Seminar for Geometry, education and visualization with applications

PROGRAM

ČETVRTAK, 8.5.2014. u 17:15, sala 301f, MI
Predavac: Branko Dragovic, Institute of Physics, Belgrade
Predavanje: ULTRAMETRICITY: BASIC PROPERTIES AND APPLICATIONS

Abstract: Ultrametricity is related to ultrametric (non-Archimedean) spaces, where distances satisfy strong triangle inequality. Ultrametric spaces have some very unusual properties from the point of view of our standard experience. Nevertheless, there are many examples of ultrametric spaces in mathematics, physics, biology, linguistics,... In fact, all systems with hierarchical structure have some utrametric properties. The most advanced examples of ultrametricity are based on p-adic numbers. In this talk I will give an introductory review on basic properties and main applications of ultrametricity.

UTORAK, 20.5.2014. u 16:30 casova, sala 301F, MI
Zajednicki sastanak sa Odeljenjem za matematiku
Speaker: Louis H. Kauffman, Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago
Title: INTRODUCTION TO VIRTUAL KNOT THEORY
Abstract: This talk is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, and virtual knot cobordism. Virtual knot theory is an extension of classical knot theory to stabilized embeddings of circles into thickened orientable surfaces of arbitrary genus. Classical knot theory is the case of genus zero. There is a diagrammatic theory for studying virtual knots and links, and this diagrammatic theory lends itself to the construction of numerous new invariants of virtual knots as well as extensions of known invariants. Many remarkable phenomena occur in the virtual domain.

ČETVRTAK, 29.5.2014. u 17:15, sala 301f, MI
Professor Graham Hall, Institute of Mathematics, University of Aberdeen, Aberdeen AB243UE, Scotland, UK
Title: SECTIONAL CURVATURE AND 4-DIMENSIONAL MANIFOLDS OF ARBITRARY SIGNATURE

Apstrakt: This talk will, first, give a general introduction to the concept of sectional curvature. Second, sectional curvature will be examined, quite generally, for metrics of indefinite signature. Finally the sectional curvature function will be described for 4-dimensional manifolds of any of the possible signatures (+,+,+,+), (+,+,+,-) and (+,+,-,-). In the 4-dimensional case it will be shown, for signature (+,+,+,+), that under reasonable conditions the sectional curvature function uniquely determines the metric from which it came. (This result was first given by Kulkarni in 1970.) A similar result will be shown for the sectional curvature function of metrics with signature (+,+,+,-), with slightly more strict, but still reasonable, conditions (and was given in the period 1982-85 by Ruh and the present author). Finally, some results will be given for the more difficult case of the sectional curvature function of metrics with signature (+,+,-,-).


ČETVRTAK, 29.5.2014. u 18:15, sala 301f MI SANU
Professor Handan Yildirim, Istambul University
Title: ON EXTENDED LEGENDRIAN DUALITIES FOR THE PSEUDO-SPHERES IN LORENTZ-MINKOWSKI SPACE

Abstract: In this talk, after one-parameter families of Legendrian dualities in [5] which are the extensions or four Legendrian dualities defined in [4] for the pseudo spheres in Lorentz-Minkowski space are showed, some applications of these extended Legendrian dualities are given. This is a joint work with Shzuichi Izumiya.
References:
[1] V.I. Arnol'd, S.M. Gusein-Zade and A.N. Varchenko, Singularities of Differential Maps, Vol. I, Birkhauser, 1986.
[2] M. Asayama, S. Izumiya, A. Tamaoki and H. Yildirim, Slant geometry of spacelike hypersurfaces in Hiperbolic space and de Sitter space, Revista Matematica Iberoamericana 28(2)(2012), 371-400.
[3] D.E. Blair, Contact manifolds in Riemannian geometry, Lecture notes in Math., Vol. 509, Springer, 1976.
[4] S. Izumiya, Legendrian dualities and spacelike hypersurfaces in the light-cone, Moskow Mathematical Journal 9 (2009), 325-357.
[5] S. Izumiya and H. Yildirim, Extendensions of the mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space, Topology and applications 159 (2012), 509-518.
[6] S. Izumiya and H. Yildirim, Slant geometry of spacelike hypersurfaces in the lightcone, Journal of the Mathematical Society of Japan 63(3)(2011), 715-752.

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