Comparing non-archimedean and logarithmic mirror families

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• Samuel Johnston, University of Cambridge
• Friday 29 April 2022, 16:00-17:00
• MR13.

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The past few years have seen much progress in the construction of mirror families associated with log Calabi-Yau varieties. We will briefly review two of these constructions, one due to Gross and Siebert using log Gromov-Witten invariants, and the other due to Keel and Yu in a slightly more restricted setting using naive non-archimedean curve counts. I will sketch a proof demonstrating that in most situations, the two mirror families agree when both can be constructed. The proof for this fact largely amounts to showing a certain log Gromov-Witten invariant is enumerative, so I will provide non mirror symmetry related motivation related to certain concrete enumerative problems, which if time permits, I will address using the above result.

This talk is part of the Junior Geometry Seminar series.

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