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Monday, April 27, 2020
4:00 PM - 5:00 PM
Annenberg 105

▶︎ CANCELED: H.B. Keller Colloquium

**CANCELLED**Cities, Voting, and Spiders Spinning under the Influence: Spatial Applications of Topological Tools
Michelle Feng, Graduate Student, Mathematics Department, University of California Los Angeles,
Speaker's Bio:
Michelle Feng is a PhD candidate in the mathematics department of UCLA, working under the supervision of Mason A. Porter. She is a recipient of the 2019 John S. McDonnell Foundation Postdoctoral Fellowship in Complex Systems, and will be joining Computing + Mathematical Sciences at Caltech. Her research focuses on developing topological methods for understanding the shape of human social and political data. Michelle's previous and current projects include characterizing voting patterns, topological models for understanding segregation, dynamical systems on networks with higher order interactions, and a variety of spatial networks. For her postdoctoral research, Michelle plans to continue work on neighborhood formation, segregation, and urban mobility in American cities.

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.

For more information, please contact Diana Bohler by phone at 626-395-1768 or by email at dbohler@caltech.edu.