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Mathematics Conferences Introduction to Gross-Siebert Program
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Conifold transitions and a proof of Morrison's conjecture
SPEAKER  |  Helge Ruddat
INSTITUTE  |  JGU Mainz, DE
DATE  |  May 10(Sun), 2015
TIME  |  14:30
PLACE  |  1114 International Conference Room, KIAS
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ABSTRACT  |  Conifold transitions and a proof of Morrison's conjecture (Ruddat) Morrison conjectured that mirror symmetry dualizes conifold transitions of Calabi-Yau threefolds. Since mirror symmetry is a phenomenon at a maximally unipotent boundary point of the Calabi-Yau moduli space, in order to prove the conjecture, one needs a theory combining conifold transitions with maximal degenerations. I will report on joint work with Siebert where we produce such a theory by giving a comprehensive account on conifold transitions in the Gross-Siebert program. We exhibit tropical homology groups that control the obstructions ? la Friedman-Tian and Smith-Thomas-Yau and that are naturally identified via discrete Legendre transform alias mirror symmetry. This proves Morrison's conjecture.
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