Bonn Topology Group - Abstracts

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Talk

December 5, 2023
Giles Gardam (Universität Bonn): The Kaplansky conjectures

Abstract

There is a series of four conjectures on group rings attributed to Kaplansky. For example, the zero divisor says that the group ring of a torsion-free group over a field has no zero divisors and the unit conjecture says that its units are all scalar multiples of group elements. I will discuss these conjectures, their relationship to other questions, and why the unit conjecture is false, including new counterexamples.