Card shuffling, quantum mechanics and representation theory
It has been known since work of Feynman in the 50s that the behaviour of quantum systems is related to cycles of random permutations,
and for some systems this can be made a precise mathematical claim. Similar problems appear in the, mostly recreational, field of card shuffling.
All these problems can be attacked by representation theory, but algebra alone is not enough, as the functions involved are not class functions.
This creates an exciting analytic-algebraic nexus which has seen lots of progress recently, which I will survey in the talk.
No prior knowledge of any of the topics will be assumed.