Department of Mathematics, SMU
Room: 126 Clements Hall (Refreshment starts 15 minutes before talks)
October 3, Wednesday, 3:30pm
Dr. Chia Wei Hsu, Physics, Yale University
Bound states in the continuum and transmission eigen-channels in complex media
I will present numerical and experimental data on two intriguing wave phenomena. The first concerns "bound states in the continuum": harmonic solutions of wave equations that remain spatially localized with no radiation, even though their frequencies are embedded in the continuous spectra of spatially extended states . We demonstrate such perfect confinement of light in periodic nanophotonic structures with open boundaries [2-3]. Second, by modulating the many spatial degrees of freedom in a light field, one can excite "transmission eigenchannels" that perfectly transmit through an opaque scattering medium. We show that such coherent control is significantly enhanced by long-range speckle correlations .
 Nature Reviews Materials 1, 16048 (2016);
 Nature 499, 188 (2013);
 arXiv:1707.01247 (2018);
 Nature Physics 13, 497 (2017).
Wade Hsu grew up in Taiwan, obtained his BA in Physics and in Math from Wesleyan University in 2010, and his PhD in Physics from Harvard University in 2015. He is currently a postdoc at Yale University and will be a faculty at the University of Southern California in 2019. His research centers around controlling light in nanoscale structures and complex systems. He is the co-author of 38 papers and 5 patents. He received the Freeman Scholarship, the LeRoy Apker Award from the American Physical Society, and was a finalist for the Blavatnik Regional Award for Young Scientists.
November 1, Thursday, 3:45pm
Prof. Qing Nie
Departments of Mathematics and Developmental & Cell Biology
NSF-Simons Center for Multiscale Cell Fate Research
University of California, Irvine
Data-driven multiscale modeling of cell fate dynamics
Cells make fate decisions in response to different and dynamic environmental and pathological stimuli. Recent technological breakthroughs have enabled biologists to gather data in previously unthinkable quantities at single cell level. However, synthesizing, analyzing, and understanding such data require new mathematical and computational tools, and in particular, dissecting cellular dynamics emerging from molecular and genomic scale details demands novel multiscale models. In this talk, I will present our recent works on analyzing single-cell molecular data, and their connections with cellular and spatial tissue dynamics. Our mathematical approaches bring together optimization, statistical physics, ODEs/PDEs, and stochastic simulations along with machine learning techniques. By utilizing our newly developed computational tools along with their close integrations with new datasets collected from our experimental collaborators, we are able to investigate several complex systems during development and regeneration to uncover new mechanisms, such as novel beneficial roles of noise and intermediate cellular states, in cell fate determination.
Dr. Qing Nie is a Chancellor’s Professor of Mathematics, Developmental and Cell Biology, and Biomedical Engineering at University of California, Irvine. Dr. Nie is the director of the new NSF-Simons Center for Multiscale Cell Fate Research jointly funded by NSF and the Simons Foundation – one of the four national centers on mathematics of complex biological systems. In research, he uses systems biology and data-driven methods to study complex biological systems with focuses on single-cell analysis, multiscale modeling, cellular plasticity, stem cells, embryonic development, and their applications to diseases. Dr. Nie has published more than 130 research articles and served in many NIH and NSF review panels, maintaining a well-funded interdisciplinary research program. In training, Dr. Nie has supervised more than 40 postdoctoral fellows and PhD students, with many of them working in academic institutions. Dr. Nie is a fellow of the America Association for the Advancement of Science and a fellow of American Physical Society.
November 8, Thursday, 3:45pm
Prof. Ming Gu, Math, UC Berkeley
Advanced techniques for low-rank matrix approximation
Low-rank matrix approximations have become a technique of central importance in large scale data science. In this talk we discuss a set of novel low-rank matrix approximation algorithms that are taylored for all levels of accuracy requirements for maximum computational efficiency. These algorithms include spectrum-revealing matrix factorizations that are optimal up to dimension-dependent constants, and an efficient truncated SVD (singular value decomposition) that is accurate up to a given tolerance. We provide theoretical error bounds and numerical evidence that demonstrate the superiority of our algorithms over existing ones, and show their usefulness in a number of data science applications.
Ming Gu received his Ph.D. in computer science in 1993, and has been a Professor of Applied Mathematics at UC Berkeley since 2008. In 2017, Ming received the best paper award at the 24th IEEE International Conference on High Performance Computing, Data, and Analytics for his work on parallel algorithms for low-rank matrix approximations.
