Dr Gregory Stevenson

  • Lecturer (Mathematics)

Research interests

Research Interests

My research concerns various aspects of the interplay between representation theory, algebraic geometry, commutative algebra, and homotopy theory. Broadly speaking, I study homological and homotopical invariants of algebraic and topological structures, usually through the formalism of triangulated categories and their various enhancements.

Somewhat more specifically, I'm interested in: derived categories in algebra, geometry, and topology, singularity categories, tensor triangular geometry, lattices of subcategories, Maximal Cohen-Macaulay modules, tilting objects and exceptional collections, cluster-tilting theory, strong generators for triangulated categories, Hochschild (co)homology, Koszul duality, brave new algebra, the representation theory of finite dimensional algebras, ...

Research Groups


Publications

List by: Type | Date

Jump to: 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013
Number of items: 21.

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)

Greenlees, J.P.C. and Stevenson, G. (2020) Morita theory and singularity categories. Advances in Mathematics, 365, 107055. (doi: 10.1016/j.aim.2020.107055)

Balmer, P., Krause, H. and Stevenson, G. (2020) The frame of smashing tensor-ideals. Mathematical Proceedings of the Cambridge Philosophical Society, 168(2), pp. 323-343. (doi: 10.1017/S0305004118000725)

2019

Baland, S. and Stevenson, G. (2019) Comparisons between singularity categories and relative stable categories of finite groups. Journal of Pure and Applied Algebra, 223(3), pp. 948-964. (doi: 10.1016/j.jpaa.2018.05.008)

Balmer, P., Krause, H. and Stevenson, G. (2019) Tensor-triangular fields: ruminations. Selecta Mathematica - New Series, 25, 13. (doi: 10.1007/s00029-019-0454-2)

Baland, S., Chirvasitu, A. and Stevenson, G. (2019) The prime spectra of relative stable module categories. Transactions of the American Mathematical Society, 371(1), pp. 489-503. (doi: 10.1090/tran/7297)

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)

Stevenson, G. (2018) Filtrations via tensor actions. International Mathematics Research Notices, 2018(8), pp. 2535-2558. (doi: 10.1093/imrn/rnw325)

Chachólski, W., Dyckerhoff, T., Greenlees, J. and Stevenson, G. (2018) Building Bridges Between Algebra and Topology. Series: Advanced courses in mathematics - CRM Barcelona. Birkhäuser: Cham, Switzerland. ISBN 9783319701561 (doi:10.1007/978-3-319-70157-8)

Stevenson, G. (2018) A tour of support theory for triangulated categories through Tensor triangular geometry. In: Herbera, D., Pitsch, W. and Zarzuela, S. (eds.) Building Bridges Between Algebra and Topology. Series: Advanced courses in mathematics - CRM Barcelona. Birkhäuser: Cham, Switzerland, pp. 63-101. ISBN 9783319701561 (doi:10.1007/978-3-319-70157-8_2)

2017

Dell’Ambrogio, I., Stevenson, G. and Šťovíček, J. (2017) Gorenstein homological algebra and universal coefficient theorems. Mathematische Zeitschrift, 287(3-4), pp. 1109-1155. (doi: 10.1007/s00209-017-1862-7)

Stevenson, G. (2017) The local-to-global principle for triangulated categories via dimension functions. Journal of Algebra, 473, pp. 406-429. (doi: 10.1016/j.jalgebra.2016.12.002)

Steen, J. and Stevenson, G. (2017) Enrichment and representability for triangulated categories. Documenta Mathematica, 22, pp. 1031-1062.

2016

Antieau, B. and Stevenson, G. (2016) Derived categories of representations of small categories over commutative noetherian rings. Pacific Journal of Mathematics, 283(1), pp. 21-42. (doi: 10.2140/pjm.2016.283.21)

2015

Steen, J. and Stevenson, G. (2015) Strong generators in tensor triangulated categories. Bulletin of the London Mathematical Society, 47(4), pp. 607-616. (doi: 10.1112/blms/bdv037)

Burke, J. and Stevenson, G. (2015) The derived category of a graded Gorenstein ring. In: Van den Bergh, M., Eisenbud, D., Iyengar, S. and Stafford, J.T. (eds.) Commutative Algebra and Noncommutative Algebraic Geometry. Vol. II. Series: Mathematical Sciences Research Institute publications (68). Cambridge University Press, pp. 93-123. ISBN 9781107149724

2014

Stevenson, G. (2014) Derived categories of absolutely flat rings. Homology, Homotopy and Applications, 16(2), pp. 45-64. (doi: 10.4310/HHA.2014.v16.n2.a3)

Stevenson, G. (2014) Duality for bounded derived categories of complete intersections. Bulletin of the London Mathematical Society, 46(2), pp. 245-257. (doi: 10.1112/blms/bdt089)

Stevenson, G. (2014) Subcategories of singularity categories via tensor actions. Compositio Mathematica, 150(02), pp. 229-272. (doi: 10.1112/S0010437X1300746X)

2013

Krause, H. and Stevenson, G. (2013) A note on thick subcategories of stable derived categories. Nagoya Mathematical Journal, 212, pp. 87-96. (doi: 10.1215/00277630-2351125)

Stevenson, G. (2013) Support theory via actions of tensor triangulated categories. Journal für die reine und angewandte Mathematik (Crelles Journal), 2013(681), (doi: 10.1515/crelle-2012-0025)

This list was generated on Mon Jul 13 23:25:53 2020 BST.
Number of items: 21.

