Differential Geometry Seminar: Coarse cohomology of partitions

Speaker: Matthias Ludewig (University of Greifswald) 

 

Title: Coarse cohomology of partitions

 

Date: 1 August 2025, 11:10am in Engineering & Math EMG07

 

Abstract: One of the challenges in the study of topological insulators is the generalization of invariants such as Chern numbers to the case of disordered (i.e., non translation-invariant) systems. In two dimensions, a proposal was made by Kitaev in his 2005 „Anyons“ paper, which uses a partition of space into three subsets and then measures the difference of clockwise and counter-clockwise hopping between these subsets. In recent work with Guo Chuan Thiang, we were able to interpret the Kitaev formula as a pairing between coarse cohomology and Roe algebra K-theory. As we explain in this talk, this provides a generalization to arbitrary dimensions, as well as a proof that the values of this Kitaev pairing are „quantized", i.e., only take a discrete set of values.