Job Description

One position is available for full-time Post-Doctoral 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 Al-Rawashdeh (aalrawashdeh@uaeu.ac.ae). The position is funded by the grant: “On the Unitary Groups of C*-Algebras” UAEU Program for Advanced Research Post-Doc 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 Post-Do will be:

• To Investigate and to extend Al-Rawashdeh-Booth-Giordano’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 K-Theory (K_0 and K_1) levels.
• To have a complete understanding of the K-Theory of a large class of simple unital C*-algebras, with sufficient conditions. Then to apply the well-known results of classifications using the K-Theory.
• 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 UHF-algebra case. By assuming the continuity, we aim to obtain the validity of the extension on simple, unital AF-algebras, 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 IUG-P for many properties of C*-algebras.
• To study more properties of the projections (p^2=p*=p) in graph C*-algebras. There is a one-to-one correspondence between projections and self-adjoint uniutaries (also called *-symmetries, or involutions) in unital C*-algebras (by sitting p=1-2u). As an isomorphism between the unitary groups sends self-adjoint unitaries to self-adjoint 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 31-03-2020

Job Category Academic - Post-Doctoral