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 relative topological complexity of a pair

Topological complexity is a homotopy invariant introduced by Michael Farber in the early 2000s. Denoted $TC(X)$, it counts the smallest size of a continuous motion planning algorithm on $X$. In this sense, it solves optimally the problem of continuous motion planning in a given topological space. In topological robotics, a part of applied algebraic topology, several variants of $TC$ are studied. In a recent paper, I introduced the relative topological complexity of a pair of spaces $(X,Y)$ where $Y\subset X$. Denoted $TC(X,Y)$, this counts the smallest size of motion planning algorithms that plan from $X$ to $Y$.

In this talk, we will provide an overview of techniques used to study relative topological complexity and compute this invariant for several simple spaces relating to real-world robotics problems.