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Critical points of a master function associated to a simple Lie algebra
come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra
. The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms...
We describe hypergeometric solutions of the quantum differential equation of the cotangent bundle of a
partial flag variety. These hypergeometric solutions manifest the Landau-Ginzburg mirror symmetry for the cotangent bundle of a partial flag variety.
We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik–Solomon manifold; it allows us to compute the intersection cohomology of certain flat connections with logarithmic singularities using some Aomoto type complexes of logarithmic forms. Using this construction we realize geometrically the Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.
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