Articles

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)

Greenlees, J.P.C. and Stevenson, G. (2020) Morita theory and singularity categories. Advances in Mathematics, 365, 107055. (doi: 10.1016/j.aim.2020.107055)

Balmer, P., Krause, H. and Stevenson, G. (2020) The frame of smashing tensor-ideals. Mathematical Proceedings of the Cambridge Philosophical Society, 168(2), pp. 323-343. (doi: 10.1017/S0305004118000725)

Baland, S. and Stevenson, G. (2019) Comparisons between singularity categories and relative stable categories of finite groups. Journal of Pure and Applied Algebra, 223(3), pp. 948-964. (doi: 10.1016/j.jpaa.2018.05.008)

Balmer, P., Krause, H. and Stevenson, G. (2019) Tensor-triangular fields: ruminations. Selecta Mathematica - New Series, 25, 13. (doi: 10.1007/s00029-019-0454-2)

Baland, S., Chirvasitu, A. and Stevenson, G. (2019) The prime spectra of relative stable module categories. Transactions of the American Mathematical Society, 371(1), pp. 489-503. (doi: 10.1090/tran/7297)

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)

Stevenson, G. (2018) Filtrations via tensor actions. International Mathematics Research Notices, 2018(8), pp. 2535-2558. (doi: 10.1093/imrn/rnw325)

Dell’Ambrogio, I., Stevenson, G. and Šťovíček, J. (2017) Gorenstein homological algebra and universal coefficient theorems. Mathematische Zeitschrift, 287(3-4), pp. 1109-1155. (doi: 10.1007/s00209-017-1862-7)

Stevenson, G. (2017) The local-to-global principle for triangulated categories via dimension functions. Journal of Algebra, 473, pp. 406-429. (doi: 10.1016/j.jalgebra.2016.12.002)

Steen, J. and Stevenson, G. (2017) Enrichment and representability for triangulated categories. Documenta Mathematica, 22, pp. 1031-1062.

Antieau, B. and Stevenson, G. (2016) Derived categories of representations of small categories over commutative noetherian rings. Pacific Journal of Mathematics, 283(1), pp. 21-42. (doi: 10.2140/pjm.2016.283.21)

Steen, J. and Stevenson, G. (2015) Strong generators in tensor triangulated categories. Bulletin of the London Mathematical Society, 47(4), pp. 607-616. (doi: 10.1112/blms/bdv037)

Stevenson, G. (2014) Derived categories of absolutely flat rings. Homology, Homotopy and Applications, 16(2), pp. 45-64. (doi: 10.4310/HHA.2014.v16.n2.a3)

Stevenson, G. (2014) Duality for bounded derived categories of complete intersections. Bulletin of the London Mathematical Society, 46(2), pp. 245-257. (doi: 10.1112/blms/bdt089)

Stevenson, G. (2014) Subcategories of singularity categories via tensor actions. Compositio Mathematica, 150(02), pp. 229-272. (doi: 10.1112/S0010437X1300746X)

Krause, H. and Stevenson, G. (2013) A note on thick subcategories of stable derived categories. Nagoya Mathematical Journal, 212, pp. 87-96. (doi: 10.1215/00277630-2351125)

Stevenson, G. (2013) Support theory via actions of tensor triangulated categories. Journal für die reine und angewandte Mathematik (Crelles Journal), 2013(681), (doi: 10.1515/crelle-2012-0025)

Books

Chachólski, W., Dyckerhoff, T., Greenlees, J. and Stevenson, G. (2018) Building Bridges Between Algebra and Topology. Series: Advanced courses in mathematics - CRM Barcelona. Birkhäuser: Cham, Switzerland. ISBN 9783319701561 (doi:10.1007/978-3-319-70157-8)

Book Sections

Stevenson, G. (2018) A tour of support theory for triangulated categories through Tensor triangular geometry. In: Herbera, D., Pitsch, W. and Zarzuela, S. (eds.) Building Bridges Between Algebra and Topology. Series: Advanced courses in mathematics - CRM Barcelona. Birkhäuser: Cham, Switzerland, pp. 63-101. ISBN 9783319701561 (doi:10.1007/978-3-319-70157-8_2)

Burke, J. and Stevenson, G. (2015) The derived category of a graded Gorenstein ring. In: Van den Bergh, M., Eisenbud, D., Iyengar, S. and Stafford, J.T. (eds.) Commutative Algebra and Noncommutative Algebraic Geometry. Vol. II. Series: Mathematical Sciences Research Institute publications (68). Cambridge University Press, pp. 93-123. ISBN 9781107149724

This list was generated on Mon Jul 13 23:25:53 2020 BST.

Supervision

Current PhD students

David Murphy ( Representations of finite dimensional algebras This project studies representations of finite dimensional algebras via a homological approach. The central idea is to study structures and properties of categories coming from representations of finite dimensional algebras, with possible focus on thick subcategories, Serre functors, lattice theory, and (tau-)tilting. )
James Rowe