Director of Research (if dissertation) or Advisor (if thesis)
Baryshnikov, Yuliy
Doctoral Committee Chair(s)
Schenck, Hal
Committee Member(s)
Baryshnikov, Yuliy
Hirani, Anil
Zharnitsky, Vadim
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Covering
Topology
Configuration space
Feedback Control
Abstract
The spaces of coverings (SoC) arise from various configuration spaces of the covering problems. We study the topology of these spaces for different domains and covering agents. In particular, we study the SoCs for grid domains and metric trees covered by balls. Characterizations of their topology are given for analysis of the topological complexities (the Betti numbers in all dimensions). We also study the spaces of fort coverings, a topological approximation of the SoCs capturing some essential features of the SoCs. The applications of the SoCs abound, in the end we present the feedback control on the SoC for metric tree coverage as a case study.
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