Speaker: Dr. Sarah Percival, Ph.D.

Abstract: As collections of data grow in size, it is increasingly important to have a means of efficiently analyzing data. Topological data analysis (TDA) uses concepts from the mathematical field of topology, which is concerned with the study of shape, to not only efficiently examine large data sets, but to make inferences related to the "shape" of data. In my research, I develop topology-based approaches to data analysis, which I leverage to study biological data sets. First, I will discuss how I use Mapper, a tool from TDA that summarizesdata into a graph, to discover an underlying structure relating the shapes of more than 3,300 Passiflora leaves from 40 different species. As the Mapper graph has a structure, or "shape" of its own, we think of it as a "shape of shapes" that provides information on the interplay between the developmental processes determining leaf shape within a single plant and the evolutionary processes between species. Next, I will discuss my work on optimization of Mapper parameter selection. The traditional Mapper algorithm requires extensive parameter selection, which affects the structure of the Mapper graph. Through the use of information criteria, I present a novel algorithm which automatically optimizes parameters for a given data set. Finally, I will briefly discuss other interdisciplinary projects I have worked on related to TDA and share my vision for future research.