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### Discrete holomorphic quadratic differentials

**Geometry/Topology**

Speaker: | Wai Yeung Lam, Brown |

Related Webpage: | https://www.math.brown.edu/~lam/ |

Location: | 2112 MSB |

Start time: | Tue, May 1 2018, 1:10PM |

In the classical theory, holomorphic quadratic differentials are tied to a wide range of objects, e.g. minimal surfaces, harmonic functions, Teichmueller space and foliation. We aim at a discretization of holomorphic quadratic differentials that preserves such a rich theory.

We introduce discrete holomorphic quadratic differentials on graphs. Examples from dynamical systems, circle patterns and energy minimization will be shown. We will talk about their connection to discrete conformal geometry and the surface theory. On one hand, they relate discrete harmonic functions, circle packings and Luo’s vertex scaling. On the other hand, they unify discrete minimal surfaces via a Weierstrass representation formula. Further problems will be discussed in the end of the talk.