Prof Neil Strickland


Teaching:
Research:
Biography:
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.