Fractalization, Quantization, and Revivals in Dispersive Systems
报告专家：Peter J Olver（University of Minnesota）
报告时间：2024年9月27日（星期五）上午10:00-11:00
报告地点：国家天元数学西南中心518报告厅
报告摘要：Dispersive quantization, also known as the Talbot effect describes the remarkable evolution, through spatially periodic linear dispersion, of rough initial data, producing fractal, non-differentiable profiles at irrational times and, for asymptotically polynomial dispersion relations, quantized structures and revivals at rational times. Such phenomena have been observed in dispersive waves, optics, and quantum mechanics, and have intriguing connections with number theoretic exponential sums. I will survey results on the analysis and numerics for linear and nonlinear dispersive wave models, both integrable and non-integrable, integro-differential equations modeling interface dynamics, and, time permitting, Fermi-Pasta-Ulam-Tsingou systems of coupled nonlinear oscillators.
专家简介：Peter J. Olver教授是非线性偏微分方程领域国际知名专家，是美国数学会（American Mathematical Society）和工业与应用数学会（ Society for Industrial and Applied Mathematics (SIAM)）fellow，曾任美国明尼苏达大学数学学院院长。Olver教授从事数学物理、非线性偏微分方程及可积系统相关领域的研究，在对称群理论、流体动力学、变分问题、微分几何、计算机视觉和图像处理、几何数值方法等方面的系列工作受到同行的广泛关注和引用。在他的研究领域在全世界范围内受邀做过500多场学术报告，发表160多篇学术论文，出版5部著作。
邀请人：李世豪
