Aristotelis Panagiotopoulos: Dynamical obstructions to classification II

Donnerstag, 22.10.2020 10:30 im Raum SRZ 216/217

Mathematik und Informatik

One of the leading questions in many mathematical research programs is whether a certain classification problem admits a 'satisfactory' solution. What constitutes a satisfactory solution depends, of course, on the context and it is often subject to change when the original goals are deemed hopeless. Indeed, in recent years several negative anti-classification results have been attained. For example: by the work of Hjorth and Foreman-Weiss we know that one cannot classify all ergodic measure-preserving transformations using isomorphism types of countable structures as invariants; and by the work of Thomas we know that higher rank torsion-free abelian groups do not admit a simple classification using Baer-invariants such as in the rank-1 case. In this talk I will provide a gentle introduction to *Invariant Descriptive Set Theory*: a formal framework for measuring the complexity of such classification problems and for showing which types of invariants are inadequate for a complete classification. In the process, I will present several anti-classification criteria which come from topological dynamics. In particular, I will discuss my recent joint work with Shaun Allison, in which we provide a new obstruction to classification by (co)homological invariants and use it to attain anti-classification results for Morita equivalence of continuous-trace C*-algebras and for the isomorphism problem of Hermitian line bundles.

Angelegt am Montag, 19.10.2020 09:55 von pfeifer
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