researchseminars.org

Giles Gardam (Münster)
2021-11-25 15:05 - 15:55 UTC | https://researchseminars.org/talk/GaTO/43/
Title: The Kaplansky conjectures (https://researchseminars.org/talk/GaTO/43/)
by Giles Gardam (Münster) as part of Geometry and topology online

Abstract
Three conjectures on group rings of torsion-free groups are commonly attributed to Kaplansky, namely the unit, zero divisor and idempotent conjectures. For example, the zero divisor conjecture predicts that if $K$ is a field and $G$ is a torsion-free group, then the group ring $K[G]$ has no zero divisors. I will discuss these conjectures and their relationship to other conjectures and properties of groups. I will then explain how modern solvers for Boolean satisfiability can be applied to them, producing the first counterexample to the unit conjecture.
