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DATE | 2016-03-03 16:10-17:00 |

PLACE | 數學館3174教室 |

SPEAKER | 郭庭榕 博士（台大數學系） |

TITLE | Painleve VI Equation and Its Application |

ABSTRACT | bstract: Painlev'e VI equation is a 2nd order nonlinear complex ODE. Hitchin in 1995 proved a beautiful theorem so called the Hitchin theorem which gives explicit expression for a class of solutions to PVI((1/8),((-1)/8),(1/8),(3/8)) (the Hitchin equation). In this talk, I will talk about a deep connection between Hitchin equation and apply it to study the smoothness of solutions to the Hitchin equation. Second, we will generalize the Hitchin theorem to the case PVI((1/2)(n+(1/2))²,((-1)/8),(1/8),(3/8)) where n∈N. As an important application of this generalization, we proved the pre-modular form obtained by Chai, Lin and Wang has simple zeros only and then confirm the Dahmen-Beukers conjecture. |