Quantum cohomology of homogeneous spaces -- Anders Buch

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.