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Date | Jul 09, 2024 |
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Speaker | Yongquan Zhang |

Dept. | Stony Brook university |

Room | 선택 |

Time | 10:00-11:00 |

Circle packings on the Riemann sphere play an important role in many problems in geometry, dynamics and number theory. For example, the Apollonian gasket is the limit set of a Kleinian group, homeomorphic to the Julia set of some rational map, and satisfies many interesting number-theoretic properties.

Given a circle packing, we can record its combinatorics by its contact graph, whose vertices and edges correspond to circles and touching points between two circles respectively. It is interesting to understand the following questions in the opposite direction: given a graph in the sphere, does there exist a circle packing with the same combinatorics? If so, is the packing unique up to Möbius transformation? These questions are answered for finite graphs by Kobe-Andreev-Thurston, and have been studied extensively for some infinite graphs (e.g. the infinite hexagonal graph).

In this talk, I will discuss some recent joint work with Yusheng Luo and give a complete answer to these questions for graphs generated by subdivision rules, using renormalization theory and iterations on Teichmüller spaces. Examples include the Apollonian gasket, and in fact all circle packings appearing as limit sets of Kleinian groups. If time permits, I will also discuss some applications to rigidity of Kleinian groups, and relatively hyperbolic groups in general.

줌 주소:

Invite Link: https://snu-ac-kr.zoom.us/j/89932707718?pwd=fNw2mmOofh2Kyhy0vc4t7AbgaMimu4.1

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