Abstract: "Condensation" is a mechanism for producing new topological quantum field theories from existing ones. Gaiotto and Johnson-Freyd have proposed a higher-categorical description of condensation in terms of higher idempotents, generalizing familiar concepts such as idempotent operators and separable algebras to defects of arbitrary codimensions.
In this talk, I will give a conceptual picture of their idea and explain how higher idempotent completions and variants can be used to construct and classify framed fully extended TQFTs. Based on joint work in progress with David Reutter.