Seminar for Geometry, education and visualization with applications

PROGRAM

ČETVRTAK, 04.03.2010. u 17 sati, sala 301f, MI
Slavik Jablan
Perception of Space in Painting

Abstract: During the history, perception of space in painting is changed from one- and two-dimensional geometric patterns, that dominate in Paleolithic and Neolithic art, through "heirarhical perspective" and orthogonal axonometry used in Egyptian painting, Byzantine counter-perspective, Renaissance linear perspective, cubistic polycentrism, perceptive perspective, to the non-orientable space of abstract painting. Trying to explain 3D-vision as the reconstruction of 3D- image from its 2D-projection, that is in genearal not unique, we will consider different extreme forms of perspective (e.g., anamorphoses), or the formation of ambiguous reconstructions of 2D-projections resulting in visual illusions and impossible figures.

Napomena: Ovo predavanje je nedavno vec bilo odrzano na Kolarcu.

ČETVRTAK, 11.03.2010. u 17 sati, sala 301f, MI
Srdjan Vukmirovic
Prikaz rada: "Minimal surfaces by moving frames", autora S.S.Chern i J.G. Wolfson, 1. deo

Apstrakt: Na predavanju ce biti prikazan rad "Minimal surfaces by moving frames", autora S.S.Chern i J.G. Wolfson, Am. Jour. Math, vol. 105, No. 1, (1983), p.p. 59-83. Autori su ovaj rad posvetili Andre Weilu. U radu se, u terminima pokretnog repera, daju rezultati koji se odnose na minimalne podmnogostrukosti Rimanovih i Kelerovih mnogostrukosti. Ti se rezultati dalje koriste za proucavanje minimalnih povrsi u sferi S^4 i kompleksnoj projektivnoj ravni CP^2.

ČETVRTAK, 18.03.2010. u 17 sati, sala 301f MI SANU
Zoran Rakic
Path integrals for quadratic Langangiams on real, p-adic, and adelic spaces

Apstrakt: Feynman's path integrals in ordinary, $p$-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes K(x'',t'';x',t') are analytically calculated for systems with quadratic Lagrangians. These exact general formulas are presented in the form which is invariant under interchange of the number fields R --> Q_p and Q_{p} --> Q_{p'} p\neq p'. According to this invariance we have that adelic path integral is an essentially fundamental object in mathematical physics of quantum phenomena.

Literature. - C. C. Grosjean, A general formula for the calculation of Gaussian path-integrals in two and
three euclidean dimensions, J. Comput. Appl. Math., 23 (1988), 199-234. - G. S. Djordjevic, B. Dragovich and Lj. Nesic, Adelic Path Integrals for Quadratic Lagrangians, publication in the IDAQPRT, World Scientific, Singapore, 2003.
- V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-Adic Analysis and Mathematical Physics, World Scientific, 1994.

ČETVRTAK, 25.03.2010. u 17 sati, sala 301f, MI SANU
Srdjan Vukmirovic
Prikaz rada: "Minimal surfaces by moving frames", autora S.S.Chern i J.G. Wolfson,2. deo

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