Prof John Greenlees

Teaching:
MAS435  Algebraic Topology  Information  Home page 
MAS6370  Algebraic Topology I  Information  Home page 
Research:
Interests:  Equivariant topology, commutative algebra, algebraic topology 
Research groups:  Topology, Algebra, Category Theory 
Publications:  Preprint page, ArXiv, MathSciNet 
Grants
Current grants, as Principal Investigator  
Rigidity and HasseTate models in algebra, geometry and topology  EPSRC 
Past grants, as Principal Investigator  
Rational equivariant cohomology theories  EPSRC 
Algebraic Rational GEquivariant Stable Homotopy Theory for Profinite Groups and Extensions of a Torus  EPSRC 
Orientability and Complete Intersections for Ring Spectra  EPSRC 
Higher Structures on Elliptic Cohomology  EPSRC 
Connective real K theory, compact Lie groups and geometry  EPSRC 
Applications of local cohomology to algebraic topology  EPSRC 
Connective Ktheory of classifying spaces and geometry  EPSRC 
Roles:
Director of Research
Biography:
Professor Greenlees was awarded his PhD by the University of Cambridge (1985). After a year
as a Senior Rouse Ball Student at Trinity College, he spent 198689 at the National University
of Singapore and 198990 at the University of Chicago. He moved to Sheffield in 1990, being
awarded a Personal Chair in 1995, and has held visiting positions at the University of Chicago
and the Isaac Newton Institute. He was Research Professor at MSRI (Berkeley) in 2014, and Visiting Researcher in CRM (Barcelona) and HIM (Bonn) in 2015.
Professor Greenlees has been Vice President of the London Mathematical Society since 2009, was a member of the REF2014 Mathematical Sciences Subpanel, and is an editor of five journals and a book series.
In the past he served as a member of the EPSRC Strategic Advisory Team (200406), on the Pure Mathematics Subpanel for RAE2008. He was Head of School (20102013) abd the Department of Pure Mathematics (200408).
Professor Greenlees was awarded a Nuffield Foundation Science Research Fellowship for 199596, and the Junior Berwick Prize of the London Mathematical Society in 1995.
Research interests:
Algebraic topology is principally concerned with geometric and
topological problems but, as its name suggests, it uses methods
from
various parts of algebra. Traditionally, this algebra has mostly
been
homological, but Professor Greenlees is concerned with the
topology of
spaces with symmetry, so group theory also plays a part. He has been a
pioneer in the use of commutative algebra in homotopy theory.
The idea of algebraic topology is to replace a slippery geometric object by a more rigid and tractable algebraic invariant. For example, compact surfaces are classified by their Euler characteristics. Accordingly the subject is principally concerned with invariants:
Professor Greenlees is particularly concerned with the topology of spaces with a group action. The group actions and topology interact in fascinating and unexpected ways, and this leads to new insights in algebra as well as topology. The relevant algebra is relatively undeveloped and is rich enough to include representation theory and commutative algebra.
The idea of algebraic topology is to replace a slippery geometric object by a more rigid and tractable algebraic invariant. For example, compact surfaces are classified by their Euler characteristics. Accordingly the subject is principally concerned with invariants:
 with the problem of defining invariants,
 with the theoretical effectiveness of invariants in solving a geometric problems,
 with the calculation of invariants, and
 with the algebra relevant to the invariants.
Professor Greenlees is particularly concerned with the topology of spaces with a group action. The group actions and topology interact in fascinating and unexpected ways, and this leads to new insights in algebra as well as topology. The relevant algebra is relatively undeveloped and is rich enough to include representation theory and commutative algebra.