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Big Data have been around since Big Bang and the beginning of life, but not yet explored till recently. In addition, data are continually being generated in rapidly increasing volumes and complexity, everywhere, and by just about everything around us. The understanding of Big Data is indeed a most challenging endeavor to the communities of mathematicians, statisticians, engineers and scientists alike. So how big is big? For instance, just consider the molecules that make up the human body: there are 37.2 trillion living cells, and over 600 billion molecules in each cell, including 92 strands of DNA double helix and 8 million RNA strands, for a total whopping number of over 2·10²⁵; and there are roughly 10 trillion galaxies, and on the average, about 100 billion stars in each galaxy, or 10²⁴ stars in the universe. These are big numbers! On top of these huge numbers is data complexity, in that when considered as point-sources, data change in time. For imagery capture, the recent exciting advancement of fluorescence light microscopy, with the capability of viewing well below the hundredth nanometer scale for studying molecular activities, are now available, overcoming the Rayleigh criterion on diffracted light barrier. This was coined ``super-resolution” by the biology and bio-chemistry communities. For observatory astronomy, the forth-coming space telescope, called James Webb (or JWST) will be launched in October, 2018, with the capability of “seeing`` the earliest stars and galaxies and to looking deep into nearby dust clouds to study the formation of stars and planets. In this talk, we will describe the background and development of this fascinating subject and present two current mathematical approaches to super-resolution of light point-sources, including my own recent joint work with Hrushikesh Mhaskar, and beyond.

Prof. Dr. Charles K. Chui

Hong Kong Baptist University / Stanford University