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Date | Aug 22, 2024 |
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Speaker | Peter Albers |

Dept. | Universität Heidelberg |

Room | 129-406 |

Time | 10:30-12:00 |

We introduce a new type of billiard dynamics about an arbitrary submanifold inside a symplectic vector space. While the definition is direct and elementary, this billiard map is motivated by a (loose) analogy/translation from the standard Euclidean billiard. We study basic dynamic questions e.g. concerning existence of periodic orbits etc. Then we explore two interesting cases, where the submanifold is a curve respectively a Lagrangian submanifold. The latter has an intriguing connection to a theorem by Hopf from 1940.

The talk does not assume prior knowledge of billiards and only rather basic knowledge of (linear) symplectic geometry. This is joint work with Ana Chavez-Caliz and Sergei Tabachnikov.

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