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Monday, February 4, 2019

**Abstract:** Courant algebroids originally appeared in the study of constrained Hamiltonian systems, but they are connected to many areas of mathematical physics, including multisymplectic geometry, double field theory, and (my personal interest) 3-dimensional topological field theory. Since a Courant structure involves a bracket that resembles a Lie bracket (but fails to be skew-symmetric), one might expect there to be some groupoid-like structure for which a Courant algebroid is the infinitesimal object. There is reason to believe that the answer should be a "symplectic 2-groupoid," but there are many devils in the details, including even the question of how "symplectic 2-groupoid" should be defined. I will describe various developments in this problem.