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DATE | 2023-06-08 16:10-17:00 |

PLACE | 數學系館 1F3174教室 |

SPEAKER | 林偉傑 教授（國立台灣大學數學系） |

TITLE | On the Geometry of the Growing Ball of First-Passage Percolation |

ABSTRACT | In first-passage percolation, one puts i.i.d. nonnegative weights on the nearest-neighbor edges, and studies the induced (pseudo)metric. It is well-known that a metric ball of radius $t$, after rescaled by $1/t$, converges to a deterministic limit shape as $t \to \infty$. However, not too much is known about the ball for finite $t$. In this talk, we will talk about the geometry of a ball of radius $t$, by looking at its boundary. We will discuss the size of the boundary of a ball (based on an earlier joint work with M. Damron and J. Hanson), and, if time allows, we will mention some recent progress on holes in a ball (based on a recent joint work with M. Damron, J. Gold and X. Shen). |