Department of Mathematics
University of Leicester
Leicester LE1 7RH, UK
Phone: +44-(0)116 252 3888
Email: ss489 (at) le.ac.uk
Office: College House 202
My research is in representation theory. Representation theory is an ubiquitous area of mathematics relevant to different subjects such as algebra (associative algebras, Lie theory, Langlands program), number theory (automorphic forms), harmonic analysis (Fournier analysis) and geometry (invariant theory).
The focus of my research is on the representation theory of finite dimensional algebras. In particular, I'm interested in cohomology theories, homological algebra, and connections to of representation theory to other areas of mathematics.
- Extensions for gentle algebras, (with I. Canakci and D. Pauksztello), preprint.
- Mapping cones in the bounded derived category of a gentle algebra, (with I. Canakci and D. Pauksztello), preprint.
- Almost gentle algebras and their trivial extensions, (with E. L. Green), arXiv:1603.03587, pdf.
- Brauer configuration algebras: A generalization of Brauer graph algebras, (with E. L. Green), arXiv:1508.03617, pdf.
- Extensions in Jacobian Algebras and Cluster Categories of Marked Surfaces, (with I. Canakci), arXiv:1408.2074, pdf.
- Special multiserial algebras are quotients of symmetric special multiserial algebras, (with E. L. Green), to appear in Journal of Algebra, pdf.
- Multiserial and special multiserial algebras and their representations, (with E. L. Green), to appear in Advances in Mathematics, pdf.
- The Ext algebra of a Brauer graph algebra, (with E.L. Green, R. Taillefer, N. Snashall), to appear in the Journal of Non-Commutative Geometry, pdf.
- Trivial extensions of gentle algebras and Brauer graph algebras, Journal of Algebra, 444, (2015), pp.183-200, pdf.
- The geometry of Brauer graph algebras and cluster mutations, (with R. Marsh), Journal of Algebra, 419, (2014), pp. 141-166, pdf.
- Group actions and coverings of Brauer graph algebras (with E.L Green and S. Snashall), Glasgow Mathematical Journal, 56, No. 02, (2014), pp. 439-464, pdf.
- A circular order on edge-coloured trees and RNA m-diagrams (with R. Marsh), Advances in Applied Mathematics, 54, (2014), pp. 11-26. pdf.
- Chebyshev polynomials on symmetric matrices (with K. Erdmann), Journal of Linear Algebra and its Applications, 434, No. 12, (2011), pdf.
- Hochschild cohomology and support varieties for tame Hecke algebras (with N. Snashall), Q. J. Math., 62, No. 4, (2011) pdf.
- On the Hochschild cohomology of tame Hecke algebras (with K. Erdmann), Arch. Math., 117, No. 2, (2010) pdf.
- Rhombus filtrations and Rauzy algebras (with A. Clark and K. Erdmann), Bull. Sci. Math., 133, No. 1, (2009) pdf.
- Weight 2 blocks of general linear groups and Alvis-Curtis duality (with K.M. Tan), Int. Math. Res. Not. IMRN 2007, Art. ID rnm130 pdf.
- On decomposition numbers and Alvis-Curtis duality (with B. Ackermann), Math. Proc. Cambridge Philos. Soc. 143, No. 3, (2007) pdf.
- Alvis-Curtis duality on q-Schur and Hecke algebras, Q. J. Math. 58, No. 2, (2007).
- On Young modules of general linear groups (with K. Erdmann), Journal of Algebra 310, No. 1, (2007).
- On the Coxeter complex and Alvis-Curtis duality for principal l-blocks of GLn(q), (with M. Linckelmann), J. Algebra Appl. 4, No. 3 (2005).
- A two-sided q-analogue of the Coxeter complex, (with M. Linckelmann), Journal of Algebra 289, No. 1, (2005).
Current PhD students:
- Drew Duffield (2013 - )
- Alex Sierra (2015 - ) (jointly supervised with E. Marcos (Sao Paolo))
- EPSRC Research Project EP/K026364/1: Geometric representations of cluster categories, Brauer graph algebras and RNA secondary structures
- Other research funding.
Upcoming and recent talks:
- Conference in Representation Theory of the Americas, Vitoria do Espirito Santo, Brazil, March 13-17 2017
- Paris, Algebra Seminar Paris 7, France, February 2017
- Graz Algebra Seminar, Austria, 16 June 2016
- Bonn, Germany, 3 June 2016
- Oxford Algebra Seminar, 26 April 2016
- East Anglia Pure Mathematics Research Seminar, 18 April 2016
- Cardiff Pure Maths Colloquium, 14 April 2016
- Workshop on Brauer Graph Algebras, 20-24 March 2016, University of Stuttgart, Germany.
- CIMPA School, Homological Methods, Representation Theory and Cluster Algebras, 7-18 March 2016, Mar del Plata, Argentina.
- Infinite-dimensional representations of finite-dimensional algebras, 14-17 September 2015, Manchester, UK
- Maurice Auslander Distinguished Lectures and International Conference, 29 April - 4 May 2015, Woods Hole, MA, USA
- Homological Interactions between Rpresentation Theory and Singularity Theory, 15-10 December 2014, Edinburgh, UK.
- 29th Summer Conference on Topology and Its Applications, 23-26 July 2014, Staten Island, NY, USA.
- ARTA III, 16-20 June 2014, Montreal, Canada.
- BLOC 64, 6 May 2014, Leicester, UK.
- Cluster Algebras and Combinatorics, 6-8 February 2014, Muenster, Germany.
- Special sixty-third BLOC Meeting: Oxford, 17-18 October 2013. This meeting is on the occasion of Karin Erdmann's 65th birthday.
- HH^4 - fourth conference on Hochschild (Co-)Homology, August 12 - 16, 2013, Universidad de Buenos Aires, Buenos Aires, Argentina.
Conferences and workshops that I have organised:
- Workshop on Cluster Algebras and Finite Dimensional Algebras, 3 - 5 June 2015 at the University of Leicester.
- Special 63rd BLOC Meeting: Oxford, 17-18 October 2013. This meeting is on the occasion of Karin Erdmann's 65th birthday.
- 62th BLOC/REPNET meeting, 10 July 2013, Leicester.
- 60th BLOC/ARTIN meeting, satellite meeting to BMC 2013, 25 March 2013, Sheffield.
- Workshop on geometry, representation theory and clusters, 21-23 June 2012, Leicester.
- 50th BLOC/REPNET meeting, 9-10 September 2010.
- 46th BLO/REPNET meeting, 1-2 July 2009, Leicester.
What's happening at Leicester:
Support material for MA7602
- LMS Good practice
- Why are there so few women professors in mathematics? BBC radio 4 Women's Hour
- The guardian on the subject: Helen Powell and Lucy Ward
- Why women leave academia (The Guardian)
- Detexify: finding Latex symbols