## MS Seminar (Mathematics - String Theory)

Speaker: | Sergey Galkin (IPMU) |
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Title: |
Mirror symmetries of P^{2} enumerated by Markov triplets. |

Date: | Tue, Jan 19, 2010, 13:15 - 14:45 |

Place: | Balcony B on the 5th floor of the IPMU new building |

Abstract: |
Triplets of integer numbers (x,y,z) satisfying Markov's equation x ^{2} + y^{2} + z^{2} = 3 xyzare in charge of two numerologies for the projective plane P ^{2}:these numbers are the ranks of exceptional bundles and their squares are the weights of Prokhorov-Hacking's degenerations of the plane to weighted projective plane P(x ^{2},y^{2},z^{2}).Batyrev's ansatz states that given a (good) toric degeneration of variety X one may construct a Landau-Ginzburg model mirror dual to X as a Laurent polynomial with the Newton polytope being the fan polytope of the degeneration. I'll show this ansatz holds in the situation of Prokhorov-Hacking's degenerations, and relate the polynomials constructed from different degenerations by birational symplectomorphic mutations. |

Contact: | Kondo |