Семинар за геометрију, визуализацију и образовање са применама, 19. децембар 2013.

• 16. Децембар, 2013
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Наредни састанак Семинара биће одржан у петак, 20. децембра 2013. са почетком у 17 часова у сали 301ф, Математичког института САНУ.

Предавач: Ана Зековић

Наслов предавања: Gordian and Smoothing Distances of Knots

Садржај: One of most complicated problems in knot theory is the computation of unknotting number. Hass, Lagarias and Pippenger proved that the unknotting problem is NP. In this paper we discuss the question can we compute unknotting number from minimal knot diagrams, Bernhard-JablanConjecture, compute unknown knot distances between non-rational knots and search for minimal distances by using a graph with weighted edges representing knot distances. Since topoizomerazes are enzymes involved in changing crossing of DNA, knots distances can be used to study topoizomerazes actions. In the existing tables of knot smoothings, knots with smoothing number 1 are computed by Abe and Kanenobu for knots with at most n = 9 crossings, and smoothing knot distances are computed by Kanenobu for knots with at most n = 7 crossings. We compute some undecided knot distances 1 from these papers, and extend the computations by computing knots with smoothing number one with at most n = 11 crossings and smoothing knot distances of knots with at most n = 9 crossings. All computations are done in the program LinKnot, based on Conway notation and non-minimal representations of knots. Authors: Slavik Jablan, Ana Zeković