Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo
“Polycyclic groups”
We’ll begin a discussion of noetherian group rings. The main (but short) theorem is that if G is polycyclic then K[G] is noetherian for all fields K; remarkably these are the only known examples. We can use Connell’s theorem to get the zero divisor conjecture for polycyclic groups. This is maybe too ambitious, but hopefully we can look at Domanov– Farkas–Passman–Roseblade’s theorem that if G is polycyclic and char(K) = 0, then K[G] is primitive if and only if ∆(G) = 1.
MC 5403