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Julianne Chung (Emory University)5/18/26, 8:30 AMPlenary TalksPlenary Talk
Iterative Krylov projection methods have become widely used for solving large-scale linear inverse problems. However, methods based on orthogonality include computations of inner-products, which becomes costly when the number of iterations is high, are a bottleneck for parallelization, and can cause the algorithms to break down due to information loss in the projections.
In this talk, I...
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Hugo Woerdeman (Drexel University)5/18/26, 9:25 AMPlenary TalksPlenary Talk
After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the settings of sequence spaces $\ell^p$ (including the finite dimensional case), the associated function space $\ell_A^p$, Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in ${\mathbb C}^n$, as well as the Hardy space on the polydisk and half-space....
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Arvind Krishna Saibaba (North Carolina State University)5/19/26, 8:30 AMPlenary TalksPlenary Talk
Estimating the trace of a matrix, that is only accessible by matrix-vector products, is a fundamental task in scientific computing and data science. This has many applications including network analysis, estimation of matrix norms and spectral densities, estimation of log-determinants, etc. Monte Carlo methods is one of the prevalent approaches for estimating the trace of the matrix. We...
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Jephian C.-H. Lin (National Yang Ming Chiao Tung University)5/19/26, 9:25 AMPlenary TalksPlenary Talk
Inverse problems on a graph investigate how spectral behaviors interact with the matrices associated with the given graph. Such problems not only uncover structural information about the graph from its spectral data, but also identify fundamental properties shared by all matrices defined on the graph. A classic example is the Colin de Verdière parameter, which characterizes planarity via the...
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Haim Avron (Tel Aviv University)5/20/26, 8:30 AMPlenary TalksPlenary Talk
The field of quantum computing offers a unique opportunity to revolutionize numerical linear algebra and scientific computing. This stems from the ability of quantum computers to efficiently model complex structures, and to represent and manipulate high-dimensional vectors and matrices using exponentially fewer qubits. These advantages arise from the fundamental principles of superposition and...
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Aida Abiad (Eindhoven University of Techonolgy)5/20/26, 9:25 AMPlenary TalksPlenary Talk
One of the main goals in spectral graph theory is to deduce the principal properties and structure of a graph from its graph spectrum. In this talk we will show how spectral graph theory provides powerful methods for obtaining results concerning substructures of graphs, and also how these results can be useful in other mathematical fields such as coding theory. In particular, we will derive...
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Sirani M. Perera (Embry-Riddle Aeronautical University, USA)5/21/26, 8:30 AMPlenary TalksPlenary Talk
Millimeter waves within the sub-terahertz band offer a plethora of applications in next-generation wireless communication. However, they also introduce severe real-time and hardware limitations, making conventional wideband multi-beam beamforming exceedingly complex. For example, an $N$-element array using true-time delay beamformers needs $\mathcal{O}(N^2)$ time delays or phase shifts, while...
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Chi-Kwong Li (College of William and Mary)5/21/26, 9:25 AMPlenary TalksPlenary Talk
The numerical range is a fundamental tool for understanding the properties of matrices and operators. In this talk, we discuss recent advances in the study of the numerical range and its generalizations, specifically focusing on their utility in analyzing operator dilations. We demonstrate how these theoretical frameworks provide critical insights into applied topics, including quantum...
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Sherry Li (LBNL)5/22/26, 10:45 AMPlenary TalksPlenary Talk
Hierarchically low-rank (H-LR) matrices have been widely used to design fast solvers for integral equations, boundary element methods, discretized PDEs, and kernel matrices in statistical and machine learning. The computational bottleneck in these solvers is often the construction algorithm which converts a standard dense matrix into an H-LR format. We will present two types of algorithms for...
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John Urschel (MIT)5/22/26, 11:40 AMPlenary TalksPlenary Talk
Given a symmetric matrix with a given sign pattern, what can the sign patterns of its eigenvectors look like? This simple question is closely related to the study of discrete nodal statistics, and draws strong parallels with classical results in analysis for Laplacian eigenfunctions. In this talk, we will give an overview of the field, covering key results on nodal sets for graphs and their...
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