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Eleny Ionel: Lectures

01/09/2020: Counting embedded curves in 3-folds

January 9, 2020
TITLE: Counting embedded curves in 3-folds

ABSTRACT: There are several ways of counting holomorphic curves in 3-folds. Counting them as maps gives rise to the Gromov-Witten invariant, but in general, these are not integer counts due to the presence of multiple covers with symmetries. In joint work with Tom Parker we constructed an integer count of embedded curves in symplectic Calabi-Yau 3-folds. It conjecturally satisfies a finiteness property. In this talk I outline some of the ideas behind this construction, as well as some of the new ingredients that enter in extending it to the Real setting (in the presence of an anti-symplectic involution). The latter is based on joint work with Penka Georgieva.