Workshop on Topology: Identifying Order in Complex Systems
Busch Campus, Rutgers University
Piscataway, NJ 08854
Speaker: Gareth Alexander, University of Warwick
Title: Topological Order: Umbilics in Chiral Liquid Crystals
Time: 9:30am – 10:30am
Abstract: Recent experimental advances have opened the door to laboratory realisations of a large range of complex textures with distinctive topological properties, including knots, skyrmions and "Hopf fibrations" in optics, fluids, helical magnets and liquid crystals. We will show how the order in these materials can be described in terms of certain naturally defined vector bundles, whose generic zeros we dub umbilics and which manifest themselves in magnetic skyrmions and the lambda defects of cholesteric liquid crystals. Focussing on the examples from liquid crystals we will explain how the geometry of these vector bundles captures the geometry of the material, while their characteristic classes convey the topology.
Speaker: Ronald Coifman, Yale University
Title: Geometries of Sensor Outputs, Inference, Fusion and Information Processing
Time: 9:30am – 10:30am
Abstract: Our goal is to describe extensions of the main tools of signal processing, denoising feature extraction, prediction, regression, to deal with more general data sources such as heterogeneous nonlinearly correlated multisensor inputs, questionnaires, text and other digital documents. In particular we introduce functional geometric dualities between data attributes and datasets.
We describe general methodologies based on various diffusion geometries for building empirical inferential structures on digital data (such as collaborative filters or recommendation engines ). We indicate natural geometries for fusing information through the combination of several inferential structures. Examples covering questionnaire data analysis, multisensor image processing and data fusion will be described.
Speaker : Elizabeth Munch, SUNY Albany
Title: Towards Predicting and Preventing Machine Chatter Using Persistent Homology
Time: 1:30am – 2:30am
Speaker : Frederick Chazal, INRIA
Title: A Few Statistical Properties of Topological Information Inferred from Data
Time: 3:00am – 4:00am
Speaker: Yasuaki Hiraoka, Kyushu University
Title: Topological Data Analysis on Amorphous Structure
Time: 4:30pm – 5:30pm