Computational Topology

Session title

Organizer

Afra Zomorodian (Dartmouth College)
Vin de Silva (Pomona College)
Pawel Pilarczyk (University of Minho)

Keywords

Computational topology; topological data analysis; persistence; simplicial and cubical complexes; applied topology; algebraic topology

Description

Computational topology is concerned with theory, algorithms, and software for computing topological invariants. Subareas include, but are not limited to

- Persistence theories:  What are theories for robust identification of 
topological features, such as persistent homology?

- Topological data analysis:  Given a point set sampled from a space, can
we recover the topology of the underlying space?

- Representation:  How can we efficiently represent a topological space on 
a computer, such as witness complexes?

- Geometric computational topology:  Can we compute geometric descriptions 
of topological attributes, such as shortest cycles, under some measures?

- Statistical computational topology:  Can we characterize topological 
phase transitions under sampling?  What is the structure of random data?

- Applied topology:  Can we apply topological tools to problems from 
other fields, such as the coverage problem in sensor networks?

- Computational algebraic topology: How can we effectively represent
topological objects (e.g. manifolds, maps) and compute
algebraic-topological invariants (homology, cohomology, etc.) in an
efficient way?

- Topological methods in dynamical systems: How can we compute
topological invariants in dynamical systems, like the Conley index,
and apply them to the analysis of dynamics?

This session is organized to discuss emerging software tools for computational topology as well as their applications. All forms of software are welcome.