Description

CAT Summary Report

Purpose
The purpose of the workshop is to bring together combinatorial algebraic topology (CAT) researchers from universities, Sandia and other national laboratories for a technical exchange. The workshop will feature talks and ample discussion time on algorithmic issues, established CAT software efforts, and novel applications. The workshop will also introduce CAT researchers and selected Sandia application owners. Most of these applications have been selected because they are not using topology currently, but could. The workshop encourages the establishment of university-labs partnerships.

Themes
The workshop themes include algorithmic challenges, software, and novel applications. Of special interest are algorithms for Betti numbers, homology generators, and Reeb graphs. The workshop encourages discussions of scalability: e.g. with respect to the dimension of the complex; the number of vertices or simplices; and parallelism on MTA, cloud, cluster, or MPP architectures.

The workshop will include a session on CAT software, including overviews and discussions of the intended scope of these efforts, as well as their maturity, scalability, and capability. Of special interest is their capabilities for homology generators, application-specific generators, filtrations and Reeb graphs for sensitivity and transients.

Issues of data sampling, manifold reconstruction, reduction, and simplicial complex types may arise but these are purposely not emphasized by this workshop.

Background
Sandia has an algorithm effort in Morse theory for understanding the process of fuel combustion, and a nascent effort in homology generators for text-based information graph analysis.

Come enjoy a workshop in Santa Fe before classes begin!