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The small quantum connection for a monotone symplectic manifold is perhaps the most elementary part of Gromov Wittten theory. Nevertheless, there are open conjectures concerning it, which are both very strong and concrete. Those conjectures in turn rest on a simpler layer of questions. I will try to give a picture of where we stand with respect to those simplest questions. (This is joint work with Dan Pomerleano.)

FHT Program Seminar: The Quantum Connection, Familiar And Yet Mysterious