Algebraic Topology in Applied Mathematics

NSF/CBMS Regional Conference

Principal Lecturer: Robert Ghrist (University of Pennsylvania)

August 3 - 7, 2009
Cleveland State University

Organizers: Peter Bubenik and John Oprea (Cleveland State University)

Conference Poster

This conference will present 10 lectures by Robert Ghrist focusing on very recent applications of algebraic topology and its methods to problems in modern technological areas. Specific applications include (1) coverage problems in sensor networks; (2) sensor fusion and data aggregation over networks; (3) statistics of (large) data sets with coarse (or coordinate-free) geometric correlation; (4) synchronization and consensus of systems; (5) robot motion planning and coordination; and (6) rigorous interpretation of experimental dynamics. Many of these problems are imperative systems-engineering challenges of direct impact in security, defense, manufacturing, and commerce.

The series will be structured in a manner that prepares students with regards to the algebraic topology, the various direct applications, and, most importantly, the global perspectives that will allow and encourage students to find new applications.

Lectures:
  1. Topology and its (engineering) applications
  2. The Euler characteristic and target counting via sensors
  3. Sheaves and network data aggregation
  4. Homology and coverage in sensor networks
  5. Persistence and high-dimensional data analysis
  6. Morse theory and data reconstruction
  7. Index theory and experimental time-series data
  8. LS-category and mode-counting in statistics
  9. Obstruction theory: synchronization, consensus, and motion-planning
  10. Configuration spaces and robot motion planning
Support (travel, accommodation and meals) is available for approximately 30 participants. Preference will be given to graduate students, postdocs, and researchers without grants.  

Applications should be sent to cbms2009@csuohio.edu and include a statement describing the candidate's interest in the conference. Graduate students should include the name of their PhD advisor, and others should include a CV.

The conference will be held in the historic Mather Mansion at Cleveland State University. Here is a campus map.

Here is a provisional schedule.

About the principal speaker:

Robert Ghrist is a Presidential Early Career Award winner and was named one of Scientific American's ''Top 50'' for research. He is the lead investigator for SToMP: Sensor Topology & Minimal Planning, a 4-year, $7.98M grant, whose goal is to create and utilize mathematical innovations to deduce global structure from local information in distributed and coordinated sensing platforms. The tools used come mostly from topology and geometry. Application domains include sensor networks, multi-agent robot coordination, and pursuit-evasion scenarios.