Classical probability theory makes the (mostly, tacit) assumption that any two random experiments can be performed jointly. This assumption seems to fail in quantum theory. A rapidly growing literature seeks to understand QM by placing it in a much broader mathematical landscape of ``generalized probabilistic theories", or GPTs, in which incompatible experiments are permitted. Among other things, this effort has led to (i) a better appreciation that many "characteristically quantum" phenomena (e.g., entanglement) are in fact generic to non-classical probabilistic theories, (ii) a suite of reconstructions of (mostly, finite-dimensional) QM from small packages of assumptions of a probabilistic or operational nature, and (iii) a clearer view of the options available for generalizing QM. This course will offer a survey of this literature, starting from scratch and concluding with a discussion of recent developments.

Mathematical prerequisites: finite-dimensional linear algebra, ideally including tensor products and duality, plus some exposure to category theory (though I will briefly review this material as needed).

Scheduling note: There will be 5 lectures from March 12-26, then a gap of two weeks before the final 2 lectures held April 16 & 18.

Format: In-person only; lectures will be recorded for PIRSA but not live on Zoom.