Seminar for Geometry, education and visualization with applications

PROGRAM

ČETVRTAK, 13.06.2013. u 17 sati, sala 301F, MI
Djordje Baralic (Matematicki Institut, SANU)
TEMA: TOTALNO KOSA ULAGANJA KVAZITORUSNIH MNOGOSTRUKOSTI NAD HIPERKOCKOM

Apstrakt: Kvazitorusne mnogostrukosti su topoloska generalizacija torusnih varijeteta. Ova interesantna klasa mnogostrukosti, ima svojstvo da im je prostor orbita desjstva torusa prost politop, a da im se kohomoloski prsten lepo opisuje pomocu kombinatornih svojstva koje imaju. To nam omogucava da dobro razumemo njihove interesantne osobine.
U nedavnom radu arXiv:1304.5924 konstruisana je kvazitorusna mnogostrukost nad kockom koje imaju ostre granice za totalno kosa ulaganja u R^n. Ove mnogostrukosti su novi primer takvih kompleksnih mnogostrukosti koje se razlikuju od dosada poznatog primera kompleksnog projektivnog prostora.

ČETVRTAK, 13.06.2013. u 18 sati, sala 301f, MI
Ljubica Velimirovic ( Faculty of Science and Mathematics, University of Nis, Serbia)
PROMENA OBLIKA PRI MALIM DEFORMACIJAMA
(VARIATION OF SHAPE UNDER SMALL DEFORMATIONS)

Abstract: Variation of geometric magnitudes play an important role in description of surfaces under infinitesimal bending. It is known that the magnitudes depending on the first fundamental form are stationary under infinitesimal bending. Variation of the area and volume of the surfaces were discussed. The importance of checking the curvature of the surface was underline. The variation of the Willmore energy under infinitesimal bending of the surface is studied . Many procedures in science, engineering and medicine produce data in the form of geometric shapes. Shape analysis of surfaces is important in biometrics, graphics, civil engineering, modern architecture.

ČETVRTAK, 20.06.2013. u 17 sati, sala 301f, MI
Marian Ioan Munteanu (University "Al.I. Cuza" of Iasi)
SOME RESULTS ON MAGNETIC CURVES IN SASAKIAN AND COSYMPLECTIC MANIFOLDS

Abstract: We investigate the trajectories of charged particles moving in a space modeled by the 3-space M2(c) R under the action of the Killing magnetic fields. We explicitly determine all magnetic curves corresponding to the Killing magnetic fields on the 3-dimensional Euclidean space (c=0). See [1]. We give the local description of the magnetic trajectories associated to Killing vector fields in S2 R, providing their complete classification (c=1). Moreover, some interpretations in terms of geometric properties are given. See [2]. We try to explain the geometry of magnetic curves in a Sasakian and a cosymplectic manifold of arbitrary dimension. See [3].
References:
[1] S.L. Druta-Romaniuc, M.I. Munteanu, Magnetic curves corresponding to Killing magnetic fields in E3, J. Math. Phys. 52 (11) (2011), art. no. 113506.
[2] M.I. Munteanu, A.I. Nistor, The classification of Killing magnetic curves in S2 R, J. Geom. Phys. 62 (2) (2012), 170 - 182.
[3] S.L. Druta-Romaniuc, J. Inoguchi, M.I. Munteanu, A.I. Nistor, Magnetic curves in Sasakian and cosymplectic manifolds, submitted.

ČETVRTAK, 27.06.2013. u 17 sati, sala 301f MI SANU
Elaine Beltaos, MacEwan University, Edmonton, Canada
D-branes of WZW models

Abstract: In string theory, a string is a finite curve of approximately the Planck length. Modern string theories contain both open and closed strings. The endpoints of open strings are attached to higher dimensional membranes called D-branes. D-branes possess charges, analogous to electrical charges in particle physics. In this talk, we discuss D-brane charges for WZW models (string theories on compact Lie groups), which form a finite abelian group. We also present a new charge group.



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