Dr. Alex McCleary (MSU School of Computing)

4/4/2024  3:10pm

Abstract: 

We present a new language for persistent homology in terms of Galois connections. This language has two main advantages over traditional approaches. First, it simplifies and unifies central concepts such as interleavings and matchings. Second, it provides access to Rota’s Galois connection theorem, a powerful tool with many potential applications in applied topology. In this talk, we'll show how Galois connections and Rota's Galois connection theorem play a crucial role in persistent homology, culminating in a simple proof of the bottleneck stability theorem.