Prof Victor Snaith
My research interests include algebraic K-theory, algebraic topology,
algebraic geometry, number theory and representation theory of groups.
These subjects are all closely linked together and I am inclined to
techniques from one to solve problems in another. For example, the idea of
cohomology runs through all these topics, even though cohomology and
homology were first developed in the context of
algebraic topology. Here is another example: stable homotopy theory is a
part of algebraic topology but back in 1985/6 I used it to find a
canonical, explicit form of an existence result in representation theory
called Brauer's Induction Theorem. My formula, called Explicit Brauer
Induction, solved a problem posed by Brauer when he discovered his famous
result in 1946.
Similarly algebraic K-theory, as developed by Quillen in 1973, is a
topological mathematical gadget for studying algebraic geometry which in
turn is used in many of the recent advances in number theory such as
proof of Fermat's Last Theorem. Incidentally the application of algebraic
geometry to number theory is called arithmetic-algebraic geometry.