讲座报告主题：Geodesics and Isometric Immersions in Kirigami
地点：腾讯会议ID：521 428 848
主讲简介：韩青，美国圣母大学数学系终身教授。美国纽约大学库朗数学研究所博士，美国芝加哥大学博士后，曾在德国莱比锡马普所和美国纽约大学库朗数学研究所进行科研工作。获美国Sloan Research Fellowship.研究专长：韩青教授长期致力于非线性偏微分方程和几何分析的研究，在调和函数的零点集和奇异集、等距嵌入、退化方程等方面做出了一系列原创性的重要研究成果。
主讲内容简介：Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. The mechanical response of a kirigami sheet when it is pulled at its ends is enabled and limited by the presence of cuts that serve to guide the possible non-planar deformations. Inspired by the geometry of this art form, we ask two questions: (i) What is the shortest path between points at which forces are applied? (ii) What is the nature of the ultimate shape of the sheet when it is strongly stretched? Mathematically, these questions are related to the nature and form of geodesics in the Euclidean plane with linear obstructions (cuts), and the nature and form of isometric immersions of the sheet with cuts when it can be folded on itself. We provide a constructive proof that the geodesic connecting any two points in the plane is piecewise polygonal. We then prove that the family of polygonal geodesics can be simultaneously rectified into a straight line by flat-folding the sheet so that its configuration is a (non-unique) piecewise affine planar isometric immersion. The talk is based on joint works with M. Lewicka and L. Mahadevan.