Advisor:  Dr. Henry Adams

Committee:  Dr. Chris Peterson, Dr. Amit Patel, Dr. Asa Ben-Hur

Title: Persistence and Metric Thickenings

Abstract: This talk will cover multiple related topics in applied topology.  Persistent homology, the main tool of applied topology, is based on the algebraic theory of persistence modules.  This theory has developed over roughly the last twenty years, and I will cover some of the most important results in the area.  Persistence modules are typically constructed as the homology of a filtration of spaces.  These filtrations can include Vietoris-Rips metric thickenings, which are relatively recent constructions based on the more familiar Vietoris-Rips simplicial complexes.  I will describe some of the known results for these spaces, including my recent proof of the homotopy types of the Vietoris-Rips metric thickenings of the circle.

Join Zoom

Meeting:https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fzoom.us%2Fj%2F94645436890%3Fpwd%3DaWlnRVlyditIeWVMVzRFWnJ1TnlDUT09&data=05%7C01%7Cjessica.hopkins%40colostate.edu%7C3f6b7b42634d4d273c2208dad2fcb5b9%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C638054280134436726%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=6d0oPfof%2FRbtVmHc3ZHt%2F9XVZAnxzU4exNvxgR0C1Q0%3D&reserved=0

<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fzoom.us%2Fj%2F94645436890%3Fpwd%3DaWlnRVlyditIeWVMVzRFWnJ1TnlDUT09&amp;data=05%7C01%7Cjessica.hopkins%40colostate.edu%7C3f6b7b42634d4d273c2208dad2fcb5b9%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C638054280134436726%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&amp;sdata=6d0oPfof%2FRbtVmHc3ZHt%2F9XVZAnxzU4exNvxgR0C1Q0%3D&amp;reserved=0>

Meeting ID: 946 4543 6890

Passcode: 497699