Seminar for Geometry, education and visualization with applications

PROGRAM

ČETVRTAK, 14.02.2013. u 17 sati, sala 301F, MI
Vladimir Balan, University Politehnica of Bucharest, Faculty of Applied Sciences, Department of Mathematics-Informatics
SPECTRA AND EIGENSPACES ASSOCIATED TO ANISOTROPIC GEOMETRIC STRUCTURES

Abstract: The talk presents the spectral theory for the symmetric covariant tensors related to m-th root type anisotropic metrics, for arbitrary dimension.
The relations between the spectral objects and the geometric background implied by the related Finslerian metrics are determined, and their specific significance to the associated relativistic models is pointed out.
Further, the prolific in applications HO-SVD and Candecomp/Parafac tensor decompositions -which rely on the tensorial spectral data - are shown to have relevance for the underlying geometry.
The developed theory is illustrated by concrete geometric structures for low dimensions, including the cases of Berwald-Moor, Bogoslovski and Chernov alternative STR models.
Selective references:
[1] V. Balan, Spectra of multilinear forms associated to notable m-th root relativistic models, Linear Algebra and Appl. (LAA), 436, 1, 1 (2012), 152-162.
[2] V. Balan, Spectral properties and applications of numerical multilinear algebra of m-root structures, Hypercomplex Numbers in Geom. Phys. 2 (10), 5 (2008), 101--107.
[3] V. Balan, N. Brinzei, Einstein equations for (h,v) - Berwald-Moor relativistic models, Balkan J. Geom. Appl. 11, 2 (2006), 20-26.
[4] V. Balan, S. Lebedev, On the Legendre transform and Hamiltonian formalism in Berwald-Moor geometry, Diff. Geom. Dyn. Syst., 12 (2010), 4-11.
[5] V. Balan, I. R. Nicola, Berwald-Moor metrics and structural stability of conformally-deformed geodesic SODE, Appl. Sci., 11 (2009), 19-34.
[6] G.Yu. Bogoslovsky, Rapidities and observable 3-velocities in the flat Finslerian event space with entirely broken 3D isotropy?, Symmetry, Integrability and Geometry, Methods and Applications, SIGMA 4, 045 (2008), 1--21.
[7] K.C. Chang, K. Pearson, T. Zhang, On eigenvalue problems of real symmetric tensors, Journal of Mathematical Analysis and Applications, 350 (2009), 416--422.
[8] V.M. Chernov, On defining equations for the elements of associative and commutative algebras and on associated metric forms, In: Space-Time Structure. Algebra and Geometry, D.G. Pavlov, Gh. Atanasiu, V. Balan (eds), Lilia Print, Moscow 2007, 189--209.
[9] L. de Lathauwer, First-order perturbation analysis of the best rank-(R1;R2;R3) approximation in multilinear algebra, J. Chemometrics 18 (2004), 2--11.
[10] L. de Lathauwer, B. de Moor, J. Vandewalle, A multilinear singular value decomposition, SIAM J. Matrix Anal. Appl. 21 (2000), 1253--1278.
[11] D.G. Pavlov, Four-dimensional time, Hypercomplex Numbers in Geom. Phys. 1 (1) (2004), 31--39.
[12] D.G. Pavlov, S.S. Kokarev, Conformal gauges of the Berwald-Moor Geometry and their induced non-linear symmetries (in Russian), Hypercomplex Numbers in Geom. Phys. 2 (10) (2008), 5, 3--14.
[13] L. Qi, W. Sun, Y. Wang, Numerical multilinear algebra and its applications, Front. Math. China, 2 (4) (2007), 501--526.

ČETVRTAK, 21.02.2013. u 17 sati, sala 301f, MI
Mileva Prvanovic, SANU, Beograd
REKURENTNI I KONFORMNO-REKURENTNI RIMANOVI PROSTORI

ABSTRACT: Bice prikazani rezultati koje su:
- 50-ih i 60-ih godina, za rekurentne prostore, dobili E.M.Patterson, H.S.Ruse, A.G.Walker i T.Y.Willmore;
- 60-ih, 70-ih i 80-ih godina, za konformno-rekurentne Rimanove prostore, dobili:
W.Roter i njegovi unici: A.Derdzinski, W.Grycak, M.Holto i Z.Olszak

ČETVRTAK, 28.02.2013.
Rada Mutavdzic, Beograd
GEODEZIJSKA PRESLIKAVANJA

Apstrakt: Tema ovog predavanja su geodezijska preslikavanja povrsi i mnogostrukosti. Bice prikazane Beltrami-jeva i Dini-jeva teorema, interesantne cinjenice o geodezijskim i konformnim preslikavanjima povrsi, kao i neki primeri koji su ilustrovani pomocu paketa Mathematica. Takodje, pored Levi-Civita jednacine za geodezijska preslikavanja mnogostrukosti bice uocena veza izmedju metrika ekvidistantnih mnogostrukosti koje se mogu geodezijski preslikati jedna na drugu u kanonskom koordinatnom sistemu, sto je deo rada I. Hinterleitner, Special mappings of equidistant spaces.



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