The CUNY Data Science and Applied Topology Reading Group is joint between the Mathematics and Computer Science programmes. We meet Fridays 11.45 -- 12.45 in GC 3209. You can contact us at cunygc@appliedtopology.nyc.

Our plan is to primarily read and discuss seminal papers in data science, in applied topology and in topological data analysis. Each seminar one participant takes the responsibility to present a paper and prepare items for discussion. We expect occasionally to be able to invite external speakers.

## Schedule

Current schedule can be found here.

We will be sending out announcements through a mailing list; you can subscribe here.

## Organizers

- Mikael Vejdemo-Johansson, Computer Science Programme, CUNY Graduate Center; Department of Mathematics, CUNY College of Staten Island
- Azita Mayeli, Mathematics Programme, CUNY Graduate Center; Department of Mathematics, CUNY Queensborough Community College

## Suggested papers

We have compiled a list of papers that might be interesting to present.

# Schedule

### The Forman gradient: a discrete tool for topology-based data analysis

Morse theory studies the relationships between the topology of a shape and the critical points of a real-valued smooth function defined on it. It has been recognized as an important tool for shape analysis and understanding in several applications, including physics, chemistry, medicine, and geography. Morse theory is defined for smooth functions, but recently a discrete counterpart, called Discrete Morse Theory (DMT), has been proposed in an entirely combinatorial setting. DMT introduces the idea of discrete Morse functions as functions that assign values to all the cells of a complex. Based on a discrete Morse function we can impose a partial pairing on such cells and eventually build a combinatorial gradient, also called Forman gradient. The Forman gradient is a very powerful tool as it provides a compact way to represent data without altering its homology. This talk will cover our contribution in developing computational tools, based on the Forman gradient, for the analysis of 2D and 3D scalar fields. I will describe in detail our compact representation for the Forman gradient defined on simplicial complexes and how it can be adapted to the n-dimensional case. Moreover, I will describe our recent work on multivariate data (i.e., collections of scalar fields), and how we can adapt the Forman gradient for analyzing such data in a computationally efficient way.