The elementary subject of finite-dimensional linear algebra becomes more exciting in either one of two familiar extensions. If we add parameters, we have the theory of bundles and bundle maps, the base of the bundle being the parameter space. If we endow our linear space with some fixed tensor decomposition so that different parts are controlled by Alice, Bob, Carol, etc., we have quantum information. Joint work by Michael H. Freedman and Matt Hastings, arXiv:2304.01072, begins to consider the “pushout” theory: parameterized entanglement. In this talk, Freedman will present examples to show how the character of entanglement is constrained as one moves in families. The audience is invited to help the authors work out the general theory, and to devise experimental applications.
Michael H. Freedman is a Fields Medal–winning mathematician whose accomplishments include a proof of the four-dimensional Poincaré conjecture, the discovery (with Donaldson and Kirby) of exotic smooth structures on Euclidean 4-space, applications of minimal surfaces to topology, and estimates for the stored energy in magnetic fields. His additional awards and honors include MacArthur, Sloan, and Guggenheim fellowships and the National Medal of Science; he is a member of the American Academy of Arts and Sciences and of the National Academy of Sciences, and a fellow of the American Academy of Arts and Sciences and of the American Mathematical Society. Freedman holds a PhD from Princeton, and has taught at UC Berkeley and UCSD and been a member of the Institute for Advanced Study. He is the founding director of Microsoft Quantum – Santa Barbara (Station Q), a project on quantum physics and quantum computation located on the UCSB campus.
This event will be held in person only.