报告题目一：An overview of the mathematical foundations and recent developments in RBF-based approximation(Ⅰ)

报告时间：2026年8月3日（周一）14:00开始（北京时间）

报告摘要：This lecture provides an overview of the mathematical foundations and recent developments in RBF-based approximation, beginning with the classical scattered data interpolation problem. Particular attention will be devoted to the role of positive definite and conditionally positive definite kernels, whose theoretical properties guarantee the existence, uniqueness, and stability of interpolants.

报告题目二：An overview of the mathematical foundations and recent developments in RBF-based approximation(Ⅱ)

报告时间：2026年8月4日（周二）9:00开始（北京时间）

报告摘要：This lecture continues the overview of mathematical foundations and recent developments in RBF-based approximation, focusing on the connections between positive definite and conditionally positive definite kernels with reproducing kernel Hilbert spaces and native spaces. Hints on error analysis and shape parameter optimization will be presented, too.

报告题目三：Variably Scaled Kernels (VSKs): Foundations and Applications (Ⅰ)

报告时间：2026年8月4日（周二）14:00开始（北京时间）

报告摘要：This lecture focuses on Variably Scaled Kernels (VSKs), an extension of classical kernels in which an additional scaling function enriches the approximation space and enables the incorporation of problem-dependent information. We will discuss how VSKs have proved particularly effective in reconstructing functions exhibiting localized features, anisotropies, or discontinuities, providing a flexible framework for capturing complex behaviors in scattered data approximation.

报告题目四：Variably Scaled Kernels (VSKs): Foundations and Applications(Ⅱ)

报告时间：2026年8月5日（周三）9:00开始（北京时间）

报告摘要：This lecture continues the discussion on Variably Scaled Kernels, focusing on recent variants designed to address specific approximation challenges. We will introduce discontinuous kernels, specifically constructed to preserve jumps and sharp interfaces without introducing spurious oscillations, and rational kernels, which provide enhanced flexibility and approximation power through nonlinear kernel constructions while retaining favorable theoretical properties.

报告题目五：The application of RBFs and VSKs to the numerical solution of partial differential equations (Ⅰ)

报告时间：2026年8月5日（周三）14:00开始（北京时间）

报告摘要：This lecture addresses the application of RBFs and VSKs to the numerical solution of partial differential equations through meshless methods. Unlike finite element or finite difference techniques, meshless approaches rely solely on scattered nodes, making them especially attractive for problems involving complex geometries, moving boundaries, adaptive refinement, and high-dimensional domains. We will discuss the fundamental advantages of meshless methods and their suitability for challenging computational scenarios.

报告题目六：The application of RBFs and VSKs to the numerical solution of partial differential equations(Ⅱ)

报告时间：2026年8月6日（周四）9:00开始（北京时间）

报告摘要：This lecture continues the discussion on RBF-based meshless methods for PDEs, focusing on the basic principles underlying global collocation, local RBF-FD methods, and kernel-based discretizations. We will highlight their accuracy, flexibility, and computational challenges, providing insights into the practical implementation and performance of these techniques across various problem settings.

上述报告地点：91麻豆 江宁校区乐学楼1108会议室

报告人：Stefano De Marchi教授（意大利帕多瓦大学）

主办单位：91麻豆

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报告人简介：Stefano De Marchi is Full Professor of Numerical Analysis at the Department of Medicine of the University of Padova. His research spans approximation theory, kernel methods, multivariate interpolation, and topological data analysis. A co-discoverer of the Padua points. He has authored over 160 publications and delivered more than 120 invited lectures. He chairs the UMI (Italian Mathematical Union) Thematic Group on Approximation Theory and Applications and is Managing Editor of Dolomites Research Notes on Approximation and editor of various mathematical journals, among them BIT Numerical Mathematics. He has been the recipient of the “Knut and Alice Wallenberg Foundation” grant, Uppsala University (Sweden), Visiting Professor programme 2025.