Topology Seminar - Bredon Cohomology and Robot Motion Planning, Prof Michael Farber (Queen Mary) Seminar

Time:: 14:00 - 15:00
Date:: 29 October 2018
Venue:: Building 54, Lecture Theatre 10B, Mathematical Sciences, University of Southampton, Highfield Campus, SO17 1BJ

For more information regarding this seminar, please email Professor Stephen Theriault at S.D.Theriault@southampton.ac.uk .

Event details

I will discuss the topological invariant TC(X) reflecting the complexity of algorithms for autonomous robot motion. Here, X stands for the configuration space of a system and TC(X) is the minimal number of continuous rules which are needed to construct a motion planning algorithm in X. I shall mainly focus on the case when the space X is aspherical; then the number TC(X) depends only on the fundamental group π = π1(X) and it is denoted TC(π). In the talk I shall characterise TC(π) in terms of various classifying spaces associated with the group π. The equivariant Bredon cohomology provides lower and upper bounds for TC(π). Joint work with Mark Grant, Gregory Lupton and John Oprea.

Speaker information

Professor Michael Farber, Queen Mary University of London. Michael Farber is Professor of Mathematics at the School of Mathematical Sciences, Queen Mary, University of London. Prior to Queen Mary, M. Farber held professorships at the Universities of Warwick, Durham and Tel Aviv. Michael Farber obtained his PhD and D.Sc. degrees in the USSR. M. Farber is known for his research in high dimensional knot theory, Morse theory and topology of closed 1-forms. One of his most signiﬁcant results is a solution of the zero-in-the spectrum conjecture. His recent research interests focus on applied and computational topology, topological robotics, applications of topology to statistics and computer science. He is the author of several monographs. M. Farber was awarded many research grants, among them the Royal Society Wolfson Research Merit Award.