报告专家：顾险峰 美国纽约州立大学石溪分校 教授
报告时间：2023年02月22日 9：00—10：00
报告地点：腾讯会议ID：935-705-479 密码：230222
正阳楼二楼会议室
报告人简介：
顾险峰，美国纽约州立大学石溪分校计算机系帝国创新教授，美国哈佛大学数学与应用中心客座教授，清华大学丘成桐数学中心客座教授。师从微分几何大师丘成桐先生，与丘先生共同创立了跨领域学科计算共形几何”，将现代拓扑与几何应用于工程和医疗等领域。曾获美国国家自然科学基金CAREER奖、中国国家自然科学基金海外杰出青年奖、“华人菲尔茨奖”:晨兴应用数学金奖等。
报告概要：
Structured mesh generation plays a fundamental role in many fields in engineering, such as geometric modelingCAD/CAE and medical imaging.Most geometric models in the CAD industry are represented as spline surfaceswhich are based on structured quadrilateral mesh generation on surfaces with general topologies.There is a long lasting open problem in the field:Does there exist a quadrilateral mesh on a torus with only two singularities.one is ofvalence 3 and the other valence 5?It turns out that this problem cannot be solved using the knowledge from differential topologyRiemanniar geometry directly, but it heavily depends on the surface conformal structure namely Riemann surface structure.In this talkwe will show the intrinsic relation between the quad-meshes and meromorphic differentials and reformulate the quad-meshes as global sections of holomorphic line bundles,the singularities as the characteristic class, which are governed by the Abel-Jacobi theorem. This discovery leads to rigorous and efficient computational algorithms,which play an important role in industrial software design.
