CURRICULUM VITAE Anar Dosi(ev)

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1 CURRICULUM VITAE Anar Dosi(ev) Work address: Middle East Technical University Northern Cyprus Campus, Guzelyurt, KKTC, Mersin 10, Turkey ( work phone: ( ). Research areas: Noncommutative analysis, Banach and topological algebras, multi-variable operator theory, topological homology, noncommutative holomorphic functional calculus, quantum functional analysis Date of Birth: 10 October, 1972, Baku, Azerbaijan Citizenship: Azerbaijan Citizen (as Dosiev), Turkish Citizen (with surname Dosi). Employment: Associate Professor Dr. ( present) Middle East Technical University, Northern Cyprus Campus, Guzelyurt; Associate Professor Dr. ( ) Department of Mathematics, Atilim University, Ankara; Associate Professor Dr. ( ) Institute of Mathematics and Mechanics NAS Azerbaijan, Baku; Visiting Researcher ( ) Moscow State University, Moscow; Assistant Professor Dr. ( ) Institute of Mathematics and Mechanics NAS Azerbaijan, Baku. Ph.D. Supervisors: Yu. V. Turovskii (Baku), A. Ya. Helemskii (Moscow) Title and year of Ph.D.: Taylor spectrum of Banach-Lie algebra representations (Baku 1998). Education: Institute of Mathematics and Mechanics NAS Azerbaijan, Ph.D. student ( ). Baku State University M.S. Mathematics, ( ). Novosibirsk State University, Russia B.S. Mathematics ( ) Languages spoken: English, Russian, Turkish. 1

2 Teaching Experience: Full teaching responsibilities of 2 courses per semester. Service courses taught: Calculus (Math 151, 152, 158, 119, 120), Di erential equations (Math 219), Complex analysis. Upper level undergraduate courses taught: Abstract algebra, Functional analysis, Homology of Banach algebras. The average of student evaluation points (accepted in METU) for service courses is about 4 within 5 points (avaiable upon request). Research Statement: My research interests are mainly focused over noncommutative analysis. This is a modern branch of mathematical, more precisely functional analysis, whose classical foundation goes back to the known calculus that we are teaching at the universities. The central idea of noncommutative analysis is to develop a calculus over elements of a certain noncommutative base algebra. The classical multivariable calculus can be quantized when we are replacing the classical commuting variables x 1 ; : : : ; x n by noncommuting (for instance 2 2) matrices A 1 ; : : : ; A n. They are called "quantum or noncommutative variables". This type of model certainly involves lots of abstract algebra, topology, geometry and functional analysis techniques. In order to have a strong and unique mathematical language of quantization there was recently created so called quantum functional analysis. The latter in turn can be treated as the basic language of quantum physics. To have a comprehensive mathematical model of quantum physics, it is also necessary to consider the linear spaces of unbounded Hilbert space operators or "noncommutative variable spaces". It is well known that if we interpret the time dependent variables as in nite matrices rather than functions then the quantum phenomena can be deduced from the equations of Newtonian physics. This is the basic idea of Heisenberg s "matrix mechanics". The "quantum variables" have provided functional analysis with the new constructions, methods and problems. Being a new and modern branch of functional analysis, quantum functional analysis is covered by normed and polynormed topics, as in the classical theory. In the last three years I have got some results on quantum polynormed spaces, namely representation theorems, duality theory, quantum systems, quantum moment problem and quantum bornology. Publications: 1. Dosi A. A., Noncommutative Mackey theorem, Intern. J. Math. 22 (3) (2011) 1-7 DOI: /S X Dosi A. A., Local operator algebras, fractional positivity and quantum moment problem, Trans. Amer. Math. Soc. 363 (2011), /home.html 3. Dosi A.A., Quotients of quantum bornological space, 2

