696727.
Preprint.

R. J. Marsh,
M. Reineke and
A. Zelevinsky.
Generalized associahedra via quiver representations.
Trans. Amer. Math. Soc.
355 no.10 (2003), 41714186.
Preprint.

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), 2242.
Preprint.

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), 545603.
Preprint.

R. W. Carter and R. J. Marsh.
Canonical bases and piecewiselinear combinatorics.
Pages 3347 in Quantum Groups and Lie Theory, edited by Andre
w Pressley, LMS Lecture Note Series 290, C.U.P., 2001.
Preprint.

R. J. Marsh.
Rectangle diagrams for the Lusztig cones of quantized enveloping algebras of
type A.
J. Algebra 249 no.2 (2002), 377401.
Preprint.

R. J. Marsh.
The Lusztig cones of a quantized enveloping algebra of type A.
J. Algebra 244 no.1 (2001), 5975.
Preprint.

R. J. Marsh.
More tight monomials for quantized enveloping algebras.
J. Algebra 204 no.2 (1998), 711732.
Preprint.

R. J. Marsh.
Canonical bases and standard monomials.
Proc. E. M. S. 41 no.3 (1998), 611623.
Preprint.

R. M.
Green and R. J. Marsh.
Quantized symmetric powers.
Quart. J. Math. 48 (1997), 479492.
Preprint.

R. J. Marsh.
Canonical bases for fundamental modules of quantized enveloping algebras of
type A.
Comm. Algebra 25 no.5 (1997), 13651386.
Preprint.

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), 13871411.
Preprint.

R. J. Marsh.
Algorithms to obtain the canonical basis in some fundamental
modules of quantum groups.
J. Algebra 186 no.3 (1996), 831860.
Preprint.
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 EPSRCfunded project
Clustertilting theory, February 2012  Present.

Yann Palu, Research Fellow on EPSRCfunded project
Clustertilting theory, September 2009  August 2011.

Jeanne Scott, Research Fellow and CoInvestigator on EPSRCfunded
project Cluster algebras and applications, May 2006  May 2009.

Karin Baur,
Research Associate on EPSRCfunded project Braid actions on
derived categories of representations of simple Lie algebras,
July 2005  August 2007.

Intan MuchtadiAlamsyah, Research Associate on EPSRCfunded project
Braid actions on derived categories of representations of simple Lie
algebras, June 2004  June 2005.

Ruth Corran, Research Associate on EPSRCfunded project
Canonical bases, reduced expressions and normal forms,
January 2001 to September 2003.
Webpages of recent meetings (co)organised

Workshop on
Mirror Symmetry and Cluster Algebras, 1113 September 2013.

Workshop on Geometry, representation theory and clusters,
University of Leicester, 2123 June 2012. Coorganiser.

32nd
Artin Meeting. Leeds, 1718 May 2012. Organiser.
 Cluster algebras and representation theory. Leeds, Thursday 17 June 2010. Coorganiser.

Workshop on quivers and integrable systems. Leeds, 2223 May 2009. Coorganiser.

PFS 2008, Rings and Modules. Lisbon, Portugal, 1619 September 2008. Coorganiser.

16th Artin Meeting. Leeds, 1415 March 2008. Organiser.

Liegrits workshop. Oxford, 39 January 2008. Scientific adviser.
Research Students

Raquel Simoes, April 2008  March 2012.

Mark Parsons, PhD University of Leicester, 2008.
Engineering and Physical Sciences Research Council Funded Projects