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
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