Fa
  • Ph.D. (2015)

    Mathematical Analysis

    Pure Mathematics, Tarbiat Modares University, Tehran, Iran

  • M.Sc. (2011)

    Pure Mathematics

    Department of Pure Mathematics , University of Tehran, Tehran, Iran

  • B.Sc. (2009)

    Mathematics

    Department of Pure Mathematics , University of Tehran, Tehran, Iran

  • Operator Algebras, K-theory
  • Topology

    I got my B.Sc. and M.Sc. in Mathematics from University of Tehran during 2004-2011, and then worked as a Ph.D. student at Tarbiat Modares University under the supervision of Professor Massoud Amini and Professor George Elliott. The thesis was about the category structure of Bratteli diagrams and functors on the category of C-algebras. I got my Ph.D. in 2015. I am an assistant professor at Tarbiat Modares University from 2015 until now. My research interests are Operator Algebras and Topological Dynamical Systems and their interactions. In the field of Operator Algebras, I am interested in the structure and classification of C-algebras and group actions on them. In Dynamical Systems, I work on Cantor systems and Symbolic Dynamics. I use K-theory in both fields.

    Contact

    Curriculum Vitae (CV)

    Simple tracially -absorbing C*-algebras

    M Amini, N Golestani, S Jamali, NC Phillips
    Journal Paper , , {Pages }

    Abstract

    Homomorphisms of C*-algebras and their K-theory

    Nasser Golestani, Parastoo Naderi, Jamal Rooin
    Journal PaperarXiv preprint arXiv:2001.00751 , 2020 January 3, {Pages }

    Abstract

    Let and be C*-algebras and be a -homomorphism. We obtain necessary and sufficient conditions for injectivity and surjectivity of in terms of properties of . Also, we verify when the quotient group is torsion free. In particular, we deal with the case when and are finite-dimensional, and we obtain a characterization for torsion freeness of the quotient group. Moreover, we show that is injective if is injective and has stable rank one and real rank zero. The quotient group is torsion free if and are commutative and unital, has real rank zero, and is unital and injective.

    Generalized quasi-Baer -rings and Banach -algebras

    Morteza Ahmadi, Nasser Golestani, Ahmad Moussavi
    Journal PaperCommunications in Algebra , Volume 48 , Issue 5, 2020 May 3, {Pages 2207-2247 }

    Abstract

    We say that a -ring R is a generalized quasi-Baer -ring if for any ideal I of the right annihilator of is generated, as a right ideal, by a projection, for some positive integer n depending on I. A unital -ring R is left primary if and only if R is a generalized quasi-Baer -ring with no nontrivial central projections. We study basic properties of such rings and we prove their permanence properties such as the Morita invariance. We show that this notion is well-behaved with respect to polynomial extensions and certain triangular matrix extensions and group rings. A sheaf representation for such -rings is also proved. We obtain algebraic examples which are generalized quasi-Baer -rings but are not quasi-Baer -rings. We show that for pre-C*-

    On Topological Rank of Factors of Cantor Minimal Systems

    Nasser Golestani, Maryam Hosseini
    Journal PaperarXiv preprint arXiv:2008.04186 , 2020 August 10, {Pages }

    Abstract

    A Cantor minimal system is of finite topological rank if it has a Bratteli-Vershik representation whose number of vertices per level is uniformly bounded. We prove that if the topological rank of a minimal dynamical system on a Cantor set is finite then all its minimal Cantor factors have finite topological rank as well. This gives an affirmative answer to a question posed by Donoso, Durand, Maass, and Petite.

    The Cuntz semigroup and the radius of comparison of the crossed product by a finite group

    M Ali Asadi-Vasfi, Nasser Golestani, N Christopher Phillips
    Journal PaperarXiv preprint arXiv:1908.06343 , 2019 August 17, {Pages }

    Abstract

    Let G be a finite group, let A be an infinite-dimensional stably finite simple unital C*-algebra, and let\alpha\colon G\to Aut (A) be an action of G on A which has the weak tracial Rokhlin property. Let A^{\alpha} be the fixed point algebra. Then the radius of comparison satisfies rc (A^{\alpha})\leq rc (A) and rc (C*(G, A,\alpha))\leq (1/card (G)) rc (A). The inclusion of A^{\alpha} in A induces an isomorphism from the purely positive part of the Cuntz semigroup Cu (A^{\alpha}) to the fixed points of the purely positive part of Cu (A), and the purely positive part of Cu (C*(G, A,\alpha)) is isomorphic to this semigroup. We construct an example in which G is the two element group, A is a simple unital AH algebra,\alpha has the Rokhlin prope

    Weak tracial Rokhlin property for finite group actions on simple C*-algebras

    M Forough, N Golestani
    Journal Paper , , {Pages }

    Abstract

    Tracial Rokhlin property for finite group actions on non-unital simple C*-algebras

    Marzieh Forough, Nasser Golestani
    Journal PaperarXiv preprint arXiv:1711.10818 , 2017 November 29, {Pages }

