Quantum cohomology of homogeneous spaces -- Anders Buch

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The Gromov-Witten invariants on a homogeneous space G/P are interesting
generalizations of the classical Schubert structure constants, which
enumerate curves rather than points.  Ideas from physics led to the
definition of an associative quantum cohomology ring, which provides an
efficient tool for computing these invariants, and which is itself an
interesting object to study.  One challenge is that quantum cohomology
lacks functoriality, so the quantum rings must be computed case by case.
I will describe highlights from our present knowledge of quantum rings and
Gromov-Witten invariants of homogeneous spaces, and the methods used to
explore them.