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Ref: RP749-522
Job description / Role
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.
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 ? 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 ?_? between the sets of projections is an orthoisomorphism, for as larger class of C*-algebras.
• To discuss more properties of idempotent, symmetries and invertible elem
Requirements
Minimum Qualification:
• PhD in Mathematics, Functional Analysis
Preferred Qualification:
• PhD in Functional analysis, C*-algebras
About the Company
Founded in 1976 by the late Sheikh Zayed Bin Sultan Al Nahyan, UAEU is a comprehensive, research-intensive university enrolling about 14,000 Emirati and international students. As the UAE’s flagship university, UAEU offers a full range of accredited, high-quality graduate and undergraduate programs through nine Colleges: Business and Economics; Education; Engineering; Food and Agriculture; Humanities and Social Sciences; IT; Law; Medicine and Health Sciences; and Science. With a distinguished international faculty, state-of-the art new campus, and full range of student support services, UAEU offers a living-learning environment that is unmatched in the UAE.
As a research-intensive university of international stature, UAEU works with its partners in industry to provide research solutions to challenges faced by the nation, the region, and the world. The University has established research centers of strategic importance to the country and the region which are advancing knowledge in critical areas ranging from water resources to cancer treatments. UAEU is currently ranked the number one research university in the GCC, number two in the Arab World, and #370 globally.
UAEU’s academic programs have been developed in partnership with employers, so our graduates are in high demand. UAEU alumni hold key positions in industry, commerce, and government throughout the region. Our continuing investments in facilities, services, and staff ensure that UAEU will continue to serve as a model of innovation and excellence.