Integral models with nonlocal operators: applications and recent development
Recent applications and theoretical developments of integral models using nonlocal operators have shown promise as effective alternatives to local models, especially in the presence of singularities and anomalies.
Overview
These models also serve as continuum limits for large-scale discrete models used in data learning and network analysis. In this talk, we give an overview of some progress on models involving a finite range of interactions. For problems defined on bounded domains, we discuss various options for modeling the nonlocal interactions both in the interior domain and on the boundary. We also present recent advances in the mathematical and numerical analysis of these problems and their applications.
Presenters
Qiang Du, Fu Foundation Professor of Applied Mathematics at Columbia University
Breif Biography
Qiang Du is the Fu Foundation Professor of Applied Mathematics at Columbia University, where he also chairs the Center of Computing Systems for Data-driven Science. He received his B.S. from the University of Science and Technology of China (USTC) and Ph.D. from Carnegie Mellon University. A Fellow of SIAM, AMS, and AAAS, he now serves as the EIC of the SIAM Journal on Applied Mathematics (SIAP) and the founding co-EIC of Communications of the American Mathematical Society (CAMS). Some of the recognitions for his work include a SIAM Outstanding Paper Prize (2016), a Gordon Bell finalist (2016), the USACM T.J.R. Hughes Medal (2021), and an ICBS Frontier of Science Award (2024).