Joint Colloquium: Ken Dykema -- Single commutators and beyond

Operators $A$ and $B$ don’t commute precisely when their commutator $AB-BA$ is nonzero.
From quantum mechanics, we know that noncommuting operators are a fact of life and the
question of which operators can arise as single commutators in various settings is of
interest, {\it e.g.,} the Heisenberg commutation relations.  We will describe some
classical results and some more recent results, as well as open problems and
conjectures, about single commutators, sums of commutators and related topics.