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Modul:   MAT770  Oberseminar: Algebraische Geometrie


A proof of Morrison's Conjecture

Dr. Helge Ruddat's talk

Date: 04.05.15   Time: 13.15 - 14.45   Room: Y27H25

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 à la Friedman-Tian and Smith-Thomas-Yau and that are naturally identified via discrete Legendre transform alias mirror symmetry. This proves Morrison's conjecture.