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The Log-Local-Open Correspondence

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If you have a question about this talk, please contact Dhruv Ranganathan.

We will explore a correspondence between three different kind of curve counts associated to a so called Looijenga pair (Y,D) which is a rational smooth projective surface Y together with a singular anti-canonical snc divisor D. Starting from such an initial data I will explain how we can construct three different geometries whose associated curve counts – the Log, Local, and Open Gromov Witten invariants – are, in ideal situations, related by a surprisingly simple formula. To give an intuition for the correspondence and to highlight some of its features we will explore it through the lens of degenerating targets and by performing some direct calculations.

This talk is part of the Algebraic Geometry Seminar series.

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