Events for 02/21/2024 from all calendars

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 123

Speaker: Alain Valette, University of Neuchâtel

Title: Maximal Haagerup subgroups in Zⁿ x SL₂(Z)

Abstract: The Haagerup property is a strong negation of Kazhdan's property (T). In a countable group, every Haagerup subgroup is contained in a maximal one. We propose to classify maximal Haagerup subgroups in the semi-direct product G_n=Zⁿ x SL₂(Z), where the action of SL₂(Z) on Zⁿ is induced by the unique irreducible representation of SL₂(R) on Rⁿ (with n>1). We prove that there is a dichotomy for maximal Haagerup subgroups in G_n: either (amenable case) they are of the form Zⁿ x K, with K maximal amenable in SL₂(Z); or (non-amenable case) they are transverse to Zⁿ. This extends work by Jiang and Skalski for n=2. In joint work with P. Jolissaint, for n even, we prove the stronger result that the von Neumann algebra of Zⁿ x K (K as above) is maximal Haagerup in the von Neumann algebra of G_n. This involves looking at the orbit equivalence relation induced by SL₂(Z) on the n-torus, and proving that it satisfies a dichotomy: every ergodic sub-equivalence relation is either rigid or hyperfinite. This extends a result by Ioana for n=2.

Student/Postdoc Working Geometry Seminar

Time: 9:00PM - 10:10PM

Location: BLOC 628

Speaker: Derek Wu, TAMU

Title: Boij-Soederberg II