Mathematics Research Seminar Series: Methods, Challenges, and Trends in Topological Data Analysis

Mathematics  Research  Seminar  Series
Methods, Challenges, and Trends in Topological  Data  Analysis

by Paul Samuel Ignacio PhD
Department  of  Mathematics  and  Computer  Science
University  of  the  Philippines  Baguio

Date:    Friday, 11 March 2022
Time:   4 pm 
Venue:  bit.ly/AdmuMathSeminar

In this series of two talks, I will discuss the main principles, mathematical machinery, obstructions and challenges, and current trends in the development of the theory and applications of Topological Data Analysis ( TDA).

In the first talk, I will provide a basic introduction to abstract simplicial homology, highlight its centrality in the recovery of topological shape information, and how such information may reveal meaningful insights from data. Along this development, I will also discuss the crucial role that functoriality and interleavings play in TDA’s cornerstone stability result, which justifies its use in data analysis.

In the second talk, I will provide descriptions of the general themes that organically arose from challenges and obstructions in the early years of TDA, and describe current directions charted by the most subscribed initiatives in the community. I will also share a quick survey of some initiatives being explored by academics in the local setting.