Gromov--Witten theory under Birational Maps and Transitions

Abstract:  In this talk I will summarize some of joint work with H.-W. Lin, C-L. Wang and F. Qu on functoriality of Gromov--Witten (GW) theory under birational transformations and extremal transition. In particular, the behavior of GW theory under special smooth flops, flips and blow-ups are discussed. Finally I will explain the functoriality of GW theory of Calabi--Yau threefolds under conifold transitions is best described together with the "B-model" (variations of Hodge structure).