报告主题：Laplacian Eigenvalues on Some Tetrahedra
主讲人：李会元
报告时间：2020年12月10日（周四）14:30—15:30
报告地点：线上讲座（腾讯会议ID:825991549）
主讲人简介：
李会元，中国科学院软件研究所研究员，博士生导师。曾经在美国普渡大学、美国南卡罗来纳大学、新加坡南洋理工大学以及香港城市大学做访问学者,主要研究方向为高性能科学计算与数学软件、流体力学谱方法与谱元方法、晶格傅立叶分析与快速变换、偏微分方程特征值问题等。在Math. Comp、SIAM. J. Numer. Analysis、Applied and Computational Harmonic Analysis、Journal of Computational Physics等国际专业SCI杂志上发表论文60余篇，主持国家重点研发计划高性能计算重点项目、国家自然科学基重大研究计划培育项目以及多项国家自然科学基金面上项目等。
报告摘要：
In the talk, we explore the Laplacian eigenpairs on some fundamental tetrahedra via Fourier analysis associated with 3-dimensiponal root systems. Firstly, admissible 3-dimensional root systems are introduced, and orthogonal families of complex exponentials are established on the primitive cells of the A3, B3 and C3 root lattices. Trigonometric functions are obtained from those complex exponentials, and then are proved to be exactly the Laplacian eigenfunctions on the fundamental tetrahedra which are defined as the asymmetric unit of these root lattices. Some properties on the Laplacian eigenvalues on the fundamental tetrahedra are studeied in the sequel.