November 15, Thursday, 3:45pm
Prof. Eric Michielssen, Electrical Engineering, University of Michigan
Butterfly+ Fast Direct Solvers for Highly Oscillatory Problems
Fast direct integral equation (IE) solvers for oscillatory problems governed by the Helmholtz and Maxwell’s equations constitute an active area of research in applied mathematics and engineering. Direct solvers represent an attractive alternative to iterative schemes for problems that are inherently ill-conditioned and/or involve many excitations (right-hand sides). Present direct solvers leveraging hierarchical (semi-separable) matrix and related constructs rely on low-rank (LR) representations of blocks of discretized forward and inverse IE operators to rein in the CPU and memory requirements of traditional direct methods. Unfortunately, when applied to highly oscillatory problems, the computational complexity and memory requirements of these solvers suffer from a lack of LR compressibility of blocks of the discretized operators. Recently, we developed a family of butterfly-enhanced direct IE solvers that circumvent this bottleneck. Contrary to LR schemes, butterfly representations are well-suited for compressing highly oscillatory operators and can be used to construct LU and Hierarchical Semi-Separable matrix-based fast direct solvers. The resulting solvers leverage randomized schemes to construct butterfly-compressed approximations of blocks obtained by adding, multiplying, and inverting previously butterfly-compressed matrices. Moreover, to render them applicable to both 2D and 3D scenarios, recursive extensions of classical butterfly structures, termed butterfly+, are called for. The CPU and memory complexities of these solvers are estimated and numerically validated to be O(N log^(2) N) and at most (O(N^(1.5) log N), respectively. Applications of the proposed solvers to radar cross section analysis, wireless propagation in complex environments, and focusing through opaque media involving millions of spatial unknowns will be discussed.
Eric Michielssen received his M.S. in Electrical Engineering (Summa Cum Laude) from the Katholieke Universiteit Leuven (KUL, Belgium) in 1987, and his Ph.D. in Electrical Engineering from the University of Illinois at Urbana-Champaign (UIUC) in 1992. From 1992 to 2005, he served on the faculty at UIUC. In 2005, he joined the University of Michigan, Ann Arbor, where he currently is the Louise Ganiard Johnson Professor of Engineering and Professor of Electrical Engineering and Computer Science. He also serves as the institution’s Associate Vice President for Advanced Research Computing and Co-Director for its Precision Health Initiative. His research interests include all aspects of theoretical and applied computational electromagnetics, with a focus on fast frequency and time domain integral-equation-based techniques for analyzing electromagnetic phenomena, and the development of robust optimizers for the synthesis of electromagnetic/optical devices.
November 29, Thursday, 3:45pm
Prof. Liliana Borcea, Math, University of Michigan
Reduced order model for active array data processing in inverse scattering
We discuss an inverse problem for the wave equation, where an array of sensors probes an unknown, heterogeneous medium with pulses and measures the scattered waves. The goal in inversion is to determine from these measurements scattering structures in the medium, modeled mathematically by a reflectivity function. Most imaging methods assume a linear mapping between the unknown reflectivity and the array data. The linearization, known as the Born (single scattering) approximation is not accurate in strongly scattering media, so the reconstruction of the reflectivity may be poor. We show that it is possible to remove the multiple scattering (nonlinear) effects from the data using a reduced order model (ROM). The ROM is defined by an orthogonal projection of the wave propagator operator on the subspace spanned by the time snapshots of the solution of the wave equation. The snapshots are known only at the sensor locations, which is enough information to construct the ROM. The main result discussed in the talk is a novel, linear-algebraic algorithm that uses the ROM to map the data to its Born approximation.
Liliana Borcea received the PhD degree in Scientific Computing and Computational Mathematics from Stanford University, in 1996. In 1996-97 she was an NSF Postoc in Applied and Computational Mathematics at Caltech, and between 1997-2013 she was a faculty in Computational and Applied Mathematics at Rice University as assistant professor (1997-2001), associate professor (2001-2007) and Noah Harding Professor (2007-2013). Since 2013 she is the Peter Field Collegiate Professor of mathematics at University of Michigan, Ann Arbor. Her research interests are in inverse problems, wave propagation in random media and sensor array imaging in such media.