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 email@example.com.
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.
Cellular Sheaves, Discrete Hodge Theory, and Applications
Cellular sheaves are a discrete and computable instantiation of the theory of sheaves over cell complexes, and naturally model many situations where data of varying types is parameterized by a space. Assigning inner products to the stalks of a cellular sheaf allows us to apply the constructions of discrete Hodge theory to its cochain complex. We obtain generalizations of the discrete Hodge Laplacians, including the ubiquitous graph Laplacian. These operators have interesting topological and geometric properties, and allow us to use the local-to-global structure of cellular sheaves in real-world systems where robustness is essential. This talk will outline the construction of cellular sheaves and their Laplacians, and sketch various avenues for their application to realistic engineering and scientific problems.