Mathematics Seminar: Topological Complexity

Academic Events
Trinity Western University
Block Hall, Neufeld Science Centre
7600 Glover Road
Langley, BC V2Y 1Y1

Enrique Torres-Giese, Part-time Instructor, TWU, Seminar, “Mathematics Seminar: Topological Complexity”

Mathematics Seminar: Topological Complexity Enrique Torres-Giese, part-time instructor, TWU

ABSTRACT: How do we assign in a continuous way a path between two points on a sphere? This question is an example of the so-called "motion planning problem" in Robotics. It turns out that it is impossible to create a single continuous motion planner on the sphere, but it is possible to solve the motion planning problem on the sphere by constructing three continuous local planners. The smallest number of continuous local planners that solve the motion planning problem of a space X is called is the Topological Complexity of X. This number is affected by the topology of the space X and indicates how difficult the motion planning in X can be. One of the most important properties of this invariant is that it turns out to be determined by only the homotopy type of X. So, for instance, solving the motion planning problem for the sphere is the same as solving the problem for the 3- dimensional Euclidean space with a point taken off. In this talk we will discuss properties and examples of Topological Complexity showing how this can be computed. We will discuss some calculations, and talk about recent progress on the development of a "symmetric" version of Topological Complexity.

SPEAKER BIO: Enrique Torres-Giese holds a PhD from the University of British Columbia. He is interested in Algebraic Topology and has worked on topics like Group Cohomology, Spaces of Representations, Group Theory, Unstable Homotopy Theory, and Topological Complexity. He has taught Mathematics at different schools including TWU, Douglas College, University of Michigan, UBC and Universidad de Guanajuato.