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

### Topological Data Analysis of Financial Time Series

We apply persistence homology to detect and quantify topological patterns that appear in multidimensional time series. Using a sliding window, we extract time-dependent point cloud data sets, for which we compute persistence homology. We use persistence landscapes to quantify the temporal changes in the time series. We test this approach on multidimensional time series generated by various non-linear and non-equilibrium models. As an alternative approach, we construct correlation networks, and track changes in the topology of these networks.

We apply this method to detect early signs for financial bubbles in market indices and asset prices. As case studies, we consider the US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009, as well as at the prices of cryptocurrencies.

This is based on joint work with Yuri Katz (Standard and Poor's Global Market Intelligence), and Pablo Roldan, Daniel Goldsmith, and Yonah Shmalo (Yeshiva University).