Research in Operator Algebra and Applications to Number Theory
Project code: PN-II-ID-PCE-2012-4-0201
Contract no. 7/2013 financed by the Romanian National Authority for Scientific Research,
CNCS - UEFISCDI
Period: September 2013- September 2016
The targets of this research proposal are Operator Algebras problems and Operator Algebra
applications to other fields of mathematics.
From a historical point of view, as a mathematical field, Operator Algebra, started with the work
of von Neumann, in the 1930ís, to formalize Quantum Mechanics. Algebras of operators on a
Hilbert space are the natural framework for understanding symmetries of quantum physical
systems. Fundamental laws of nature such as the Heisenberg uncertainty principle appear as a
natural consequence of von Neumann's abstract theory. Operator Algebra represents a global
framework for treating different concrete problems; it has developed in the last decade into
different areas such as Free Probability, K-theory, Index theory and Non-commutative Geometry.
It has found numerous applications in areas like Topology, Number Theory, Classical Probability,
Logic. The purpose of this project is to explore some new directions in this area, mostly connected
with applications to Number Theory, Subfactors Theory, measure preserving equivalence relations
and approximation properties of discrete groups.
Conferences organised and co-organised:
Scientific seminars organized:
Publications produced as a result of this research
- Goulnara Arzhantseva; Liviu Paunescu; Almost commuting permutations are near commuting permutations, Journal of Functional Analysis, Volume 269, Issue 3, 1 August 2015, Pages 745-757.
- Maria Joita, A new look at the crossed product of pro-C*-algebras, Annals of Functional Analysis,
6(2015),2, 184-203; doi: 10.15352/afa/06-2-16.
- Massoud Amini; Mohammad B. Asadi; Maria Joita; Reza Rezavad, Morita equivalence of Hilbert C*-modules,
Banach Journal of Mathematical Analysis, 9(2015), 1, 102-110; doi: 10.15352/ bjma/09-1-8.
- Liviu Pãunescu, All automorphisms of the universal sofic group are
class-preserving, Revue Roumaine de Mathematiques Pures et Appliquees, Volume LVIII(2014), no 2.
- Florin Rãdulescu, On unbounded, non-trivial Hochschild cohomology in finite von Neumann algebras
and higher order Berezin's quantization, Revue Roumaine de Mathematiques Pures et Appliquees, Volume LVIII(2014), no 2.
- Florin Rãdulescu, Conditional expectations, traces, angles between
spaces and representations of the Hecke algebras, Libertas Mathematica NS, Volume 33(2013), No. 2, 53-83 (doi:10.14510/lm-ns.v33i2.xx).
- Florin Rãdulescu, Free group factors and Hecke operators, notes taken
by N. Ozawa, Proceedings of the 24th Conference in Operator Theory, Theta Advanced Series in Mathematics, Theta Foundation, 2014.
- Maria Joita; Ioannis Zarakas, A construction of pro-C*-algebras from pro-C*-correspondence,
Journal of Operator Theory, Volume 74(2015), 1, 195-211.
- Henri Moscovici, Equivariant Chern classes in Hopf cyclic cohomology, Bulletin
Mathematique de la Societe des Sciences Mathematiques de Roumanie, Volume 58(2015), 317-330.
- Liviu Pãunescu, Convex structures revisited, Ergodic Theory and Dynamical Systems, Volume 36(2016), 1596-1615.
- Florin Rãdulescu, On the countable, measure preserving relation induced on an homogeneous quotient,
by the action of a discrete group, Complex Analysis and Operator Theory, Volume 9(2015), 1633-1662.
- Alexandru Buium, Differential modular forms attached to new forms mod p, Juornal of Number Theory, Volume 155(2015), 111-128.
- Florin Rãdulescu, Endomorphisms of spaces of virtual vectors fixed by a discrete group, Russian Math. Surv.Voulme 71(2016), 291-343.
Conference participations and research visites
Iasi June 2015, The Eighth Congress of Romanian Mathemticians - Florin Radulescu, Florin Boca, Maria Joita, Liviu Paunescu
Timisoara July 2014, 25th International Conference on Operator Theory - All team members have participated as speakers
University of Vienna, May-June 2014, Long term research visit and collaboration - Liviu Paunescu
University of Vienna, May 5-12 2014, Research visit and seminar talk - Florin Radulescu
Universita Sapienza Roma 1, November 2013, Research visit and seminar talk - Liviu Paunescu
Noncommutative geometry and mathematical physics, Scalea June 2014, Invited speaker - Florin Radulescu
Raport Stiintific Sept 2013-Sept 2016
Scientic Report Sept 2013-Sept 2016