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Abstracts and Talk Materials
June 15-26, 2009
Topological data analysis: Understanding optical flow
June 22, 2009 2:00 pm - 3:30 pm
June 22, 2009 2:00 pm - 3:30 pm
"Applied topology: motivations from data"
point-set topology intro
motivations from data, statistics, biology, etc.
June 15, 2009 9:00 am - 10:30 am
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
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
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
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
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
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
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
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
June 25, 2009 9:00 am - 10:30 am
Introduction to homotopy limits and colimits
June 25, 2009 2:30 pm - 3:30 pm
June 25, 2009 2:30 pm - 3:30 pm
Gait states for a torus and a disk: "How to talk with robots"
June 18, 2009 2:00 pm - 3:30 pm
June 18, 2009 2:00 pm - 3:30 pm
"Applied topology: motivations from systems"
euler characteristic intro
motivations from networks, sensors, robotics, etc.
June 15, 2009 11:00 am - 12:30 pm
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
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
June 17, 2009 9:00 am - 10:30 am
"Network coverage via homology"
coverage in sensor networks
June 19, 2009 11:00 am - 12:30 pm
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
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
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
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
June 25, 2009 11:00 am - 12:30 pm
The role of information in pursuit evasion: Graph theoretic models
June 16, 2009 2:00 pm - 3:30 pm
June 16, 2009 2:00 pm - 3:30 pm
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