    Abstract

    We introduce the tracial Rokhlin property for finite group actions on simple not necessarily unital C*-algebras which coincides with Phillips' definition in the unital case. We study its basic properties. Our main result is that if $\alpha: G\to\mathrm {Aut (A)} $ is an action of a finite group $ G $ on a simple (not necessarily unital) C*-algebra $ A $ with tracial topological rank zero and $\alpha $ has the tracial Rokhlin property, then $ A\rtimes _ {\alpha} G $ and $ A^{\alpha} $ have tracial topological rank zero. The main idea to show this is to prove that a simple non-unital C*-algebra has tracial topological rank zero if and only if it is Morita equivalent to a simple unital C*-algebra with tracial topological rank zero. Moreover, w

    The category of ordered Bratteli diagrams

    Massoud Amini, George A Elliott, Nasser Golestani
    Journal PaperarXiv preprint arXiv:1509.07246 , 2016 January , {Pages }

    Abstract

    A category structure for ordered Bratteli diagrams is proposed such that isomorphism in this category coincides with Herman, Putnam, and Skau's notion of equivalence. It is shown that the one-to-one correspondence between the category of essentially minimal totally disconnected dynamical systems and the category of essentially simple ordered Bratteli diagrams at the level of objects is in fact an equivalence of categories. In particular, we show that the category of Cantor minimal systems is equivalent to the category of properly ordered Bratteli diagrams. We obtain a model (diagram) for a homomorphism between essentially minimal totally disconnected dynamical systems, which may be useful in the study of factors and extensions of such syste

    Discretization of topological spaces

    Massoud Amini, Nasser Golestani
    Journal PaperThe Quarterly Journal of Mathematics , 2016 October 15, {Pages 19-Jan }

    Abstract

    There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in the categorical sense) to compactification and give examples of discretizations. Especially, a discretization functor from the category of α-scattered Stonean spaces to the category of discrete spaces is constructed, which is the converse of the Stone–Čech compactification functor. The interpretations of discretization in the level of algebras of functions are given.

    The category of ordered Bratteli diagrams

    Massoud Amini, George A Elliott, Nasser Golestani
    Journal PaperarXiv preprint arXiv:1509.07246 , 2016 January , {Pages }

    The category of Bratteli diagrams

    Massoud Amini, George A Elliott, Nasser Golestani
    Journal PaperCanadian Journal of Mathematics , Volume 67 , Issue 5, 2015 October , {Pages 990-1023 }

    Abstract

    A category structure for Bratteli diagrams is proposed and a functor from the category of AF algebras to the category of Bratteli diagrams is constructed. Since isomorphism of Bratteli diagrams in this category coincides with Bratteli’s notion of equivalence, we obtain in particular a functorial formulation of Bratteli’s classification of AF algebras (and at the same time, of Glimm’s classification of UHF algebras). It is shown that the three approaches to classification of AF algebras, namely, through Bratteli diagrams, K-theory, and a certain natural abstract classifying category, are essentially the same from a categorical point of view.

    On classifications of transformation semigroups: Indicator sequences and indicator topological spaces

    Fatemah Ayatollah Zadeh Shirazi, Nasser Golestani
    Journal PaperFilomat , Volume 26 , Issue 2, 2012 January 1, {Pages 313-329 }

    Abstract

    In this paper considering a transformation semigroup with finite height we define the notion of indicator sequence in such a way that any two transformation semigroups with the same indicator sequence have the same height. Also related to any transformation semigroup a topological space, called indicator topological space, is defined in such a way that transformation semigroups with homeomorphic indicator topological spaces have the same height. Moreover any two transformation semigroups with homeomorphic indicator topological spaces and finite height have the same indicator sequences.

    Functional Alexandroff spaces

    Fatemah Ayatollah Zadeh Shirazi, Nasser Golestani
    Journal PaperHacettepe Journal of Mathematics and Statistics , Volume 40 , Issue 4, 2011 January , {Pages }

    Abstract

    In the following text a proper subclass of Alexandroff topological spaces, namely functional Alexandroff topological spaces, is introduced. We discuss relation between Alexandroff spaces and functional Alexandroff spaces, functional Alexandroff spaces as dynamical systems, and other related topics.

    Functional Alexandroff spaces

    F Ayatollah Zadeh Shirazi, N Golestani
    Journal PaperHacettepe Journal of Mathematics and Statistics , Volume 40 , Issue 4, 2011 January , {Pages 515-522 }

    More about functional Alexandroff topological spaces

    F Ayatollah Zadeh Shirazi, Nasser Golestani
    Journal PaperScientia Magna , Volume 6 , Issue 4, 2010 October 1, {Pages 64-69 }

    Abstract

    In the following text we study the product of functional Alexandroff spaces and obtain a theorem on functional Alexandroff topological groups which recognize all functional Alexandroff topologies on a group which made it a topological group, this theorem is parallel to a well-known theorem on Alexandroff topological groups.

    Current Teaching

    • MS.c.

      Functional Analysis I

    Teaching History

    • Ph.D.

      Advanced Engineering Mathematics

    • MS.c.

      Complementary Mathematics

    • MS.c.

      Real Analysis I

    • Alimohammadi Prize, 2017
    • First Prize, 32th National Mathematics Competition for University Students, Iran, 2008
    • Functional Analysis Award, 2016
    • Second Prize, 15th International Mathematics Competition for University Students (IMC), Bulgaria, 2008
    • The 22th Kharazmi Youth Award, 2021
    • Third Prize, 10th International Scientific Olympiad for University Students (Mathematics), Iran, 2009
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