Projects / Programmes
Positivity in noncommutative real algebraic geometry
| Code |
Science |
Field |
Subfield |
| 1.01.04 |
Natural sciences and mathematics |
Mathematics |
Algebra |
| Code |
Science |
Field |
| P120 |
Natural sciences and mathematics |
Number theory, field theory, algebraic geometry, algebra, group theory |
positivity, ordered rings, sums of squares, valuations, real spectrum
Researchers (1)
| no. |
Code |
Name and surname |
Research area |
Role |
Period |
No. of publicationsNo. of publications |
| 1. |
22353 |
PhD Igor Klep |
Mathematics |
Head |
2007 - 2008 |
310 |
Organisations (1)
Abstract
The aim of this project is the study of positivity in real algebra. In particular, we focus on T. Craven's approach via positivity under homomorphisms from a given ring to ordered skew fields. We also introduce a new approach via traces of matrix algebras and von Neumann algebras. Points of our geometric object are homomorphisms from a given ring to finite von Neumann (or matrix) algebras.
Significance for science
These results are important for the development of the mathematical sciences. Since I have studied problems that were raised in the international mathematical community, I expect that they will attract a considerable amount of attention. The results are important for the development of algebra and its application to operator algebras. Many of the results have already attracted a considerable amount of attention. I expect that the same will be the case for our future results. I successfully started (in some cases already continued) with scientific collaboration with many mathematicians around the world. I have published results in refereed scientific journals, presented them at international scientific meetings and at invited lectures at established foreign universities.
Significance for the country
Sustainable socio-economic and cultural development
Research described above has or will develop and strengthen scientific potential in Slovenia, and consolidate the status of Slovenia as a country which contributes significantly to the progress of algebra and its links with operator algebras. Equally important will be the education of new generations of researchers, thus, indirectly, contributing to popularization of mathematics and science in general in Slovenia.
international recognition and connections to international and foreign research programs and projects
The results of the project have already been noticed in the international mathematical community, as reflected for example by numerous lectures at international conferences and foreign universities. At the same time I am the PI of a bilateral cooperation with France via the PROTEUS program.
Most important scientific results
Final report,
complete report on dLib.si
Most important socioeconomically and culturally relevant results
Final report,
complete report on dLib.si
