# Computational Topology : Theory and Applications

### FEB 2021

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

MW 11:00-12:30; MS Teams

[Note: First meeting is on Wednesday, Feb 24 at 11:00am. Meeting link. Links for all courses will also be posted on the academic intranet page. ]
#### Instructors:

**Vijay Natarajan**

*Office:* Rm 242, CSA

*Email:* vijayn [AT] iisc.ac.in
**Gugan Thoppe**

*Office:* Rm 336, CSA

*Email:* gthoppe [AT] iisc.ac.in

#### TAs:

**Raghavendra Sridharamurthy**

*Office:* VGL (Rm 241, CSA)

*Email:* raghavendrag [AT] iisc.ac.in
**Mohit Sharma**

*Office:* VGL (Rm 241, CSA)

*Email:* mohitsharma [AT] iisc.ac.in

#### 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