Title: Sliding window embeddings of quasiperiodic functions

Event: 16th Graduate Student Topology and Geometry Conference

Where: Department of Mathematics, University of Illinois at Chicago

Date: April 8, 2018

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 define 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 a strategy to study their persistent homologies.

Picture by: Sujoy Mukherjee