27 citations · 296 across the 81 of their papers we have counts for
92 papers
Topology of medial regime random simplicial complexes
Jonathan Ariel Barmak, Michael Farber
We analyse topology of random simplicial complexes in the medial regime. We show that these complexes are highly connected and have homotopy type of iterated suspensions. One of ou…
Parametrized topological complexity of bundles of real projective spaces, I
Michael Farber, Amit Kumar Paul, Lucile Vandembroucq
Analysis of motion algorithms for autonomous systems operating under variable external conditions leads to the concept of parametrized topological complexity \cite{CFW}. In \cite{C…
Sequential parametrized topological complexity of sphere bundles
Michael Farber, Amit Kumar Paul
Autonomous motion of a system (robot) is controlled by a motion planning algorithm. A sequential parametrized motion planning algorithm \cite{FP22} works under variable external co…
Large simplicial complexes: Universality, Randomness, and Ampleness
Michael Farber
The paper surveys recent progress in understanding geometric, topological and combinatorial properties of large simplicial complexes, focusing mainly on ampleness, connectivity and…
Sequential parametrized motion planning and its complexity, II
Michael Farber, Amit Kumar Paul
This is a continuation of our recent paper in which we developed the theory of sequential parametrized motion planning. A sequential parametrized motion planning algorithm produced…
The homology of random simplicial complexes in the multi-parameter upper model
Michael Farber, Tahl Nowik
We study random simplicial complexes in the multi-parameter upper model. In this model simplices of various dimensions are taken randomly and independently, and our random simplici…