Date | 2018-04-30 |
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Speaker | 천세훈 |

Dept. | 연세대학교 |

Room | 129-307 |

Time | 16:30-19:30 |

Abstract: The world is full of curved objects of anisotropic materials that are mostly not stationary but moving at varying speed. Even state-of-the-art computational techniques are often inaccurate and unstable, or at least very expensive to model this kind of geometrically-realistic physical and biological phenomena. One of the ways to overcome this difficulty has been regarded to hammer the realistic objects by the projection of Euclidean framework without being hassled by the metric tensor. However, another breakthrough was achieved through a peculiar perspective of Elie Cartan who saw the world 100 years ago as the collection of infinitesimally Euclidean, isotropic, and possibly stationary objects. It is called method of moving frames. A handful attempts have been made to make this beautiful mathematical theory into practical methodologies, but applications to solving PDEs has been unknown. In this talk, I will explain how Cartan’s unique geometric theory in the continuous world has been adapted to the discrete world of scientific computation to provide us an efficient perspective and consequently tool to computationally model the natural phenomena on the realistic geometry, or we may say the blue print, of the world, especially in meteorology, electrodynamics, cardiology, and data science.

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