CBMS Conference on Topological Data Analysis and Persistence Theory

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This award provides funding for the conference "Topological Data Analysis and Persistence Theory" organised as part of the Conference Board of the Mathematical Sciences series. The event will take place at Valdosta State University in Valdosta, Georgia during August 8-12, 2022. The main goal of this event is to provide an introduction to topological data analysis (TDA) and persistence theory (PT) to a broader audience. TDA and PT are relatively recent methods useful for discovering important features in large data sets using theoretical ideas from several branches of mathematics including algebra and topology. This conference consists of a series of daily lectures given by Dr. Peter Bubenik of the University of Florida, Gainesville. The topics of these lectures include a review of the basic mathematical concepts related to TDA and PT, interactions with statistical methods and machine learning as well as current applications and software implementations. This lecture series will also include a discussion of advanced topics and current research related to TDA and PT. There will be also be two structured Lab Sessions where the participants will be introduced to software that can be used to compute various TDA functions on data sets. Specific elements to be covered during the lectures include: a review of basic concepts related to TDA and PT such as simplicial and cubical complexes, homology, persistence homology (PH), and Vietoris-Rips complexes; interactions of TDA and PT with theoretical algebraic concepts such as commutative rings, graded modules and representation theory of quivers; interactions of TDA and PT with statistical methods such as hypothesis testing and permutation tests as well as interactions with methods from machine learning such as deep learning and multilayer perceptrons; and finally, software implementation and current trends and advances in the research on TDA and PT. There will be also two structured Lab Sessions were the participants will be introduced to software that can be used to compute PH and other TDA functions on data sets. Further information about the conference will be available at the website: https://www.cbmsweb.orgThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.