Persistent Holes in the Universe

Monday, October 14, 2013 - 11:00am - 12:00pm
Lind 305
Pratyush Pranav (Rijksuniversiteit te Groningen)
I will present a new topological formalism that, for the first time,
describes topology as a multi-scale concept. This has a direct and strong
relevance to the topological analysis of structure formation process in
the cosmos, given that this proceeds in a hierarchical fashion. Rooted in
algebraic topology, the concepts I will describe stem from (persistence)
homology and Morse theory. Although the mathematical theory behind the
concepts have been known for over a century, only recently have they
become of practical relevance, due to breakthroughs in computational
topology over the last decade.

Taking gaussian random fields and the web-like spatial distribution of
matter in the Universe as running examples, I will demonstrate that the
formalism allows us to describe topology at a level of detail that far
supersedes those provided by the standard topological descriptors like
Euler characteristic and genus. In this context, I will introduce
persistence and ratio landscapes as an empirical statistical description
of persistence homology. They prove to be powerful tools to discriminate
between the spatial structure emanating in different cosmologies. Most
promising is our recent realization that it provides for a novel way of
hunting for primordial non-gaussianities.

In a related aspect, I will present a software for interactive
visualization of the hierarchical topological structures. It exploits the
geometric aspects of Morse theory, to detect, describe and quantify the
filamentary patterns of the Cosmic web. The software is a promising tool
applicable to the analysis of structural patterns in a wide range of
astronomical areas of interest -- the detection and characterization of
stellar streams at galactic scales being a promising candidate.