[Turkmath:602] DEU math seminerleri

[cenap ozel]

Degerli Liste uyeleri

04 Agustos 2015 saat 16.00 da  *Bursa Tekni Universitesi'nden Ayse BORAT*

*"Higher  dimensional motion planners for F(R^n,k)"* adlı bir konuşma
verecektir Sizleri konusmalara bekliyoruz.

Ekte konusmanin ozeti sunulmustur.

Selamlar ve saygilar

cenap ozel




HIGHER DIMENSIONAL MOTION PLANNERS FOR F(R n, k)

AYS¸E BORAT

Abstract Two of the main problems in Topological Robotics are to compute
the topological complexity and to give a motion planner of a given space.
The importance of motion planners follow not only from the fact that they
give explicit motion planning algorithms but also from the fact that such
algorithms can be used to compute topological complexity.
In this talk, we will introduce m-dimensional motion planners for the
spaces F(R n, k) = {(x1, x2, · · · , xk) ∈ R n|xi ̸= xj}.
This construction of the m-dimensional motion planners tells that that
TCm(F(R n, k)) ≤ m(k −1)+ 1.
On the other hand, regarding Theorem 1.3 in [1], this result is optimal
when n is odd, but it is 1 unit away from being optimal when n is even.

References
[1] J. Gonzalez, M. Grant, Sequential motion planning of non-colliding
particles in Euclidean spaces (accepted for publication in the Proceedings
of the American Mathematical Society).
[2] H. Mas-Ku, E. Torres-Giese, Motion planning algorithm for configuration
spaces, Bol. Soc. Mat. Mex., DOI: DOI 10.1007/s40590-014-0046-2.
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