Paul Seidel MIT https://math.mit.edu/~seidel/ Thursday, October 30, 2025 - 4:00pm Boyd 304 Title: The quantum connection: topology, analysis, arithmetic Abstract: The class of Fano varieties (or monotone symplectic manifolds) includes many of the most commonly encountered manifolds (complex projective spaces, Grassmannians, flag varieties, quadrics, cubic surfaces...). The classical enumerative geometry of rational curves becomes the theory of genus zero Gromov-Witten invariants. In spite of its ancient nature, there are many open conjectures relating the topology of these manifolds to their Gromov-Witten theory (such as the Gamma conjectures of Galkin-Iritani). More recently, we've added another layer of mystery by considering the Gromov-Witten invariants to take values in the homology mod p, or with p-adic coefficients. I'm not sure how much of this story I can tell in an hour, but I will try! One advantage is that many questions are formulated in elementary terms, using linear ordinary differential equations (the quantum connection from the title)
