Applied Algebraic Topology

Course Info

Contacts: Crichton Ogle, o g l e @ m a t h . o h i o - s t a t e . e d u
Facundo Mémoli, m e m o l i @ m a t h . o s u . e d u
Tom Needham, n e e d h a m . 7 1 @ o s u . e d u
Course code Math 4570 -- Spring 2018
Times: MWF 10:20-11:15.
Location: Campbell 335.
Description: In recent years Topology has contributed key ideas to a new discipline sitting at the crossroads of mathematics, computer science, and statistics. These fields interact to create new methods that can be applied to interpret data coming from the life sciences, chemistry, engineering, etc.

This course will teach the main concepts in Applied Algebraic Topology. The course will serve as an introduction to algebraic topology, with a view toward persistent homology of point clouds for applications to data analysis. In order to keep the material accessible to a wide audience, an emphasis will be placed on homology of simplicial complexes over a field. We will focus on building up intuition about what homology measures through concrete examples. We will then move on to the more specialized notion of persistent homology of persistence modules. Real-world applications to data analysis will be provided.

Intended audience and Prerequisites: The prerequisites are Discrete Math and Linear Algebra; in particular, no prior knowledge of topology or abstract algebra will be assumed. Students with familiarity in these subjects are welcome, as there is not a significant overlap with the standard courses. The course will also be appropriate for computer science and data analytics majors with a strong math background.
Tentative Syllabus: [PDF].
Lecture Notes: [PDF].


Meeting 1 (TBA). First meeting. Introduction to the main ideas. Readings: TBA.


Synergistic activities