Roger Picken, Departamento de Matemática, Instituto Superior Técnico
Quantum theory via (higher) groupoids and quantum measures

The idea of this informal seminar is to present, in cherry-picking fashion, some fascinating work by Ciaglia, Ibort and Marmo, who formulate the Schwinger approach to quantum theory using the contemporary language of groupoids and $2$-groupoids. By bringing in the notion of quantum measures, due to Sorkin, they achieve an elegant description of examples like the qubit or the two-slit experiment.

The aim is for the seminar to be comprehensible also to students with some awareness of quantum theory, and hopefully will be followed up by future seminars around quantum maths topics such as topological quantum computation and entanglement.

Main references

Ciaglia, Ibort, Marmo: https://arxiv.org/abs/1905.12274, https://arxiv.org/abs/1907.03883, https://arxiv.org/abs/1909.07265