3 Taiwanese J. Math (to appear). 4. Dosi A. A., Formally radical functions in elements of a nilpotent Lie algebra and noncommutative localizations, Algebra Colloquium 17 (Spec 1) (2011) Dosi A. A., Quantum duality, unbounded operators and inductive limits, J. Mathematical Physics 51 (6) (2010) Dosi A. A., Taylor functional calculus for supernilpotent Lie algebra of operators, J. Operator Theory 63 (1) (2010) Dosi A.A., Taylor spectrum and transversality for a Heisenberg algebra of operators, Matem. Sbornik, 201 (3) (2010) Dosi A. A., Noncommutative holomorphic functions in elements of a Lie algebra and noncommutative localizations, Izvestiya Math. RAN, 73 (06) (2009) Dosiev A. A., Local left invertibility for operator tuples and noncommutative localizations, J. K-theory, 4 (01) (2009) Dosiev A.A., Perturbations of nonassociative Banach algebras, Rocky Mountain J. Math., 39 (2) (2009) Dosiev A.A., Frechet sheaves and Taylor spectrum for supernilpotent Lie algebra of operators, Mediterr. J. Math. 6 (2009) Dosiev A. A., Regularities in noncommutative Banach algebras, Integ. Eq. Oper. Th., 61 (3) (2008) Dosiev A. A., Local operator spaces, unbounded operators and multinormed C*-algebras, J. Funct. Anal., 255 (7) (2008) Dosiev A.A., Quantized moment problem, Comptes Rendus Mathématique 344 (10) (2007) Dosiev A.A., The representation theorem for local operator spaces, Funct. Anal. and its Appl., 41 (4) (2007) Dosiev A.A., Quasispectra of solvable Lie algebra homomorphisms into Banach algebras, Studia. Math. 174 (1) (2006) Dosiev A.A., Cartan-Slodkowski spectra, splitting elements and noncommutative spectral mapping theorems, J. Funct. Anal., 230 (2) (2006)

4 18. Dosiev A.A., Spectral mapping framework, Proceedings of the Conference on Topological Algebras, Banach Center Publications, 67 (2005) Dosiev A.A., Cohomology of sheaves of Frechet algebras and spectral theory, Funct. Anal. and its Appl., 39 (3) (2005) Dosiev A.A., Algebras of power series in elements of a Lie algebra and Slodkowski spectra, J. Math. Sciences (translated from: Zapiski POMI, St-Petersburg), 124 (2) (2004) Dosiev A.A., Homological dimensions of the algebra formed by entire functions of elements of a nilpotent Lie algebra, Funct. Anal. and its Appl., 37 (1) (2003) Dosiev A.A., Spectra of in nite parametrized Banach complexes, J. Operator Theory, 48 (3) (2002) Dosiev A.A., Ultraspectra of a representation of a Banach Lie algebra, Funct. Anal. and its Appl., 35 (3) (2001) Dosiev A.A., Holomorphic functions of a basis of a nilpotent Lie algebra, Funct. Anal., and its Appl. 34 (4) (2000) National type papers: 25. Dosiev A.A., Note on algebras of power series in elements of a Lie algebra, Trans. NAS Azerb., 12 (7) (2004) Dosiev A.A., Projection property of spectra for solvable Lie algebra representations, Trans. NAS Azerb., 23 (1) (2003) Dosiev A.A., On fredholm pairs of operators, Proc. IMM NAS Azerb., 13 (2000) Dosiev A.A., Cartan type criterion for solvability of subalgebras of an associative Banach algebra, Proc. IMM NAS Azerb., 10 (1999) Dosiev A.A., Holomorphic functions on polydisk of Heisenberg algebra generators, Trans. NAS Azerb., 19 (1999) Dosiev A.A., On Arens-Michael hull of the universal enveloping algebra of a nilpotent Lie algebra, Trans. NAS Azerb., 18 (1997) (in russian). 31. Dosiev A.A., The Taylor joint spectrum of noncommuting variables, 4

5 Proc. IMM NAS Azerb., 5 (1996) (in russian). International conference presentations: 1. Dosi A.A., Quantum duality and noncommutative Arens-Mackey theorem, Banach algebras 2009, Bedlewo, Poland Dosiev A.A. Local operator spaces and noncommutative rational functions, Operator algebras and topology, Moscow (2007), Russia 3. Dosiev A.A., Local operator systems and multinormed C*-algebras, 21-th International Conference on Operator Theory, Timisoara (2006) Romania, 4. Dosiev A.A., Frechet algebra sheaf cohomology and spectral theory (talk I), Perturbations of nonassociative Banach algebras (talk II), 20-th International Conference on Operator Theory, Timisoara (2004) Romania, Dosiev A.A., Multi-operator functional calculus for supernilpotent operator Lie subalgebras, Conference on Topological Algebras, their Applications, and Related Topics, Bedlewo 2003, Poland, 6. Dosiev A.A., Taylor spectrum and holomorphic functions of noncommuting variables, 3-th Linear algebra workshop, Bled 2002, Slovenia, 7. Dosiev A.A., Holomorphic functions of noncommuting variables, 15-th International Conference on Banach algebras, Balticon 2001, Odense, Denmark, 8. Dosiev A.A., Noncommutative spectral mapping theorem, 18-th International Conference on Operator Theory, Timisoara (2000) Romania, 5

6 References: (Avaiable upon request) S. Alpay, METU, Turkey D. Blecher, Department of Mathematics, University of Houston, Houston, TX A. Ya. Helemskii, Moscow State University F.-H. Vasilescu, Universite de Lille 1, France V. I. Lomonosov, Kent State University, USA M. Putinar, University of California, Santa Barbara, USA 6