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Matt Kerr: K_2 and quantum curves

Time: Thu 2021-11-04 15.30 - 16.30

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

Participating: Matt Kerr (Washington University in St. Louis)

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Abstract: The basic objects for this talk are motives consisting of a curve together with a \(K_2\) class, and their mixed Hodge-theoretic invariants. My main objective will be to explain a connection (recently proved in joint work with C. Doran and S. Sinha Babu) between (i) Hodge-theoretically distinguished points in the moduli of such motives and (ii) eigenvalues of operators on \(L^2(R)\) obtained by quantizing the equations of the curves. (Here “distinguished” turns out not to be “special” in the Tannakian sense discussed in B. Klingler's recent talk, but rather a mixed analogue of rank-1 attractor points.) By local mirror symmetry, this gives evidence for a conjecture in topological string theory relating enumerative invariants of toric CY 3-folds to spectra of quantum curves.