Linear Analysis Seminar

Date: September 4, 2015

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Alexandru Chirvasitu, University of Washington

Title: Negative curvature and quantum rigidity

Abstract: Hopf algebra coactions are studied in non - commutative geometry as analogues of algebraic or compact group actions on various structures (algebras, graphs, metric or measure spaces, etc.). Some structures exhibit a rigidity property whereby they admit no``truly non-commutative`` symmetries: Whenever a nice enough Hopf algebra coacts inner faithfully on such a structure, the Hopf algebra in question is commutative and consists of functions on an ordinary compact / algebraic group. I will talk about this phenomenon in the context of metric spaces. Having defined the notion of isometric coaction of a Hopf algebra on a compact metric space, the main result is that the underlying geodesic metric spaces of negatively curved Riemannian manifolds are rigid in the sense above. Conjecturally, the curvature condition should be unnecessary.