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Gromov-Witten theory revolves around the enumerative question of counting algebraic
curves in a smooth algebraic variety X meeting n given cycles - the utmost
generalization of the question "how many lines pass through two given points".
Enumerative geometry, degeneration techniques, and mirror symmetry lead us to consider
the analogous question where one also imposes contact orders with a suitable divisor.
I will introduce our work laying general foundations for such a theory. This is joint work with Q. Chen, M. Gross, and B. Siebert. |