Algebraic Topology in Applied Mathematics
NSF/CBMS Regional Conference
Principal Lecturer: Robert
Ghrist (University of Pennsylvania)
August 3 - 7, 2009
Cleveland State University
Bubenik and John
Oprea (Cleveland State University)
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.
Support (travel, accommodation and meals) is available for
approximately 30 participants. Preference will be given to graduate
students, postdocs, and researchers without grants.
- Topology and its (engineering) applications
- The Euler characteristic and target counting via sensors
- Sheaves and network data aggregation
- Homology and coverage in sensor networks
- Persistence and high-dimensional data analysis
- Morse theory and data reconstruction
- Index theory and experimental time-series data
- LS-category and mode-counting in statistics
- Obstruction theory: synchronization, consensus, and motion-planning
- Configuration spaces and robot motion planning
Applications should be sent
to firstname.lastname@example.org 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