Termine

Abstract: I'll give biLipschitz models for the Ricci flow on some 4-manifolds (minimal surfaces of general type) that exhibit a combination of expanding and static behavior.

Abstract: Motivated by the question of understanding topological invariants of hyperbolic three-manifolds arising from Floer theory, I will discuss the problem of determining the spectra of Dirac operators on hyperbolic three-manifolds associated with flat spin^c connections. In particular, I will focus on the case of first Betti number one: in joint work with M. Lipnowski we introduce a method (taking as input natural quantities arising in hyperbolic geometry) which determines in concrete examples the locus corresponding to Dirac operators with kernel.

The landmark completion of the Elliott classification program for unital separable simple nuclear C*-algebras saw three regularity properties rise to prominence: Z-stability, a C*-algebraic analogue of von Neumann algebras' McDuffness; finite nuclear dimension, an operator algebraic version of having finite Lebesgue dimension; and strict comparison, a generalization of tracial comparison in II_1 factors. Given their relevance to classification, most of the investigations into their interplay have focused on the simple nuclear case. The purpose of this talk is to advertise the general study of these properties and discuss their applications both within and outside operator algebras. Concretely, I will explain how characterizing when certain twisted group C*-algebras are Z-stable can provide new partial solutions to a well-known problem in generalized time-frequency analysis; this is joint work with U. Enstad. If time allows, I will also briefly discuss how a different incarnation of tracial comparison (finite radius of comparison) for non-commutative tori relates to the existence of smooth Gabor frames; this last part is joint work with U. Enstad and also H. Thiel.

wissenschaftliches Kolloquium am IDMI