226 Gray Hall

michaelr at american {dot} edu

Prof. Michael Robinson is using algebraic topology to develop powerful new algorithms that will be of immediate use to practitioners. He's focusing on the relationship between complex sets of data, and how they may predict, for example, the network of interactions between biological proteins, or the sonar echoes of mines buried deep at sea.

This page contains supplemental material for a tutorial for mathematicians and scientists to show them this exciting new work. You can view the proceedings through his YouTube channel. Slides and direct links to the videos for these lectures are available through links below.

- Python, via the SciPy stack:

www.scipy.org/install.html

(Includes python, numpy, scipy, and matplotlib). Windows useres might consider WinPython.**Beware: you need Python 2; Python 3 is incompatible with the other libraries we need.** - Pandas python library:

http://pandas.pydata.org/ - Pysheaf library:

https://github.com/kb1dds/pysheaf/ - Perseus persistent homology:

www.sas.upenn.edu/~vnanda/perseus/

- NetworkX Python software package:

http://networkx.github.io/

- Lecture 1: Sheaf Theory: the Mathematics of Data Fusion (slides) (video)
- Lecture 2: What is Topology? (slides) (video)
- Lecture 3: What is a Sheaf? (slides) (video)
- Lecture 4: Data Structures as Sheaves (slides) (video)
- Lecture 5: Categorification and Chain Complexes (slides) (video)
- Lecture 6: Computing Topological Features (slides) (video)
- Lecture 7: Sheaf Cohomology and its Interpretation (slides) (video)
- Lecture 8: How do we Deal with Noisy Data? (slides) (video)

- Shmuel Weinberger,

What is persistent homology?

(intro to applied topology) - Robert Ghrist,

Barcodes: the persistent topology of data

(further on applied topology) - Cliff Joslyn, Emilie Hogan, Michael Robinson,

Towards a topological framework for integrating semantic information sources

(intro to sheaves in data) - Michael Robinson, Cliff Joslyn, Emilie Hogan, Chris Capraro, Conglomeration of heterogeneous content using local topology

(further on sheaves in data)