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1:00pm to 2:00pm - RH 340N - Dynamical Systems Grigorii Monakov - (UCI) TBA |
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3:00pm - RH 440R - Logic Set Theory Yash Lodha - (Purdue University) Generic torsion-free groups and Rubin actions We investigate the question of whether a generic countable torsion-free group admits sufficiently rich actions on topological spaces. We are motivated primarily by the problem of deciding whether or not there exists a countable torsion-free group which admits no non-trivial action on a compact manifold. We use model theoretic forcing to prove that a generic countable torsion-free group does not admit any non-trivial locally moving action on a Hausdorff topological space, and yet admits a rich Rubin poset. This is joint work with Thomas Koberda. |
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4:00pm - RH 306 - Colloquium Yash Lodha - (Purdue University) A solution to the Wiegold problem on perfect groups One of the most fundamental notions in group theory is the notion of the normal rank of a group. This is the smallest size of a set of elements, which if included in the set of relations, render the group trivial. The smallest number of factors in the direct sum decomposition of the group abelianization provides a natural lower bound for the normal rank. The 1976 Wiegold problem on perfect groups asks whether there exist finitely generated perfect groups whose normal rank is greater than one. We demonstrate that free products of finitely generated perfect left orderable groups have normal rank greater than one. This solves the Wiegold problem in the affirmative, since a plethora of such examples exist. This is joint work with Lvzhou Chen. |