Abordarea noţiunilor de simetrie şi spaţiu din perspectiva grupoizilor (A groupoid approach to notions of symmetry and space)


Grant CNCSIS (Romanian National University Research Council)
Code At 127/2004 ( for young researchers)
2004-contract no. 33346/29.06.2004, 2005-contract no. 34682/24.06.2005.
Project manager: Mădălina Roxana Buneci
Research team: Constantin Cercel, Alina Dincă (students)


Abstract

The notion of symmetry is of fundamental importance in all of the sciences. At present it is generally recognized that groups are not sufficient to characterize the symmetry. For example, objects such as crystals containing only a few unit cells, or crystals with extensive voids and inclusions like nanotechnology crystals exhibit "symmetry" but admit few automorphisms. A possibility to describe such symmetries is to use groupoids.

The main theme of this proposal is the study of the convolution algebras associated to groupoids (more precisely, we focus on two open problems concerning the C*-algebras associated to a locally compact groupoid). They play a major part in the field of noncommutative geometry, which is a rapidly growing new area of mathematics with links to many branches in mathematics and physics. It introduce a completely new concept of space (noncommutative space), by unifying methods of classical geometry with noncommutative C*-algebras.

Another goal of this proposal is to acquaint the students in the project with the way in which groupoids measure symmetry and to encourage them to apply this concept to computer graphics.

Reports
List of papers that are (partially) supported by this grant
Other papers (in connection with the theme of this project)
Other results in this project

Contantin Cercel and Alina Dincă (students at Automatics) have been encouraged to attend national and international conferences. They have obtained second prize to student meeting StudIT 2004 Timisoara. Also they have been part of team that obtained first prize at 13th Summer school for image processing (June 30-July 8 2005, Szeged, Hungary).
But the main achievement is given by the fact that they learnt new mathematical concepts and applied these concepts in their field of interest.