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Professor John Greenlees


John Greenlees

Professor of Mathematics

Office: C1.13
Phone: +44 (0)24 765 28335


John Greenlees obtained his PhD from Cambridge in 1986, and spent 3 years at the National University of Singapore and a year at the University of Chicago before moving to Sheffield in 1990. He spent 28 years there, serving as Head of Pure Maths and then Head of the School of Mathematics and Statistics before moving to Warwick as Head of Department in 2018. He has published over 90 papers and 4 books on algebra and topology, and serves on the editorial boards of 3 algebraic topology journals. He has acted as undergraduate External Examiner for 5 institutions, and conducted external reviews for 7 departments.

John was an organizer of the Oberwolfach Homotopy Theory meetings between 2007 and 2015, a meeting on the Kervaire Invariant at the ICMS in 2011, a 4 month programme at the Isaac Newton Institute in 2002 and the 6 month programme Homotopy Harnessing Higher structures in 2018. He was on the Scientific Committee of the ICMS 2011-20, and has been on the INI Management Committee since 2020.

John was Vice President of the London Mathematical Sciences from 2009 to 2019, and a member of the Board of the Council for Mathematical Sciences. He was Deputy Chair of the REF2021 Mathematical Sciences Subpanel, and also served on subpanels in REF2014 and RAE2008.

Research Interests: Algebraic topology, commutative algebra, representation theory

Recent research grants: Adelic models, rigidity and equivariant cohomology theories (2017-22)

Koszul duality and the singularity category for the enhanced group cohomology ring (2023-27)

Most relevant recent publications:

J.P.C.Greenlees ''Ausoni-Bokstedt duality'' Journal of Pure and Applied Algebra 220 (2016), pp. 1382-1402, arXiv:1406.2162

J.P.C.Greenlees ''Rational equivariant cohomology theories with toral support '' Algebraic and Geometric Topology 16 (2016) 1953-2019, arXiv:1501.03425

D. Barnes, J.P.C.Greenlees, M.Kedziorek a nd B.E.Shipley ''Rational SO(2)-equivariant spectra.''Algebraic & Geometric Topology 17-2 (2017), 983--1020. arxiv:1511.03291

J.P.C.Greenlees and L.Meier ''Gorenstein duality for real spectra.'' Algebraic & Geometric Topology 17-6 (2017), 3547--3619, arXiv: 1607.0233

J.P.C.Greenlees ''Homotopy invariant commutative algebra over fields''CRM IRTATCA lectures (2015), Birkhauser, 2018, 103-169, arXiv:1601.024737

J.P.C.Greenlees and B.E.Shipley ''An algebraic model for rational torus-equivariant spectra.'' J.Top 11 (2018) 666-719, arXiv:1101.2511

J.P.C.Greenlees and G. Stevenson ''Morita equivalences and singularity categories.'' Advances in Maths 365 (2020), 44 pp, arXiv: 1702.07957

J.P.C.Greenlees “Borel cohomology and the relative Gorenstein condition for classifying spaces of compact Lie groups” JPAA 224 (2020) 806-818, arXiv:1808.07342

T.Barthel, J.P.C.Greenlees, M.Hausmann “On the Balmer spectrum for compact Lie groups” Compositio 156 (2020) 39-76, arXiv: 1810.04698

S.Balchin and J.P.C.Greenlees ``Adelic models for tensor triangulated categories'' Adv. Math. 375 (2020), 107339, 30pp, arXiv: 1903.02669

D. Barnes, J.P.C.Greenlees and M.Kedziorek ``Rational equivariant naive-commutative ring spectra for SO(2) and equivariant elliptic cohomology revisited''
Math Z 297 (2021) 1205-1235 arXiv:1810.03632

D.J.Benson and J.P.C.Greenlees ``Massey products in the homology of the loop space of a p-completed classifying space: finite groups with cyclic Sylow p-subgroups.'' Proc Edinburgh Math Soc (6pp), arXiv: 2006.07160

R.R.Bruner, J.P.C.Greenlees and J. Rognes ``The local cohomology spectral sequence for topological modular forms'' Math. Z (to appear) Preprint 49pp, arXiv: 2107.02272

D.J.Benson and J.P.C.Greenlees ``The singularity and cosingularity categories for groups with cyclic Sylow subgroup'' Algebras and Representation Theory, 33pp, arXiv:2107.09389

S.Balchin and J.P.C.Greenlees
``Adelic models for 1-dimensional tensor triangulated categories'' JPAA 226 (2022), 34pp, arXiv: 2106.09156

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