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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/

Topological data analysis: Understanding optical flow
June 22, 2009


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

Introduction to Jplex
June 17, 2009


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

"Topology & data: The future"
June 26, 2009


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

"Mapper for mapping" mapper as an imager. Importance of mapping. Applications of homology to mapping
June 25, 2009


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

"Homology 1" intro to homology simplicial, cellular, cech, & more: simple applications
June 16, 2009


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

"Imaging data sets" linear regression, projection pursuit, multidimensional scaling as methods of imaging data sets
June 24, 2009


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

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


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

"Persistence and point clouds" Functoriality, diagrams, difficulties in classifying diagrams, multidimensional persistence, Gröbner bases
June 23, 2009


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

Introduction to homotopy limits and colimits
June 25, 2009


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

"Computing homology 2: practice" intro to algorithms/software; plex
June 17, 2009


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

"Visualizing data via homology" image statistics data, range patches, neuroscience
June 19, 2009


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


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

"Zig-zags and statistics" bootstrap method, zig-zag persistence, other applications of zig-zag persistence
June 23, 2009


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

Naive counting with sensors
June 19, 2009


Frederick R. 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


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

"Homology 2" morse, morse-conley, hodge & more: simple applications
June 16, 2009


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

Sensor networks and coverage
June 18, 2009


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

"Network coverage via homology" coverage in sensor networks
June 19, 2009


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


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

"Computing homology 1: theory" intro to exact sequences
June 17, 2009


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

"Sheaves and Euler integration" Euler integration and target enumeration
June 22, 2009


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

"Topological signal processing" target localization; integral transforms and euler calculus
June 22, 2009


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

"Consensus and distributed computation" not so sure about this one...
June 25, 2009


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

"Unimodal decompositions" lyusternik-schnirelman category; unimodal category and mode-decomposition in statistics; applications to coordinate-free data
June 24, 2009


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

"Topology & systems: The future"
June 26, 2009


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


William D. Kalies (Florida Atlantic University)
http://math.fau.edu/kalies

Verified homology of nodal domains
June 23, 2009


William D. Kalies (Florida Atlantic University)
http://math.fau.edu/kalies

Computational Conley theory
June 24, 2009


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