Seminar for Geometry, education and visualization with applications

PROGRAM

ČETVRTAK, 04.04.2013. u 17 sati, sala 301F, MI
Slavik Jablan, Ana Zekovic
THE THEORY OF PSEUDOKNOTS AND UNKNOTTING INVARIANTS
(SLAVIK JABLAN, ANA ZEKOVIC, ALLISON HENRICH, REBECCA HOBERG, LEE JOHNSON, ELIZABETH MINTEN, AND LJILJANA RADOVIC)

Abstract: The Theory of Pseudoknots and Unknotting Invariants Classical knots in R^3 can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes over at that point. A {\em pseudodiagram} is a knot diagram that may be missing crossing information at some of its crossings. At these crossings, it is undetermined which strand passes over. Pseudodiagrams were first introduced by Ryo Hanaki in 2010. Here, we introduce the notion of a pseudoknot, i.e. an equivalence class of pseudodiagrams under an appropriate choice of Reidemeister moves. In order to begin a classification of pseudoknots, we introduce the concept of a weighted resolution set, or WeRe-set, an invariant of pseudoknots. We compute the WeRe-set for several pseudoknot families and discuss extensions of crossing number, homotopy, chirality for pseudoknots and different unknotting invariants connected with pseudoknots and their homotopy classes.

ČETVRTAK, 11.04.2013. u 17 sati, sala 301f, MI
Sofia Lambropoulou, National Technical University, Department of Mathematics
FROM KNOTS TO BRAIDS IN VARIOUS TOPOLOGICAL SETTINGS

Abstract: In this talk we present the L-moves between braids, which can serve for establishing and proving braid equivalence theorems for various diagrammatic settings, such as: for classical knots, for knots in knot complements, in c.c.o. 3-manifolds and in handlebodies, as well as for virtual knots, for welded knots and for singular knots. The L-moves are local and they provide a uniform ground for formulating and proving geometric braid equivalence theorems by adapting to any diagrammatic setting where the notion of braid and diagrammatic isotopy is defined. The L-move equivalences are then reformulated gradually from geometric to algebraic using the braid groups related to each topological setting.

ČETVRTAK, 18.04.2013. u 17 sati, sala 301f, MI
ČETVRTAK, 25.04.2013. u 17 sati, sala 301f, MI
Marko Stosic (Lisabon, Beograd)
Tema: TOPOLOSKA REKURZIJA: OD KATALANOVIH BROJEVA DO KVANTIZACIJE

Apstrakt: U ovoj seriji predavanja bice predstavljena Topoloska rekurzija - jedna od najinteresantnijih modernih metoda u topologiji, algebarskoj i enumerativnojgeometriji, statistickoj fizici ali i sire. Ovaj rekurzivni postupak je prvi put pronadjen u statistickoj fizici 2007. godine (Eynard-Orantin), ali se ubrzo ispostavilo da je izuzetno univerzalan i da ima primene u raznim oblastima kao sto su: kombinatorika, enumerativna geometrija, Gromov-Viten invarijante, Hurvicovi brojevi, moduli prostori algebraskih krivih, imerzije Lagranzijana, (beskonacno-dimenzioni) integrabilni sistemi, matricni integrali, teorija struna (ogledalska simetrija), kvantizacija, teorija cvorova itd.
Mnoge od ovih primena i objasnjenja povezanosti sa topoloskom rekurzijom su dale potpuno novi pogled na pojedine oblasti, ali su brojne veze i dalje "misteriozne" i nude jos mnogo otvorenih pitanja. Tokom ovih predavanja pokusacemo da pomenemo neke od ovih primena i damo jedan osvrt na topolosku rekurziju.
Predavanja ce biti sa dosta primera i akcentom na glavnim idejama i bice namenjena siroj publici.





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