Computational Topology : Theory and Applications

JAN 2022

Topology is a branch of mathematics which studies how spaces are connected. And, computational topology, specifically, concerns algorithms useful for computing the topological properties of a given space. This is a young and rapidly growing field that is fueled by interesting data analysis applications in domains such as medicine, cosmology and materials science. This growing interest is not at all surprising since the present day need to deal with large and high dimensional data sets necessitates use of tools that help visualize objects in dimensions four and beyond. The fascination also stems from the fact that some of the topological tools are robust to random noise and do not depend extensively on the exact numerical coordinates used to represent the given data.

In line with the above view, this course will focus on topics that lie at the intersection of topology, algorithms, probability, and data analysis.

Time and Place

TTh 09:30-11:00; MS Teams initially

[Note: First meeting is on Tuesday, Jan 04 at 09:30am. Meeting link. We will give an overview of the course and discuss prerequisites during this first meeting. Links for all courses will also be posted on the academic intranet page. ]



Course Announcements and Discussion:

All announcements, assignment submission, discussion will be on Microsoft Teams

Academic Integrity

Discussion on lecture topics is allowed and encouraged. However, you are expected to acknowledge any inputs you received when you turn in your assignments/projects and give reference to resources (code samples, tutorials, research articles etc.) that you used. Collaboration means that you can disuss the assignments with other students, clarify concepts, etc. However, you should think, design, and write down the answers in your own words. Of course, no discussion is allowed during exams.
CSA and IISc guidelines