We consider (chiral, bosonic) rational conformal field theory from
the operator point-of-view, i.e., vertex operator algebras (VOAs).
We discuss rational VOAs and recent work on their structure as
it relates to representations of loop groups. This leads naturally
to a discussion of ideas which allow one to characterize toroidal
compactifications (i.e., lattice VOAs) by numerical invariants.
(Based on joint work with Chongying Dong).
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