University of Notre Dame
3:00 PM (EST)
Meeting ID: 944 5222 1633
Title: Some Vignettes in Applied Topology
Abstract: In this talk I will give an overview of my current research program as a new member's introduction to the Department. The unifying theme is applied topology: theory and applications for assigning topological descriptors to data sets.
Most of the talk will discuss a new image analysis pipeline which extracts localized topological summaries from images and uses them to segment out distinct geometric structures. While the pipeline is generally applicable to grayscale images, I will show some results from the motivating data set: Microscopy images of cells' actin cytoskeletons that have undergone various genetic and drug perturbations.
I will also briefly summarize two other research directions: combining applied topology with numerical algebraic geometry to analyze real algebraic varieties and new theoretical results in persistent homology.