Professor Neil Strickland
School of Mathematical and Physical Sciences
Professor
+44 114 222 3852
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School of Mathematical and Physical Sciences
J26
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
 Profile

Neil Strickland was awarded his PhD by the University of Manchester in 1992. He was then a C.L.E. Moore Instructor at the Massachusetts Institute of Technology, then a Research Fellow at Trinity College Cambridge, before moving to Sheffield in 1998. He was awarded the Whitehead Prize of the London Mathematical Society in 2005.
 Research interests

Prof Strickland works in stable homotopy theory, a branch of topology in which one studies phenomena that occur uniformly in all sufficiently high dimensions. On the one hand, the subject involves many direct geometrical constructions with interesting spaces such as complex algebraic varieties, coset spaces of Lie groups, spaces of subsets of Euclidean space, and so on. On the other hand, one can use generalised cohomology theories to translate problems in stable homotopy theory into questions in pure algebra, in a strikingly rich and beautiful way. The algebra involved centres around the theory of formal groups, which is essentially a branch of algebraic geometry, although not one of the most familiar branches. It has connections with commutative algebra, Galois theory, the study of elliptic curves, finite and profinite groups, modular representation theory, and many other areas. To translate efficiently between algebra and topology we need to make heavy use of category theory, and this also has applications both on the purely algebraic and the purely topological side, so it forms another significant part of Prof Strickland's research. Students considering research with Prof Strickland are encouraged to consult his personal home page.
 Publications

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Journal articles
 A combinatorial model for the known Bousfield classes. Algebraic and Geometric Topology, 19(6), 26772713. View this article in WRRO
 Large selfinjective rings and the generating hypothesis. Algebra and Number Theory.
 An abelian embedding for Moore spectra. Algebraic and Geometric Topology, 13(4), 21012139.
 Chains on suspension spectra. ALGEBR GEOM TOPOL, 9(3), 16811725.
 Triangulated categories without models. Inventiones Mathematicae, 170(2), 231241.
 Comodules and Landweber exact homology theories. Advances in Mathematics, 192(2), 427456.
 Local cohomology of BP*BPcomodules. Proceedings of the London Mathematical Society, 90(2), 521544.
 The sigma orientation is an Hinfinity map. AM J MATH, 126(2), 247334.
∞ map. American Journal of Mathematics, 126(2), 247334.
The sigma orientation is an H  Realising formal groups. Algebraic and Geometric Topology, 3, 187205 (electronic).
 Common subbundles and intersections of divisors. Algebraic and Geometric Topology, 2, 10611118 (electronic).
 The Hopf rings for KO and KU. Journal of Pure and Applied Algebra, 166(3), 247265.
 Elliptic spectra, the Witten genus and the theorem of the cube. INVENT MATH, 146(3), 595687.
 Chern approximations for generalised group cohomology. TOPOLOGY, 40(6), 11671216.
 Complex cobordism of involutions. Geometry and Topology, 5, 335345.
 Weil pairings and Morava Ktheory. TOPOLOGY, 40(1), 127156.
 GrossHopkins duality. TOPOLOGY, 39(5), 10211033.
 MODEL CATEGORIES (Mathematical Surveys and Monographs 63). Bulletin of the London Mathematical Society, 32(4), 497499.
 K(N)local duality for finite groups and groupoids. TOPOLOGY, 39(4), 733772.
 The BP
cohomology of elementary abelian groups . Journal of London Mathematical Society, 61, 93109.  Varieties and local cohomology for chromatic group cohomology rings. TOPOLOGY, 38(5), 10931139.
 Products on MUmodules. T AM MATH SOC, 351(7), 25692606.
 Morava Ktheories and localisation. Memoirs of the American Mathematical Society, 139, viii+100viii+100.
 Morava Etheory of symmetric groups. Topology, 37, 757779.
 Phantom maps and homology theories. Topology, 37, 339364.
 Axiomatic stable homotopy theory. Memoirs of the American Mathematical Society, 128, x+114x+114.
 Finite subgroups of formal groups. Journal of Pure and Applied Algebra, 121, 161208.
 Rational Morava Etheory and DS^0. Topology, 36, 137151.
 View this article in WRRO Iterated chromatic localisation.
Chapters
 Axiomatic Stable Homotopy, Axiomatic, Enriched and Motivic Homotopy Theory (pp. 6998). Springer Netherlands
 Formal schemes and formal groups In Meyer JP, Morava J & Wilson WS (Ed.), Homotopy Invariant Algebraic Structures: A Conference in Honor of J. Michael Boardman (pp. 263352). Providence, RI: American Mathematical Society.
 The Morava $K$theory Hopf ring for $BP$ In Broto C, Casacuberta C & Mislin G (Ed.), Algebraic Topology: New Trends in Localization and Periodicity: Barcelona Conference on Algebraic Topology, Sant Feliu de Guixols, Spain, June 17, 1994 (pp. 209222). Basel: Birkhäuser.
 On the $p$adic interpolation of stable homotopy groups, Adams Memorial Symposium on Algebraic Topology, 2 (Manchester, 1990) (pp. 4554). Cambridge: Cambridge Univ. Press.
Conference proceedings papers
 Axiomatic stable homotopy  a survey. AXIOMATIC, ENRICHED AND MOTIVIC HOMOTOPY THEORY, Vol. 131 (pp 6998)
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 Research group
 Grants

Past grants, as Principal Investigator
Symmetric Powers of Spheres EPSRC Equivariant elliptic cohomology and class field theory EPSRC Past grants, as Coinvestigator
Higher Structures on Elliptic Cohomology EPSRC
 Teaching activities

MAS334 Combinatorics MAS435 Algebraic Topology