Abstract
Flying patterns of bumblebees are intriguing to ecologists, while propagating cracks in materials are serious concerns of engineers. Recent development of nonlocal mathematical models which serve as alternatives to traditional continuum models based on partial differential equations, has led to a common framework for the study of these different phenomena.
In this lecture, the speaker will introduce some basic elements of nonlocal models such as nonlocal vector calculus, nonlocal function spaces, asymptotically compatible discretization, and seamless coupling of local and nonlocal models. He will also discuss connections to discrete calculus for graph analysis and manifold learning and numerical approximation of partial differential operators based on their integral relaxations.
About the speaker
Prof Qiang Du received his BS in Mathematics from University of Science and Technology of China in 1983 and PhD in Mathematics from Carnegie Mellon University in 1988. He then joined the University of Chicago and moved to the Michigan State University in 1990 as an Assistant Professor. In 1996, Prof Du joined HKUST as a Senior Lecturer and eventually became a Professor. In 2001, he was appointed a Professor of Mathematics in the Pennsylvania State University and he is currently the Fu Foundation Professor of Applied Mathematics in Columbia University since 2014.
Prof Du’s research interests focused on mathematical modeling and applications, numerical analysis and scientific computing. He received numerous awards including the Feng Kang prize in scientific computing (2005) and SIAM Outstanding Paper Prize (2016). He was also selected as a SIAM Fellow in 2013 for contributions to applied and computational mathematics with applications in materials science, computational geometry, and biology.
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