Nonlocality has become increasingly noticeable in nature. The interests in the effective modeling and the numerical simulation of its presence bring on new challenges to mathematicians. In this talk, we will discuss nonlocal models with a finite horizon of interactions and theirs roles in various applications. We will also reveal some practical risks due to inappropriately developed nonlocal models and numerical discretizations. We will show how systematic mathematical analysis can help making nonlocal modeling and simulations more effective and robust for problems in solid and fluid mechanics, autonomous vehicle traffic flows, and deep learning.

杜强教授1988年获美Carnegie Mellon大学Ph.D博士学位。现任Columbia University 傅氏基金应用数学讲席教授（Fu Foundation Applied Mathematics Professor），应用数学课程主任和数据科学研究所成员，主要研究方向为偏微分方程数值解及其在材料、生物和计算几何中的应用等。杜强教授是美国科学促进协会（AAAS）会士（2017）、美国工业与应用数学学会会士（2013），且获得过冯康科学计算奖 、SIAM杰出论文奖（2016）等奖项，并曾入选中国科学院“百人计划”并担任科技部973计划“大规模科学计算研究”首席专家。杜强教授在应用和计算数学及其在材料、生物和计算几何中应用等研究领域做出了杰出贡献，是2018年国际数学家大会45分钟大会报告人。