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Abstract:
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Matter in our Universe tends to aggregate around lower-dimension structures, weaving our Universe into a web-like structure known as the cosmic web. The cosmic web consists of several distinct substructures such as galaxy clusters, filaments, walls/sheets, and voids. The existence of the cosmic web has been observed in realistic sky surveys and computer simulations. Astrophysical theories have predicted the effect of the cosmic web on its nearby celestial bodies. However, testing these astrophysical theories is a non-trivial problem for several reasons. First, the precise definition of the cosmic web remains unclear -- we only know a few characteristics of these structures but there is no consensus on where the cosmic web starts and ends. Second, the effect of the cosmic web is often a complex process and so the quantification of its effect is non-trivial. Moreover, cosmic webs are complex structures and their detections in a large astronomy survey present a non-trivial computational challenge. In this talk, we will present geometric approaches in statistics and machine learning that show great potential in capturing the cosmic web and we will discuss both statistical and computati
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