Perleseminar by Professor Yuliy Baryshnikov, University of Illinois
21.03.2018 kl. 12.15 - 13.15
"Multi-colored configuration spaces"
Configuration spaces in topology are just the spaces of n-tuples of *disjoint* points in a topological space X. For X being 2- or 3-dimensional Euclidean space, the configuration spaces are hugely relevant to classical mechanics. Topologists spent a lot of energy studying these configuration spaces, uncovering many deep and beautiful connections to other parts of mathematics.
Little is known, however, about the configuration spaces when X has singularities. Even less is known about the generalized configuration spaces, when some groups of points are allowed to collide. On the other hand such configuration spaces can be really useful for the engineering applications dealing with control of swarms of robots subject to some colocation constraints.
In this talk, besides giving a general survey of the area touching on the feedback control stabilization and Bjorner-Lovasz-Yao lower bounds on algebraic complexity, I'll present a general formula for the Euler characteristics of the generalized configuration spaces for general triangulated X.
Institut for Matematiske Fag
Skjernvej 4A, auditorum 5.018
19.03.2018 kl. 12.00