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Roger Howe (Texas A&M and Yale)


Mathematics Around the Heisenberg Group


The Heisenberg group is the group-theoretic embodiment of the Canonical Commutation Relations (CCR) of quantum mechanics, formulated by Werner Heisenberg just under a century ago. In the intervening years, the CCR and the Heisenberg group have come to be seen as a central nexus in mathematics, connecting and unifying many seemingly disparate phenomena, in harmonic analysis, partial differential equations, operator theory, mathematical physics, Lie theory, representation theory, classical invariant theory, number theory, and more. This talk will survey topics where the Heisenberg group plays an important role, with an emphasis on the connections.