Title: Sliding window embeddings

Event: Graduate Student Geometry and Topology Seminar

Where: Department of Mathematics, Michigan State University

Date: March 13, 2019

Abstract: Classically, Sliding Window Embeddings were used in the study of dynamical systems to reconstruct topology of underlying attractors from generic observation functions. In 2015, Perea and Harer studied persistent homology of sliding window embeddings from L^2 periodic functions. We defi ne a quasiperiodic function as a superposition of periodic functions with incommensurate frequencies. As it turns out, sliding window embeddings of quasiperiodic functions are dense in high dimensional torii. In this talk, I will present some results for the quasiperiodic case.

Picture by: Tyler Bongers