Title: Piecewise Interpretable Hilbert spaces
Abstract: We will discuss a class of Hilbert spaces which are interpretable in first order continuous logic theories in an appropriate sense. These Hilbert spaces offer a unified context for studying definable measures, L^2-spaces associated to absolute Galois groups, and unitary representations of omega-categorical structures. As an application of this systematic study, we will recover a theorem of Tsankov about unitary representations of omega-categorical structures.
This will be an online seminar.