Job Description
One position is available for fulltime PostDoctoral Researcher at the Department of Mathematical Sciences/ College of Science, UAE University. The focus of the research is in area of Operator algebras, C*algebras and von Neumann algebras. For more details, please contact Dr. Ahmed AlRawashdeh (aalrawashdeh@uaeu.ac.ae ). The position is funded by the grant: “On the Unitary Groups of C*Algebras” UAEU Program for Advanced Research PostDoc Grant 2019, Fund No. 31S404 for two years.
Qualifications:
The candidate is expected to have a solid background in functional analysis, and precisely has interest in the subject of operator algebras, von Neumann algebras and C*algebras.
Duties of the PostDo will be:
 To Investigate and to extend AlRawashdehBoothGiordano’s results for a larger class of simple, unital C*algebras, i.e. to discuss their unitary groups as complete invariant. Then. Indeed, to show that an isomorphism φ between the unitary groups of a larger class of simple unital C*algebras, will establish an isomorphism on the KTheory (K_0 and K_1) levels.
 To have a complete understanding of the KTheory of a large class of simple unital C*algebras, with sufficient conditions. Then to apply the wellknown results of classifications using the KTheory.
 To study again Extension Problem for some types of simple, unital C*algebras. Precisely, to extend the results of a continuous unitary group iautomorphiosms on the UHFalgebra case. By assuming the continuity, we aim to obtain the validity of the extension on simple, unital AFalgebras, or even on other types of simple C*algebras.
 To study deeply the special projections P_{I,j}(a) in the matrix algebra M_n(A) introduced by Dye and which were essentially used in the extension problem. We will deduce some properties of these special projections in certain C*algebras.
 To construct unitary group isomorphisms which are NOT Fully *Extendable.
 To investigate the IUGP for many properties of C*algebras.
 To study more properties of the projections (p^2=p*=p) in graph C*algebras. There is a onetoone correspondence between projections and selfadjoint uniutaries (also called *symmetries, or involutions) in unital C*algebras (by sitting p=12u). As an isomorphism between the unitary groups sends selfadjoint unitaries to selfadjoint unitaries, hence we establish a bijection between the sets of projections.
 To extend the known results and deduce that the induced mapping θ_φ between the sets of projections is an orthoisomorphism, for as larger class of C*algebras.
 To discuss more properties of idempotent, symmetries and invertible elements.
Minimum Qualification PhD in Mathematics, Functional Analysis
Preferred Qualification PhD in Functional analysis, C*algebras
Expected Skills/Rank/Experience
Special Instructions to Applicant
Division College of Science  (COS)
Department Mathematical Sciences  (COS)
Job Close Date 31032020
Job Category Academic  PostDoctoral
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