Presented by: 
Clément Maria, UQ
Date: 
Tue 17 Feb, 3:00 pm - 3:45 pm
Venue: 
Building 1 (Forgan Smith), Room E219

Persistent homology studies the decomposition of persistence modules. A persistence module consists of a collection of homology groups connected by homomorphisms. Two cases will be of particular interest to us. The first of these will be the case of standard persistence, where the homology groups form a sequence, and there is exactly one homomorphism from the i-th to the (i+1)-st group in the sequence. The second case is that of zigzag persistence, which is identical, except that the homomorphism between the i-th and the (i+1)-st homology group is permitted to go in the reverse direction. Standard and zigzag persistence modules admit decompositions into interval modules that have a topological interpretation.

In this talk we give a uniform presentation of standard and zigzag persistence through ideas of quiver theory. We also present algorithms to compute the decomposition of a standard persistence module and of a zigzag persistence module.