# Mathematical Sciences Research Institute

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# Seminar

RAS - Research Seminar (Part 2): Action on Cantor spaces and macroscopic scalar curvature December 07, 2020 (10:00 AM PST - 11:00 AM PST)
Parent Program: Random and Arithmetic Structures in Topology -- Virtual Semester MSRI: Online/Virtual
Speaker(s) Roman Sauer (Karlsruhe Institute of Technology)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

Video

#### Action On Cantor Spaces And Macroscopic Scalar Curvature

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

Abstract: We prove the macroscopic cousins of three conjectures: 1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound, 2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature, 3) a conjectural bound of l2-Betti numbers of aspherical Riemannian manifolds in the presence of a lower scalar curvature bound. The macroscopic cousin is the statement one obtains by replacing a lower scalar curvature bound by an upper bound on the volumes of $1$-balls in the universal cover. Group actions on Cantor spaces surprisingly play an important role in the proof. The talk is based on joint work with Sabine Braun.