## Next Talks

**Date: May 3, 2019****Speaker: Eric Goubault**

*Title: Directed topological complexity*

### Abstract:

I will introduce in this talk a variant of topological complexity, that can be applied to help classify directed spaces, and
has applications to the study of dynamical systems in the large, such as differential inclusions. Directed topological complexity
looks for specific partitions {F1,…,Fn,…} of the set of reachable states of some directed space X, such that there is a continuous section from
each of the Fi to the space of directed paths which is right inverse to the end points map. As in the classical case, this sheds an interesting light on
a number of directed invariants, and we discuss in particular dicontractibility. We will also show some examples of calculations
on directed graphs, non-positively curved cubical complexes, and directed spheres.

This ongoing work with Aurélien Sagnier and Michael Farber.

### Keywords:

directed algebraic topology, topological complexity, directed invariants, homotopy theory, differential inclusions, control theory

### STREAMING TIME:

- 8 am (Los Angeles)
- 10 am (Mexico City)
- 11 am (New York)
- 4 pm (London)
- 5 pm (Paris)
- 6 pm (Moscow)
- 11 pm (Beijing)
- 12 pm (Tokyo)