Abstract: One of the leading questions in many mathematical research programs is whether a certain classification problem admits a “satisfactory” solution. As it turns out, however, some classification problems are intrinsically too complex to admit complete classification by "simple" invariants. Hjorth's theory of turbulence, for example, provides conditions under which a classification problem cannot be solved using only isomorphism types of countable structures as invariants. In this talk we will discuss "unbalancedness": a new dynamical obstruction to classification by orbits of a Polish group which admits a two-side invariant metric (TSI). We will illustrate how "unbalancedness" can be used for showing that a classification problem cannot be solved by classical homology and cohomology invariants, and we will apply these ideas to attain anti-classification results for the problem of classifying Hermitian line bundles up to isomorphism and the problem of classifying continuous trace C*-algebras up to Morita equivalence. This is joint work with Shaun Allison.

univienna.zoom.us/j/63166383248