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DATE | 2023-03-09 15:10-16:00 |

PLACE | 數學系館 1F3174教室 |

SPEAKER | Dr. Kuan-Wen Lai(賴冠文)（University of Bonn） |

TITLE | Nielsen Realization Problem: from Classical to Modern |

ABSTRACT | The Nielsen realization problem was originally a question posted by Jakob Nielsen in 1932 and answered by Steven Kerckhoff in 1983. The question asks, given an oriented topological surface, whether every finite subgroup of its mapping class group can be realized as an isometry group of a hyperbolic metric on that surface or not. Equivalently, it asks whether the action of the finite subgroup on the moduli space of hyperbolic metrics, called the Teichm?ller space, has a fixed point or not. In recent years, the classical Teichm?ller theory has guided, in various aspects, the development of the theory of stability conditions on triangulated categories. In this talk, I will introduce a categorical analogue of the Nielsen realization problem and its state of art. |