Z1-9570 — Final report
1.
a shortened collection of invited talks at international conferences

Sums of hermitian squares, Connes' embedding problem and the BMV Conjecture, Reelle Algebraische Geometrie-Mathematisches Forschungsinstitut Oberwolfach, Germany (March 2007); A Stellensatz for nowhere negative semidefinite polynomials, Workshop on Real Algebra, Model Theory and Quadratic Forms in Paris, France (November 2005); A Nirgendsnegativsemidefinitheitsstellensatz, RAAG Annual meeting in Passau, Germany (September 2005); *-ordered groups, 6th Annual Colloquiumfest: Positivity, the Multi-Dimensional Moment Problem and Noncommutative Real Geometry, Saskatoon, Canada (April 2005)

B.03 Paper at an international scientific conference

COBISS.SI-ID: 14443353
2.
Organizer of the international conference The Fifth Linear Algebra Workshop in Kranjska Gora (May 2008)

Prof. Omladič regularly organizes a big linear algebra conference. In 2008 I organized special section on Real Algebra and its interactions with Functional Analysis, where around 25 international experts have participated, see e.g. http://www.law05.si/index.php?stran=special_RAFA

B.01 Organiser of a scientific meeting

3.
Positivity in noncommutative real algebraic geometry (Z1-9570-0101-06)

Head of this postodoctoral research project (January 2007-December 2008). The goal of the project was to study notions of positivity in noncommutative real algebraic geometry.

D.01 Chairing over/coordinating (international and national) projects

4.
Positive noncommutative polynomials

Head of the bilateral cooperation project between Slovenia and France 2009-2010 within the Proteus program (the PI on the French side is M. Schweighofer).

D.01 Chairing over/coordinating (international and national) projects

5.
B.04 in B.05: invited talks and visiting positions

B.04 (summary) Positivity and sums of hermitian squares, University of Saskatchewan, Saskatoon, Canada (June 2006); Positive Matrizenpolynome, Universität Regensburg, Germany (February 2006); Angeordnete Schiefkörper, Universität Konstanz, Germamy (April 2005); B.05 visiting professor: UCSD San Diego, USA, September 2007-January 2009; Université de Rennes 1, France, May 2008; Universität Konstanz, Germany, July-August 2007, September 2006; University of Saskatchewan, Saskatoon, Canada, June 2006-August 2006

B.04 Guest lecture

COBISS.SI-ID: 14895449