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 firstname.lastname@example.org.
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.
Current schedule can be found here.
We will be sending out announcements through a mailing list; you can subscribe here.
- 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
We have compiled a list of papers that might be interesting to present.
Morse-Witten Theory for Real Operators
Accelerated by applications in mathematical physics from the late 20th century, the interaction of Morse and Hodge Theory in smooth geometry has propelled remarkable advances in geometric topology over the past four decades. Progress in this domain has considerably outpaced parallel investigations in combinatorial topology, where several of the most basic questions regarding spectral analysis of discrete Morse structures remain outstanding. The present talk introduces a discrete Morse-Witten theory for real-linear operators, a direct extension of the Morse-Witten theory for CW complexes pioneered by Forman in the late 1990’s. Time permitting, we will discuss some consequences for spectral analysis of cellular spaces, the surprisingly categorical underpinnings of the Morse-Witten complex, and several future directions. No prior knowledge of Morse-Witten theory will be assumed, smooth or otherwise.