Abstracts and Talk Materials:June 15-26, 2009 Henry H. Adams (Stanford University) Introduction to Jplex
June 17, 2009 2:00 pm - 3:30 pm
Henry H. Adams (Stanford University) 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
Gunnar Carlsson (Stanford University)
http://math.stanford.edu/~gunnar/ "Homology 1"
intro to homology
simplicial, cellular, cech, & more: simple applications
June 16, 2009 9:00 am - 10:30 am
Gunnar Carlsson (Stanford University)
http://math.stanford.edu/~gunnar/ "Computing homology 2: practice"
intro to algorithms/software; plex
June 17, 2009 11:00 am - 12:30 pm
Gunnar Carlsson (Stanford University)
http://math.stanford.edu/~gunnar/ "Spaces 1: complexes"
cech, v-rips, witnesses, alpha, etc. & uses in data
June 18, 2009 9:00 am - 10:30 am
Gunnar Carlsson (Stanford University)
http://math.stanford.edu/~gunnar/ "Visualizing data via homology"
image statistics data, range patches, neuroscience
June 19, 2009 9:00 am - 10:30 am
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 9:00 am - 10:30 am
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 11:00 am - 12:30 pm
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 9:00 am - 10:30 am
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 9:00 am - 10:30 am
Gunnar Carlsson (Stanford University)
http://math.stanford.edu/~gunnar/ Introduction to homotopy limits and colimits
June 25, 2009 2:30 pm - 3:30 pm
Gunnar Carlsson (Stanford University)
http://math.stanford.edu/~gunnar/ "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
Frederick Cohen (University of Rochester)
http://www.math.rochester.edu/people/faculty/cohf/ Naive counting with sensors
June 19, 2009 2:00 pm - 3:30 pm
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.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
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.edu/~ghrist/ "Homology 2"
morse, morse-conley, hodge & more: simple applications
June 16, 2009 11:00 am - 12:30 pm
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.edu/~ghrist/ "Computing homology 1: theory"
intro to exact sequences
June 17, 2009 9:00 am - 10:30 am
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.edu/~ghrist/ Sensor networks and coverage
June 18, 2009 11:00 am - 12:30 pm
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.edu/~ghrist/ "Network coverage via homology"
coverage in sensor networks
June 19, 2009 11:00 am - 12:30 pm
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.edu/~ghrist/ "Sheaves and Euler integration"
Euler integration and target enumeration
June 22, 2009 9:00 am - 10:30 am
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.edu/~ghrist/ "Topological signal processing"
target localization; integral transforms and euler calculus
June 22, 2009 11:00 am - 12:30 pm
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.edu/~ghrist/ "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
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.edu/~ghrist/ "Consensus and distributed computation"
not so sure about this one...
June 25, 2009 11:00 am - 12:30 pm
Robert Ghrist (University of Pennsylvania)
http://www.math.uiuc.edu/~ghrist/ "Topology & systems: The future"
June 26, 2009 9:00 am - 10:00 am
Volkan Isler (University of Minnesota)
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 D. Kalies (Florida Atlantic University)
http://math.fau.edu/kalies Verified homology of nodal domains
June 23, 2009 2:00 pm - 3:30 pm
William D. Kalies (Florida Atlantic University)
http://math.fau.edu/kalies Computational Conley theory
June 24, 2009 2:00 pm - 3:30 pm
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