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 4419. 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.

## SEMINAR CANCELLED FOR SPRING 2020

With the fast developing situation around CUNY and NYCs reactions to the Coronavirus, we have decided to cancel the Data Science and Applied Topology seminar for the remainder of the spring semester 2020.

We expect to welcome you back for the fall seminar early September.

## 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

### Super-resolution, subspace methods, and non-harmonic Fourier matrices

This talk is concerned with the super-resolution problem of recovering a discrete measure on the torus consisting of S atoms, given M consecutive noisy Fourier coefficients. Super-resolution recovery is sensitive to noise when the distance between two atoms is less than 1/M and many algorithms fail in this regime. In this talk, we connect this problem to the minimum singular value of non-harmonic Fourier matrices. New results for the latter are presented, and as consequences, we derive results regarding the super-resolution limit of subspace methods (namely, MUSIC and ESPRIT). These results rigorously establish the super-resolution phenomena of these algorithms that were empirically discovered long ago, and numerical results indicate that our bounds are sharp or nearly sharp. Information theoretic lower bounds imply that both algorithms are near optimal for super-resolution. Time permitting, we will discuss how to quantize the Fourier measurements using distributed beta encoding in order to minimize the reconstruction error using either convex or subspace methods. Joint work with Albert Fannjiang, Sinan Gunturk, and Wenjing Liao.