A generalization of the Hori-Vafa conjecture
-- Ionuţ Ciocan-Fontanine

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A few years ago, Hori and Vafa conjectured that the
Landau-Ginzburg model mirror to the nonlinear sigma-model on a Grassmannian
can be obtained by "symmetrizing" the Landau-Ginzburg model mirror to a
product of projective spaces. In particular, this conjecture predicts a
precise relation between the J-functions (generating functions for certain
genus zero Gromov-Witten invariants) of these varieties. This talk will
describe joint work with Aaron Bertram and Bumsig Kim in which we argue
that the appropriate general context for the above relationship is that of
twisted GW invariants of abelian and nonabelian GIT quotients. As a
concrete example, I will present a theorem giving closed formulas for the
J-functions of all isotropic partial flag varieties of classical type.