The present page contains a brief description of what I do, and gives
some links.
My research interests are homological algebra and some of
its areas of application including algebraic geometry, algebraic
topology, representation theory, and ring theory. These are all
related to the part of mathematics called algebra.
A classical aim of homological algebra is to produce invariants. You
take a mathematical gadget (a space, a group, an algebra...), and
apply a homological construction to produce one or more invariants
(typically a sequence of numbers) which describe the gadget. A
discussion of this from the topological side is here,
written by Joseph Neisendorfer. [This page also illustrates the
wasteful use of fabric in international iceskating.]
A more modern point of view is that homological algebra is
unmasking similarities between otherwise distinct areas of
mathematics. For instance, it is possible to find the homological
structures known as triangulated categories in both analysis, algebra, and
topology. Such similarities often make it possible to borrow ideas
from one area into another.
Links