The arrival of massive amounts of data from imaging, sensors, computation and the internet brought with it significant challenges for data science. New methods for analysis and manipulation of big data have come from many scientific disciplines. The first focus of this presentation is the application of ideas from differential equations, such as variational principles and nonlinear diffusion, to image and data analysis. Examples include denoising, segmentation and inpainting for images. The second focus is the development of new ideas in information science, such as compressed sensing and machine learning. The subsequent application of these ideas to differential equations and numerical computation is the third focus of this talk. Examples include solutions with compact support and “compressed modes” for differential equations that come from variational principles, and applications of machine learning to differential equations and physics.

报告人简介：

Caflisch教授是纽约大学库朗数学科学研究所主任，曾经在Stanford和UCLA担任教职，并任基础与应用数学研究所(IPAM)主任，2013年当选美国艺术与科学院院士。

他的主要研究方向为应用数学，包括：偏微分方程、流体动力学、等离子物理、材料科学、蒙特卡罗方法及计算金融。他先后成为工业和应用数学学会Fellow（2009年），美国数学学会Fellow（2012年）。他应邀在2006年国际数学家大会上作了报告。