Seminar for Combinatorics, Geometry, Algebra and Topology
Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)
PLAN RADA ZA DECEMBAR 2017:
PONEDELJAK, 04.12.2017. od 13:00, Matematički institut SANU, sala 301 (3. sprat)
Petar Pavešić, Matematički fakultet, Ljubljana
MINIMALNE TRIANGULACIJE I DOBRI POKRIVAČI
A classical problem in combinatorial geometry is to determine minimal triangulations of triangulable spaces, the most interesting case being the triangulations of closed manifolds. We will relate this question to the concept of covering type of a space which is a new homotopy invariant that was recently introduced by Karoubi and Weibel. Our main results are estimates of the covering type based on the Lusternik-Schnirelmann category and the cohomology ring.
This is joint work with D. Govc and W. Marzantowicz
PONEDELJAK, 04.12.2017. od 14:00, Matematički institut SANU, sala 301 (3. sprat)
Neža Mramor - Kosta, Fakultet za računarstvo, Ljubljana
SIMPLICIAL TOPOLOGICAL COMPLEXITY: TOWARDS A TOPOLOGICAL ALGORITHM FOR MOTION PLANNING
Topological complexity is a relatively new invariant of topological spaces that was introduced with the goal to provide a topological sound approach to motion planning of robots and other mechanical devices. Topological space are not a practical category for devising algorithms and specific implementations, though, therefore a reasonable step towards practically implementable algorithms is to define these concepts in the context of simplicial complexes. In the talk we will describe two recent approaches to simplicial topological complexity, as well as the idea behind an implementable algorithm for a motion planning algorithm, and discuss its efficiency and complexity.
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