Prof. Alex Suciu
MATH 8450 · Research Seminar in Mathematics
Applied and Computational Topology
Fall 2014
Tuesday 2:00pm to 5:00pm in 544NI
|
 Overview
|
The course will be geared towards scientific and engineering
applications of Topology. The goal of the course will be to familiarize
students with modern techniques in algebraic and geometric topology,
and to expose them to topological methods which allow the analysis of
data that is otherwise difficult to investigate using classical methods.
|
|
Data obtained by sampling from highly curved manifolds or singular
algebraic varieties in Euclidean space are typical examples where
such methods apply. Many standard tools rely on linear approximations,
which do not work well in strongly curved or singular problems.
Topological tools such homotopy groups and cohomology rings
measure more qualitative properties of the spaces involved, such
as connectedness, or the number of holes in a space.
|
Topics
Here are some of the topics that we may discuss:
- Combinatorial constructions in topology.
- Configuration spaces and polyhedral products.
- Topological complexity.
- Delaunay triangulations.
- Random simplicial complexes.
- Persistent homology.
|
And here are some of the applications that we may explore:
- Motion planning and topological robotics.
- Random complexes.
- Protein matching.
- Topology and geometry of networks.
- Configuration spaces.
- Topological data analysis.
|
References
|
a.suciu@neu.edu
