Dr Sira Gratz

  • Senior Lecturer (Mathematics)

email: Sira.Gratz@glasgow.ac.uk

School of Mathematics and Statistics, Office 439, University of Glasgow, University Place, G12 8QQ

ORCID iDhttps://orcid.org/0000-0002-5333-0869

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 units

Publications

List by: Type | Date

Jump to: 2021 | 2020 | 2019 | 2018 | 2016 | 2015 | 2014
Number of items: 12.

2021

Erdmann, K., Gratz, S. and Lamberti, L. (2021) Cluster tilting modules for mesh algebras. Linear Algebra and Its Applications, 630, pp. 112-157. (doi: 10.1016/j.laa.2021.07.021)

Baur, K., Faber, E., Gratz, S. , Serhiyenko, K. and Todorov, G. (2021) Friezes satisfying higher SL_k-determinants. Algebra and Number Theory, 15(1), pp. 29-68. (doi: 10.2140/ant.2021.15.29)

2020

Gratz, S. and Stevenson, G. (2020) Homotopy invariants of singularity categories. Journal of Pure and Applied Algebra, 224(12), 106433. (doi: 10.1016/j.jpaa.2020.106433)

2019

Gratz, S. , Holm, T. and Jorgensen, P. (2019) Cluster tilting subcategories and torsion pairs in Igusa-Todorov cluster categories of Dynkin type A infinity. Mathematische Zeitschrift, 292(1-2), pp. 33-56. (doi: 10.1007/s00209-018-2117-y)

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: Cham, pp. 47-68. ISBN 9783319986838 (doi:10.1007/978-3-319-98684-5_4)

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)

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 Mathématiques, 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 Mon Sep 27 14:21:10 2021 BST.
Jump to: Articles | Book Sections
Number of items: 12.

Articles

Erdmann, K., Gratz, S. and Lamberti, L. (2021) Cluster tilting modules for mesh algebras. Linear Algebra and Its Applications, 630, pp. 112-157. (doi: 10.1016/j.laa.2021.07.021)

Baur, K., Faber, E., Gratz, S. , Serhiyenko, K. and Todorov, G. (2021) Friezes satisfying higher SL_k-determinants. Algebra and Number Theory, 15(1), pp. 29-68. (doi: 10.2140/ant.2021.15.29)

Gratz, S. and Stevenson, G. (2020) Homotopy invariants of singularity categories. Journal of Pure and Applied Algebra, 224(12), 106433. (doi: 10.1016/j.jpaa.2020.106433)

Gratz, S. , Holm, T. and Jorgensen, P. (2019) Cluster tilting subcategories and torsion pairs in Igusa-Todorov cluster categories of Dynkin type A infinity. Mathematische Zeitschrift, 292(1-2), pp. 33-56. (doi: 10.1007/s00209-018-2117-y)

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)

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 Mathématiques, 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: Cham, pp. 47-68. ISBN 9783319986838 (doi:10.1007/978-3-319-98684-5_4)

This list was generated on Mon Sep 27 14:21:10 2021 BST.