22M:305:001 (MATH:7450:0001)
Topics in Topology
Spring 2013
12:30P - 1:45P TTh 113 MLH
Instructor: Dr. Isabel
Darcy
Office:B1H MLH
Phone: 335- 0778
Email: idarcy AT math.uiowa.edu
Office Hours: MF 11:40 - 12+, Tu 2:00pm - 3:20pm, Th 2:00 - 3:00pm
and by appt.
Note: + means I will be also available directly after the office hour,
normally for as long as needed
Text: We will use the online textbook available at
http://www.math.upenn.edu/~ghrist/notes.html , plus supplementary
material.
Syllabus:
http://www.math.uiowa.edu/~idarcy/COURSES/305/SPRING10/syl305.html
Tentative Schedule (for additional course material, also see ICON)
| Week 1 |
Ch 1 |
| Week 2 |
Ch 2 |
| Week 3 |
References:
On the
Topology of Plans
Michael Erdmann
On the
Topology of Discrete Planning with Uncertainty,
Michael Erdmann
On
the Topology of
Discrete Strategies, Michael Erdmann
|
| Week 4 |
nms.csail.mit.edu/~aklmiu/6.838/L7.ppt
www.cse.yorku.ca/~andy/courses/6114/Slides/CG9-Voronoi.pptx
|
| Week 5 |
Gunnar Carlsson notes
IMA
Lecture 7: Persistent Homology, Gunnar Carlsson (pdf)
IMA Lecture 7 video
|
| Week 6 |
Computing Persistent
Homology
|
| Week 7 |
On the nonlinear statistics
of
range image patches
"Visualizing Data via Homology" image statistics data, range patches, neuroscience (video),
slides
Topological data analysis: Understanding optical flow(video)
|
| Week 8 |
On Persistent Homotopy, Knotted Complexes
and the Alexander Module,
|
| Spring Break |
| Week 9 |
The Theory of Multidimensional Persistence |
| Week 10 |
Computing
Multidimensional
Persistence,
Grobner basis (in MathJax),
Discriminative
persistent homology of brain networks
|
| Week 11 |
Persistent
Homology of Complex Networks
Discriminative
persistent homology of brain networks
Persistent
Brain Network Homology From the Perspective of Dendrogram
Applications of
computational homology to the analysis of treatment response in breast cancer
patients
Topological
analysis of gene expression arrays identifies high risk molecular subtypes in breast
cancer
|
| Week 12 |
Topological
analysis of population activity in visual cortex.
Arousal
increases the representational capacity of cortical tissue
video: "Visualizing Data via Homology"
image statistics data, range patches, neuroscience,
slides
Topology
and Data
Topology based data analysis
identifies a subgroup of breast cancers with a unique mutational profile and excellent
survival
Extracting
insights from the shape of complex data using topology
A
Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology
Structure
of the afferent terminals in terminal ganglion of a cricket and persistent homology
Topological
Analysis of Variance and the Maxillary Complex,
video,
data
|
| Week 13 |
|
| Week 14 |
|
| Week 15 |
|