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: 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013
Number of items: 19.

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)

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)

Balmer, P., Krause, H. and Stevenson, G. (2018) The frame of smashing tensor-ideals. Mathematical Proceedings of the Cambridge Philosophical Society, (doi:10.1017/S0305004118000725) (Early Online Publication)

Balmer, P., Krause, H. and Stevenson, G. (2018) Tensor-triangular fields: ruminations. Selecta Mathematica - New Series, (Accepted for Publication)

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 Fri Jul 19 13:22:59 2019 BST.
Number of items: 19.

Articles

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)

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)

Balmer, P., Krause, H. and Stevenson, G. (2018) The frame of smashing tensor-ideals. Mathematical Proceedings of the Cambridge Philosophical Society, (doi:10.1017/S0305004118000725) (Early Online Publication)

Balmer, P., Krause, H. and Stevenson, G. (2018) Tensor-triangular fields: ruminations. Selecta Mathematica - New Series, (Accepted for Publication)

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 Fri Jul 19 13:22:59 2019 BST.

Supervision

Current PhD students

James Rowe