报告题目： Hearing the triangles
报 告 人：刘晓东 研究员 中国科学院数学与系统科学研究院
报告时间：2023年3月31日 10:00-11:00
报告地点：腾讯会议 ID：854-1722-5585
会议链接：https://meeting.tencent.com/dm/FGrbTYZp7mze
校内联系人：刁怀安 diao @ jlu.edu.cn
报告摘要： Since the landmark paper by Marc Kac in 1966, the question "Can one hear the shape of a drum?" has attracted and inspired many mathematicians. This forms the subject of the mathematical discipline called spectral geometry. We introduce a two-step numerical scheme for reconstructing the shape of a triangle by its Dirichlet spectrum. With the help of the asymptotic behavior of the heat trace, the first step is to determine the area, perimeter, and the sum of the reciprocals of the angles of the triangle. The shape is then reconstructed, in the second step, by solving a nonlinear system of equations on the angles using the Newton iterative method. To our best knowledge, this is the first numerical simulation for the classical inverse spectrum problem in the plane. Numerically, we have used only finitely many eigenvalues to reconstruct the triangles. We give a counter example to show that, even if we have infinitely many eigenvalues, the shape of an quadrilateral may not be heard.
报告人简介：刘晓东，2004年本科毕业于北京师范大学，2010年在中科院数学院博士毕业后留所工作，先后任助理研究员，副研究员和研究员，期间于2011年到2013年在德国卡鲁理工大学做洪堡博士后。刘晓东主要研究方向是偏微分方程反问题，特别是基于波散射的数学理论和数值算法。目前，在SIAM系列，JCP, IP等杂志发表40余篇文章。基于这些工作，先后入选数学院陈景润未来之星计划，中科院青年创新促进会和国家高层次人才计划。
