Final Report Summary - GEOMANGROUP (Geometry and Analysis of Group Rings)
One of the main breakthroughs was a solution of a Conjecture of Deninger and a Conjecture of Lück about the entropy of algebraic actions of amenable groups and the vanishing of L2-torsion for amenable groups. These (at first sight) unrelated conjectures could be proved in joint work with Hanfeng Li from SUNY Buffalo using an astonishing combination of homological algebra and entropy theory. These results were published in the Journal of the AMS.
The understanding of the class of sofic groups and the classes of groups satisfying similar approximation properties could be deepened considerably. A relationship between the cost of a group and Dixmier’s Unitarisability Conjecture could be proved. In general, the project provided evidence that the multidisciplinary approach of Andreas Thom can yield substantial progress when applied to various longstanding problems.