Back to Departmental Colloquium: Spring 2022
Departmental Colloquium
Date: Thursday, Apr 7, 2022
Time: 4:00PM
Location: JWB 335
Elizabeth Munch
Michigan State University
Title |
Interleaving Distances for Reeb Graphs |
Abstract |
Reeb graphs and other related graphical signatures have extensive use in applications, but only recently has there been intense interest in finding metrics for these objects. The idea is that graphical signatures such as Reeb graphs, merge trees, and contour trees encode data in both a space and a real valued function, and we want to build metrics that are sensitive to this information. In this talk, we will focus on a particular metric for comparing Reeb graphs known as the interleaving distance which is a categorical reformulation of the eponymous metric from persistence modules arising in Topological Data Analysis. These ideas come from viewing the data of a Reeb graph as stored in a sheaf, allowing both for more combinatorial views of the distance, as well as generalizations to other categorical frameworks which fit this model. |
Commutative Algebra
Combinatorics
Topology