  These notes were born out of a five-hour lecture series for graduate students
at the May 2018 Snowbird workshop Crossing the Walls in Enumerative Geometry.
After a short primer on equivariant cohomology and localization, we provide
proofs of the genus-zero mirror theorems for the quintic threefold, first in
Fan-Jarvis-Ruan-Witten theory and then in Gromov-Witten theory. We make no
claim to originality, except in exposition, where special emphasis is placed on
peeling away the standard technical machinery and viewing the mirror theorems
as closed-formula manifestations of elementary localization recursions.
