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Explore a comprehensive lecture on distinguishing groups and the group isomorphism problem delivered by James Wilson at the Hausdorff Center for Mathematics. Delve into the intricacies of the scale function on totally disconnected, locally compact (t.d.l.c.) groups, examining its continuity and positive integer values. Investigate special cases where the scale can be computed, such as in linear or geometric representations. Analyze the challenges in obtaining representations for all t.d.l.c. groups that allow for scale computation and other group features. Gain insights into the current limitations of our understanding regarding the extent to which such representations are possible. This 56-minute talk, part of the Hausdorff Trimester Program on Logic and Algorithms in Group Theory, offers a deep dive into advanced concepts in group theory and their computational aspects.
