Primoz Skraba: The Persistence Lattice

Abstract

Persistent homology and its variants are actively studied in applied/computational topology. In this talk I will introduce a generalized version of persistence based on lattice theory. I will show how algorithmic construction lead to two operations on homology groups which turn a diagram of spaces into a lattice. This interpretation reduces to known definitions of persistence in the cases of standard persistence, zig-zag persistence and multi-dimensional persistence (specifically a bifiltration). I will discuss some of the properties of this lattice, the algorithmic implications of it, and possible applications.

About the speaker

Primoz Skraba finished his Electrical Engineering PhD at Stanford University in 2008, working for Leo Guibas in the graphics lab on computational topology. Since then he has had postdoctoral appointments at INRIA-Saclay in Paris working on computational geometry and topology before his current position as a Researcher in the AI-Laboratory at the Jozef Stefan Institute in Ljubljana.

Skraba is also the coordinator of the TOPOSYS FP7 grant, which in addition to JSI also involves CVAP/CAS at KTH, Professor Mrozek at Jagellonian University in Krakow, Professor Edelsbrunner at the Institute for Science and Technology, Austria, and Professor Adler at Technion in Haifa.