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Prof. Josiah Park
November 2, 2022 @ 4:15 pm - 5:30 pm
Title: Packing lines, minimizing energy, and applications to communications
Speaker: Josiah Park, Department of Mathematics, Texas A&M University
Abstract: Structured geometric point sets play important roles in coding theory, mathematical biology, computational chemistry, wireless communications, compressed sensing, and ‘big data’ applications due to their often desirable statistical properties for measurement and transmission. Best packings of lines (known as Grassmannian packings) have desirable properties for Multiple-Input Multiple-Output (MIMO) wireless transmission and specific instances of these minimal coherence systems, like equiangular tight frames have a number of interesting mathematical properties. I’ll describe in this talk some research which investigates numerical phenomena related to the point sets, detailing several results on continuous ‘probabilistic’ energies. In addition I’ll talk about some experiments using parallelized computation and optimization methods like trust-region conjugate gradient to numerically generate good packings. Parts of the talk are represented by collaborations with D. Bilyk, A. Glazyrin, R. Matzke, C. Saltijeral, O. Vlasiuk, and M. Zhong.
Josiah Park, Ph. D. is a Visiting Assistant Professor and NSF TRIPODS postdoctoral fellow at Texas A&M University working on the “Neural Network Approximation” project within the Center for Approximation and Mathematical Data Analytics. Josiah is currently a core member at UCLA for the IPAM program on computational microscopy. Previously, he received his doctorate in mathematics at the Georgia Institute of Technology in 2020 under supervision of Professors Christopher Heil and Michael Lacey.