Extremal Transitions and Quantum D-modules 
-- Rongxiao Mi, September 14, 2018

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Extremal transitions are a fundamental surgery that connects topologically distinct Calabi-Yau 3-folds. In order to extend mirror symmetry to larger classes of Calabi-Yau 3-folds, we hope to understand how Gromov-Witten invariants change under such transitions. In this talk, I will outline a conjectural framework in which the change of Gromov-Witten theories is formulated in terms of quantum D-modules. I will then focus on the example of cubic extremal transitions, and also explain how the FJRW theory of the cubic singularity naturally enters the picture.