报告题目1：Shift-invariant, bandlimited and shift-invariant reproducing kernel spaces on undirected graphs

报告人：孙颀彧教授，美国中佛罗里达大学

报告时间：2025年5月19日（周一）15:00-16:00

报告地点：20-200

报告摘要：A shift-invariant space of functions on the line is a linear space invariant under integer shifts, which has been widely used in approximation theory, wavelet analysis, sampling theory, Gabor analysis and many other mathematical and engineering fields. In this talk, I will introduce the concept of graph shift-invariant space (GSIS) on an undirected finite graph, and study its bandlimiting, kernel reproducing and sampling properties.

Based on the nested Krylov structure of GSISs in the spatial domain, we propose a novel sampling and reconstruction algorithm with finite steps, with its  performance tested for  flight delay dataset of the  50 busiest airports in the USA. 

The talk is based on a joint paper with Seok-Young Chung.

报告人简介：孙颀彧，美国中佛罗里达大学数学系教授。主要从事傅里叶分析、小波分析、框架理论、信号采样和处理等方面的研究工作。在国际顶尖权威杂志Memoirs of American Mathematical Society, Transaction of American Mathematical Society, Applied and Computational Harmonic Analysis, Advances in Computational Mathematics, IEEE Transaction on Information Theory, IEEE Transaction on Signal Processing, Journal of Fourier Analysis and Applications等发表论文100多篇，被引3000多次。先后担任Journal of Fourier Analysis and Applications,  Sampling Theory in Signal and Imaging Processing, Numerical Functional Analysis and Optimization等期刊的编委。

报告题目2：Theory of Directional Multivariate (Quasi)-tight Wavelet Framelets

报告人：韩斌教授，University of Alberta, Canada

报告时间：2025年5月19日（周一）16:00-17:00

报告地点：20-200

报告摘要：Directional representation systems can effectively capture edge singularities for many high-dimensional problems such as image processing. In this talk, we first discuss directional complex tight framelets and their applications to image/video processing. However, constructing compactly supported multivariate tight framelets is known to be a challenging problem because it is linked to sum of squares and factorization of multivariate Laurent polynomials in algebraic geometry. To circumvent this difficulty, next we introduce the notion of quasi-tight framelets, which behaves almost identical to a tight framelet. From an arbitrary compactly supported multivariate refinable function (such as refinable box splines) with a general dilation matrix, we constructively prove that we can always derive a directional compactly supported quasi-tight framelet with vanishing moments. Moreover, any 1D wavelets or framelets can be adapted into bounded intervals. Consequently, their tensor products can avoid the boundary effects and can be applied to many problems such as manifold data processing and spherical data processing.

报告人简介：Han Bin is a professor in the Department of Mathematical and Statistical Sciences at the University of Alberta, Canada. He graduated from the Department of Applied Mathematics at Fudan University, obtained his Master's degree from the Institute of Mathematics at the Chinese Academy of Sciences, and received his Ph.D. degree from the Department of Mathematical Sciences at the University of Alberta, Canada. He previously worked as a visiting assistant professor at Oklahoma State University and as a postdoctoral fellow in the Department of Mathematics at Princeton University, where his advisor was Professor Ingrid Daubechies (one of the main founders of wavelet analysis).

His main research area is applied and computational harmonic analysis, including wavelet and frame analysis, signal and image processing, computer graphics, and approximation theory. He has published over 90 papers in leading journals in the field, such as Mathematics of Computation, SIAM Journal on Mathematical Analysis, and Applied and Computational Harmonic Analysis, and has authored one monograph published by Springer. He currently serves as an editorial board member for four international academic journals, including Applied and Computational Harmonic Analysis and Journal of Approximation Theory, and has been invited multiple times to give plenary talks at international academic conferences such as the International Conference on Computational Harmonic Analysis.

邀请人：现代分析及其应用数学研究所