Program

Friday, August 28, 2009

A reception will be held from 7:00 pm to 10:00 pm. You can pick up your registration materials at this
time. Welcome address, Scott Mitchell (Sandia National Laboratories) at 8:00 pm, continuous slideshow
7:00-10:00 pm.

Saturday, August 29, 2009

7:00 am - 8:00 am	Breakfast & Registration
8:00 am - 8:35 am	JPlex, Henry Adams (Stanford)
8:35 am - 9:10 am	The Linbox library, Clement Pernet (INRIA, Université de Grenoble)
9:10 am - 9:40 am	Break
9:40 am - 10:15 am	An Overview of Trilinos, Heidi Thornquist (Sandia National Laboratories)
10:15 am - 10:50 am	Reeb Graphs (presentation unavailable), Attila Gyulassy (University of Utah)
10:50 am - 11:25 am	A Mathematical Tour of Geomagic Software, Yates Fletcher (Geomagic, Inc.)
11:25 am - 12:30 pm	Lunch
12:30 pm - 1:10 pm	Morse-Smale structures for understanding large-scale 3d combustion simulations (presentation unavailable), Ray Grout (Sandia)
1:10 pm - 1:50 pm	Fracture and Fragmentation of Simplicial Finite Element Meshes using Graphs, Alejandro Mota (Sandia National Laboratories)
1:50 pm - 2:20 pm	Break
2:20 pm - 3:00 pm	Homology of Complicated and Random Evolving Patterns, Thomas Wanner (George Mason University)
3:00 pm - 3:40 pm	Topology in Image Analysis for Distinguishing Tampering from Environmental Degradation of Unique Tags, Kurt Larson (Sandia National Laboratories)
3:40 pm - 4:10 pm	Break
4:10 pm - 4:50 pm	Persistent homology for parameter sensitivity in large-scale text-analysis (informatics) graphs, Daniel Dunlavy (Sandia National Laboratories)
4:50 pm - 5:30 pm	Topological exploration of the variety of minimum-energy cyclo-octane molecular conformations (presentation unavailable), Shawn Martin (Sandia National Laboratories)

Software
The Saturday morning session focuses on existing software efforts for combinatorial algebraic topology. The intended audience is those wishing to use their tools for research framework or application solutions. Speakers are asked to address the following items

scope, current and planned
capabilities, especially:
Betti numbers, homology generators, generators meeting application-specific criteria filtrations & Reeb graphs for sensitivity and transients; Smith Normal Form factorization, other linear algebra capabilities
scalability
software maturity/usability
availability and usage models
please try to limit time on reduction, sampling, and initial complex generation

Talks - Morning (5)

Software talks are 35 min = 25 minutes followed/interspersed by 10 minutes of discussion.

JPlex, Henry Adams (Stanford)
The Linbox library, Clement Pernet (INRIA, Université de Grenoble)
An Overview of Trilinos, Heidi Thornquist (Sandia National Laboratories)
Reeb Graphs, Attila Gyulassy (University of Utah)
A Mathematical Tour of Geomagic Software, Yates Fletcher (Geomagic, Inc.)

Applications
The Saturday afternoon session focuses on laboratory applications, especially those that are not currently using topology, but could. Format consists of an overview talk, together with a discussion session to explore what is possible. The intent is for application owners to engage topology experts for help in solving their problems, with the potential for longer term partnerships. Speakers are asked to address the following aspects of their applications:

geometry, if any
dimension: 3d, higher-d, arbitrary-d
questions needing solution methods
interesting structural features one would like to discover and compute

Talks - Afternoon (6)

Application talks are 40 min = 25 minutes followed/interspersed by 15 minutes of discussion.

Morse-Smale structures for understanding large-scale 3d combustion simulations, Ray Grout (Sandia)
Fracture and Fragmentation of Simplicial Finite Element Meshes Using Graphs, Alejandro Mota (Sandia National Laboratories)
Homology of Complicated and Random Evolving Patterns, Thomas Wanner (George Mason University)
Topology in Image Analysis for Distinguishing Tampering from Environmental Degradation of Unique Tags, Kurt Larson (Sandia National Laboratories)
Persistent homology for parameter sensitivity in large-scale text-analysis (informatics) graphs, Daniel Dunlavy (Sandia National Laboratories)
Discrete combinatorial optimization fitness landscapes, Jean-Paul Watson (Sandia National Laboratories)

Sunday, August 30, 2009

7:00 am - 8:00 am	Breakfast & Registration
8:00 am - 8:35 am	Fast Construction of the Vietoris-Rips Complex, Afra Zomorodian (Dartmouth)
8:35 am - 9:10 am	Linear Algebra Algorithms for Betti Numbers and Torsions, Jean-Guillaume Dumas (Université de Grenoble)
9:10 am - 9:45 am	Approximating Shortest Homology Loops, Tamal Dey (Ohio State)
9:45 am - 10:15 am	Break
10:15 am - 10:50 am	(presentation unavailable) Valerio Pascucci (University of Utah)
10:50 pm - 11:25 am	Computational Homology Project (CHomP), Konstantin Mischaikow (Rutgers)
11:25 am - 12:00 am	Panel Discussion

Algorithmics
The Sunday morning session focuses on algorithmic challenges. The intended audience is those already familiar with the algorithm basics, rather than application owners. Speakers are asked to address one or more of the following aspects of their algorithmic approaches:

algorithmic complexity, including dependence on genus, dimension, number of vertices, number of simplices, coefficient ring, filtration size, and number of critical points what's the hope for explicit bounds, tight bounds, and improvements?
capabilities for sensitivity analysis and transient features, including Reeb graphs, filtrations, and new math structures
application-tailored solutions, e.g. homology generators with specific geometry or cardinality; cycle homotopies
visualization techniques that use topology
visualization techniques for understanding topology

Talks (5)

Algorithm talks are 35 min = 25 minutes followed/interspersed by 10 minutes of discussion.

Fast Construction of the Vietoris-Rips Complex, Afra Zomorodian (Dartmouth)
Jean-Guillaume Dumas(Université de Grenoble), LinBox algorithms: rank and Smith form using blackbox and sparse elimination methods
Tamal Dey (Ohio State)
Valerio Pascucci (University of Utah)
Computational Homology Project (CHomP), Konstantin Mischaikow (Rutgers)

Panel Discussion

Panel:
David Saunders
Peer-Timo Bremer
Dmitriy Morozov
Shawn Martin
Michael Robinson

Panel members will answer one or two of the following questions, followed by a group discussion. Rank applications in terms of low hanging fruit that topology can pluck.
What are the key open problems, or main roadblocks, for advancing algorithms? In particular, comment on scalability, and techniques for high dimensional data. In particular, comment on generalizations of filtrations
What new software or software mechanisms/structure would most benefit the community? "New software" means, what techniques would be valuable to have in accessible and general purpose
format such as LinBox and Plex? "mechanisms/structure" means, would an open-source effort be helpful? And should general and available versions be developed of Reeb graphs, complex generation methods, or anything else in particular?