CMSA Mathematical Physics Seminar: Log Gromov-Witten invariants via degenerations

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January 27, 2020 12:00 pm - 1:00 pm
CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138

Lawrence Barrott - Boston College

A classical question in algebraic geometry asks to count the number of plane curves of degree d meeting a smooth elliptic curve in a single point tangent to order 3d. This question is best reformulated in terms of log Gromov--Witten invariants which I will introduce. By considering the degeneration of the elliptic curve to the toric boundary Navid Nabijou and I provide a localisation formalism to count these curves. We uncover a refined set of enumerative invariants which we believe are related to certain scattering diagram calculations. If time permits I will explain what happens in higher dimension.