Talk
The Kaplansky conjectures
- Giles Gardam (University of Münster)
Abstract
There is a series of four long-standing conjectures on group rings that are attributed to Kaplansky. For example, the zero divisor conjecture states that the group ring of a torsion-free group over a field has no zero divisors. I will discuss my recent disproof of the unit conjecture and the connections between the remaining three Kaplansky conjectures and open questions about $L^2$-invariants, K-theory and geometric group theory.
