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Kaplansky's conjectures

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Kaplansky made various related conjectures about group rings, especially for torsion-free groups. 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 survey what is known about the conjectures, including their relationships to each other and to other group properties such as orderability, and present some recent progress.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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