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Abstracts and Talk Materials
Applied Algebraic Topology
June 15-26, 2009


Henry Adams - Stanford University
http://www.ima.umn.edu/~henrya/

Introduction to Jplex
June 17, 2009 2:00 pm - 3:30 pm


 

Topological data analysis: Understanding optical flow
June 22, 2009 2:00 pm - 3:30 pm


Gunnar Carlsson - Stanford University
http://math.stanford.edu/~gunnar/

"Applied topology: motivations from data" point-set topology intro motivations from data, statistics, biology, etc.
June 15, 2009 9:00 am - 10:30 am


 

"Homology 1" intro to homology simplicial, cellular, cech, & more: simple applications
June 16, 2009 9:00 am - 10:30 am


 

"Computing homology 2: practice" intro to algorithms/software; plex
June 17, 2009 11:00 am - 12:30 pm


 

"Spaces 1: complexes" cech, v-rips, witnesses, alpha, etc. & uses in data
June 18, 2009 9:00 am - 10:30 am


 

"Visualizing data via homology" image statistics data, range patches, neuroscience
June 19, 2009 9:00 am - 10:30 am


 

"Persistence and point clouds" Functoriality, diagrams, difficulties in classifying diagrams, multidimensional persistence, Gröbner bases
June 23, 2009 9:00 am - 10:30 am


 

"Zig-zags and statistics" bootstrap method, zig-zag persistence, other applications of zig-zag persistence
June 23, 2009 11:00 am - 12:30 pm


 

"Imaging data sets" linear regression, projection pursuit, multidimensional scaling as methods of imaging data sets
June 24, 2009 9:00 am - 10:30 am


 

"Mapper for mapping" mapper as an imager. Importance of mapping. Applications of homology to mapping
June 25, 2009 9:00 am - 10:30 am


 

Introduction to homotopy limits and colimits
June 25, 2009 2:30 pm - 3:30 pm


 

"Topology & data: The future"
June 26, 2009 10:30 am - 11:30 am


Frederick Cohen - University of Rochester
http://www.math.rochester.edu/people/faculty/cohf/

Gait states for a torus and a disk: "How to talk with robots"
June 18, 2009 2:00 pm - 3:30 pm


 

Naive counting with sensors
June 19, 2009 2:00 pm - 3:30 pm


Robert Ghrist - University of Pennsylvania
http://www.math.upenn.edu/~ghrist/

"Applied topology: motivations from systems" euler characteristic intro motivations from networks, sensors, robotics, etc.
June 15, 2009 11:00 am - 12:30 pm


 

"Homology 2" morse, morse-conley, hodge & more: simple applications
June 16, 2009 11:00 am - 12:30 pm


 

"Computing homology 1: theory" intro to exact sequences
June 17, 2009 9:00 am - 10:30 am


 

Sensor networks and coverage
June 18, 2009 11:00 am - 12:30 pm


 

"Network coverage via homology" coverage in sensor networks
June 19, 2009 11:00 am - 12:30 pm


 

"Sheaves and Euler integration" Euler integration and target enumeration
June 22, 2009 9:00 am - 10:30 am


 

"Topological signal processing" target localization; integral transforms and euler calculus
June 22, 2009 11:00 am - 12:30 pm


 

"Unimodal decompositions" lyusternik-schnirelman category; unimodal category and mode-decomposition in statistics; applications to coordinate-free data
June 24, 2009 11:00 am - 12:30 pm


 

"Consensus and distributed computation" not so sure about this one...
June 25, 2009 11:00 am - 12:30 pm


 

"Topology & systems: The future"
June 26, 2009 9:00 am - 10:00 am


Volkan Isler - University of Minnesota, Twin Cities
http://www-users.cs.umn.edu/~isler/

The role of information in pursuit evasion: Graph theoretic models
June 16, 2009 2:00 pm - 3:30 pm


William Kalies - Florida Atlantic University
http://math.fau.edu/kalies

Verified homology of nodal domains
June 23, 2009 2:00 pm - 3:30 pm


 

Computational Conley theory
June 24, 2009 2:00 pm - 3:30 pm


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