▶︎ CANCELED: H.B. Keller Colloquium

Persistent Homology (PH) has been used to study the topo-

logical characteristics of data across a variety of scales. In this talk, I will

focus on a variety of spatial applications, as the geometric and topolog-

ical features of PH are well suited to exploring data sets which are em-

bedded in space. I will introduce two novel constructions for transforming

network-based data into simplicial complexes suitable for PH computations

and compare these constructions to state of the art. Additionally, I will

discuss some results from applying these constructions to a variety of ge-

ographic and spatial applications, including voting data, cities and urban

networks, and spiderwebs. I will highlight the computational performance

of our constructions and discuss the implications of the PH computations

for identifying and classifying certain features in our various data sets. In

particular, I will talk about spatial patterns which emerge in each case, and

how those patterns relate to existing scholarship. I will also discuss future

directions for the application of topological tools to social science and urban

analytics.