Mathematics Colloquia and Seminars

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Special values of Riemann Zeta function appear in many places in mathematics quite unexpectedly. In the first part I'll talk about my own encounter with Zeta(1-2g), g > 0, through counting the number of cell decompositions of a Riemann surface of genus g. This process is parallel to the Feynman diagram expansion of a QFT, which leads to the concept of quantum curves. My more recent interest is in Zeta(3), which has a direct relevance to the mirror symmetry of symplectic manifolds and families of complex manifolds. I'll describe the relation between the Gromov-Witten invariants of a Fano variety and Zeta(3).