Seminar for Geometry, education and visualization with applications

PROGRAM

ČETVRTAK, 07.03.2013. u 17 sati, sala 301F, MI
Nevena Pusic, Novi Sad
O INVARIJANTAMA KRIVINSKOG TIPA KOD HOLOMORFNO-SEMISIMETRICNIH KONEKSIJA NA PROSTORIMA SA ODREDJENIM STRUKTURAMA

Abstrakt: Posmatrali smo F,g-holomorfno-semisimetricne koneksije, F-holomorfno semisisimetricne koneksije i g-holomorfno semisimetricne koneksije na anti-Kelerovim (ili Kelerovim prostorima sa Nordenovom metrikom) i na produkt prostorima. Ispostavilo se da na obe vrste prostora prve dve koneksije imaju invarijantu krivinskog tipa koja je jednaka konformnoj invarijanti na tim prostorima. Invarijanta g-koneksije je u oba slucaja bila drugacija i komplikovanija za izracunavanje. Posto je geometrija hiperbolicnog Kelerovog prostora (ili produkt prostora sa Nordenovom metrikom), i sama definicija ovih koneksija mora da bude drugacija. Svaka od njih pod odredjenim pretpostavkama ima invarijantu krivinskog tipa, sve su izmedju sebe razlicite i nijedna nije jednaka HB-tenzoru.

ČETVRTAK, 14.03.2013. u 17 sati, sala 301f, MI
Miroslava Antic, Matematicki Fakultet, Beograd
JEDNA INVOLUCIJA U ODNOSU NA EKVIDISTANTU HIPERBOLICKE RAVNI I DVA MODELA EUKLIDSKE GEOMETRIJE U HIPERBOLICKOJ RAVNI

Abstrakt: Prikazacemo jednu involuciju u odnosu na ekvidistantnu krivu u hiperbolickoj ravni koja zadovoljava neke od osobina kao osna refleksija ili inverzija u odnosu na krug i pomocu nje, koristeci elementarni trigonometrijski racun hiperbolicke ravni konstruisati jedan neograniceni i iz njega izvedeni ograniceni model euklidske geometrije.

ČETVRTAK, 21.03.2013. u 17 sati, sala 301f, MI
Bozidar Jovanovic, Matematicki Institut u Beogradu
GEODEZIJSKI TOKOVI NA ELIPSOIDU, SEPARABILNE PERTURBACIJE I BILIJARI

Apstrakt: Prikazujemo Laksovu reprezentaciju za separabilne mehanicke probleme na elipsoidu i bilijare unutar elisoida. Daje se analogon Salove i Ponseleove teoreme.
Refererence
[1] Dragovic V., Radnovic M., Poncelet porisms and beyond. Integrable billiards, hyperelliptic Jacobians and pencils of quadrics. Frontiers in Mathematics. Birkhauser/Springer Basel AG, Basel, 2011.
[2] Fedorov Yu. N., An ellipsoidal billiard with quadratic potential. Funct. Anal. Appl. 35 (2001), no. 3, 199-.208

ČETVRTAK, 28.03.2013. u 17 sati, sala 301f MI SANU
Slavik Jablan, Ana Zekovic
MIRROR CURVES, KNOT MOSAICS, AND THEIR APPLICATIONS
(SLAVIK JABLAN, ANA ZEKOVIC, LJILJANA RADOVIC, AND RADMILA SAZDANOVIC)

APSTRAKT: 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.



Sednice seminara odrzavaju se u zgradi Matematickog instituta SANU, Knez-Mihailova 36, na trecem spratu u sali 301f.