Peter A. Linnell
I consider problems in algebra that use some analysis and topology. One problem I have studied is the so-called zero divisor conjecture. This states that if G is a torsion-free group and k is a field, then the group algebra kG is a domain. Though this conjecture has been investigated for over 80 years, it is still open. One can consider similar problems for l^2(G), the Hilbert space with basis the elements of G. This leads to L^2-cohomology, which has topological applications. These problems have been investigated in the case G is an ordered group. Recently these groups have become important in their own right, and involve ergodic theory and looking at the homeomorphisms of the real line.