Dr Sira Gratz

  • Lecturer (Mathematics)

Research interests

Research Interests

My research focuses on applying combinatorial methods to solve questions arising in representation theory; in suitable frameworks, abstract concepts from representation theory can be made tangible using combinatorics and, quite simply, pictures.

More specifically I am interested in cluster algebras and cluster categories of infinite rank, in classification problems in triangulated categories, and in the relations between cluster algebras and representation theory.

Research Groups


Publications

List by: Type | Date

Jump to: 2018 | 2016 | 2015 | 2014
Number of items: 9.

2018

Gratz, S. and Stevenson, G. (2018) On the graded dual numbers, arcs, and non-crossing partitions of the integers. Journal of Algebra, 515, pp. 360-388. (doi:10.1016/j.jalgebra.2018.08.023)

Baur, K., Faber, E., Gratz, S. , Serhiyenko, K. and Todorov, G. (2018) Conway-Coxeter friezes and mutation: a survey. In: Deines, A., Ferrero, D., Graham, E., Seong Im, M., Manore, C. and Price, C. (eds.) Advances in Mathematical Sciences. Series: Association for Women in Mathematical Sciences (15). Springer. ISBN 9783319986838 (In Press)

Grabowski, J. E. and Gratz, S. (2018) Graded quantum cluster algebras of infinite rank as colimits. Journal of Pure and Applied Algebra, 222(11), pp. 3395-3413. (doi:10.1016/j.jpaa.2017.12.014)

Gratz, S. , Holm, T. and Jorgensen, P. (2018) Cluster tilting subcategories and torsion pairs in Igusa-Todorov cluster categories of Dynkin type A infinity. Mathematische Zeitschrift, (doi:10.1007/s00209-018-2117-y) (Early Online Publication)

Baur, K. and Gratz, S. (2018) Transfinite mutations in the completed infinity-gon. Journal of Combinatorial Theory, Series A, 155, pp. 321-359. (doi:10.1016/j.jcta.2017.11.011)

Baur, K., Faber, E., Gratz, S. , Serhiyenko, K. and Todorov, G. (2018) Mutation of friezes. Bulletin des Sciences Mathematiques, 142, pp. 1-48. (doi:10.1016/j.bulsci.2017.09.004)

2016

Gratz, S. (2016) Mutation of torsion pairs in cluster categories of Dynkin type D. Applied Categorical Structures, 24(1), pp. 79-104. (doi:10.1007/s10485-014-9387-2)

2015

Gratz, S. (2015) Cluster algebras of infinite rank as colimits. Mathematische Zeitschrift, 281(3-4), pp. 1137-1169. (doi:10.1007/s00209-015-1524-6)

2014

Grabowski, J. E. and Gratz, S. (2014) Cluster algebras of infinite rank. Journal of the London Mathematical Society, 89(2), pp. 337-363. (doi:10.1112/jlms/jdt064)

This list was generated on Sun Dec 16 08:12:15 2018 GMT.
Number of items: 9.

Articles

Gratz, S. and Stevenson, G. (2018) On the graded dual numbers, arcs, and non-crossing partitions of the integers. Journal of Algebra, 515, pp. 360-388. (doi:10.1016/j.jalgebra.2018.08.023)

Grabowski, J. E. and Gratz, S. (2018) Graded quantum cluster algebras of infinite rank as colimits. Journal of Pure and Applied Algebra, 222(11), pp. 3395-3413. (doi:10.1016/j.jpaa.2017.12.014)

Gratz, S. , Holm, T. and Jorgensen, P. (2018) Cluster tilting subcategories and torsion pairs in Igusa-Todorov cluster categories of Dynkin type A infinity. Mathematische Zeitschrift, (doi:10.1007/s00209-018-2117-y) (Early Online Publication)

Baur, K. and Gratz, S. (2018) Transfinite mutations in the completed infinity-gon. Journal of Combinatorial Theory, Series A, 155, pp. 321-359. (doi:10.1016/j.jcta.2017.11.011)

Baur, K., Faber, E., Gratz, S. , Serhiyenko, K. and Todorov, G. (2018) Mutation of friezes. Bulletin des Sciences Mathematiques, 142, pp. 1-48. (doi:10.1016/j.bulsci.2017.09.004)

Gratz, S. (2016) Mutation of torsion pairs in cluster categories of Dynkin type D. Applied Categorical Structures, 24(1), pp. 79-104. (doi:10.1007/s10485-014-9387-2)

Gratz, S. (2015) Cluster algebras of infinite rank as colimits. Mathematische Zeitschrift, 281(3-4), pp. 1137-1169. (doi:10.1007/s00209-015-1524-6)

Grabowski, J. E. and Gratz, S. (2014) Cluster algebras of infinite rank. Journal of the London Mathematical Society, 89(2), pp. 337-363. (doi:10.1112/jlms/jdt064)

Book Sections

Baur, K., Faber, E., Gratz, S. , Serhiyenko, K. and Todorov, G. (2018) Conway-Coxeter friezes and mutation: a survey. In: Deines, A., Ferrero, D., Graham, E., Seong Im, M., Manore, C. and Price, C. (eds.) Advances in Mathematical Sciences. Series: Association for Women in Mathematical Sciences (15). Springer. ISBN 9783319986838 (In Press)

This list was generated on Sun Dec 16 08:12:15 2018 GMT.

Supervision

Current PhD students

James Rowe