Семинар за геометрију, образовање и визуализацију са применама, 28. март 2013.

• 25. Март, 2013
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Наредни састанак Семинара биће одржан у четвртак, 28. марта 2013, у 17 часова у сали 301ф, МИ САНУ.

Предавачи: Славик Јаблан, Ана Зековић

Наслов предавања: Mirror Curves, Knot Mosaics, and their Applications (аутори: Славик Јаблан, Ана Зековић, Љиљана Радовић, Радмила Саздановић)

Садржај: Inspired by the paper on quantum knots and knot mosaics by S. Lomonaco and L. Kauffman and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology, we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. After showing that the following constructions: knot mosaics, mirror-curves, and grid diagrams are equivalent to the tame knot theory, we introduce codes for mirror-curves treated as knot or link diagrams placed in rectangular square grid, suitable for software implementations. We provide tables of minimal mirror-curve codes for knots and links obtained from rectangular grids of size 3x3 and px2 (p<5), and describe an efficient algorithm for computing the Kauffman bracket and L-polynomials directly from mirror-curve representations. We present the program for mirror curve recognition, written by Ana Zekovic and consider some applications of mirror curves in chemistry of nematic chiral coloids. Because this program offers the possibility to work with virtual knots as well, we discuss the possible use of mirror curves in the virtual knot theory.