فاطمه محمد مصطفى العظمى

   

بسم الله الرحمن الرحيم

 

Dr. Fatima Mohammad Azmi Assistant Professor

Address:                                                             Department of Mathematics, King Saud University. Women Studies-Medical studies and Sciences section. Riyadh 11495- P.O. Box 22452. Saudi Arabia

·        E-mail: fazmi@ksu.edu.sa

·        Phone: ext. 1539

·        Fax: 4727975

·        Office: Building 21, third floor. Room 29.

 EDUCATION :

  B.A. Department of Mathematics, King Saud University. Riyadh, Saudi Arabia. with first degree honors.    

  M.A. Department of Mathematics, University of Colorado at Boulder.USA.

  Ph.D Department of Mathematics, University of Colorado at Boulder.USA, 1996

Thesis advisor: Prof. Jeffrey S. Fox. 

Thesis title  : ``Computation Of The Equivariant Cocycle Of The Dirac Operator".

Description of the Thesis work:  we developed  a new  formula for the equivariant Chern -Connes Character associated with the Dirac operator, by incorporating the JLO formula and the canonical order calculus, in the presence of a finite group action on a compact spin Riemannian Manifold.            

 

TEACHINGS AND POSITIONS:

1-       Teaching Assistant,  Dept. of Mathematics, University Of Colorado at Boulder, Colorado, USA (1993 – 1996).

2-      Professional Research Assistant,  Dept. of Mathematics, University Of Colorado at Boulder, USA   (1997).

3      -    Assistant Professor,  Joint the Dept. of Mathematics at King Saud University,  Riyadh, Saudi Arabia, ( since 1998 ). Taught many graduate and under graduate  courses mostly in the following areas:    Real analysis, measure and integration, Topology,  Algebraic Topology, Differential Geometry. 

             Currently, I am supervising a master’s student. 

COMMITTEES AND MATH. DEPARTMENT INVOLVEMENT: 

A- Co-organizer of:

       1- CBMS Regional Conference in:  Index Theory, Coarse Geometry and Topology of Manifolds, University of Colorado at Boulder, USA, summer 1995.

       2- Perspectives in K-homology : Conference which was held at the  University of Colorado, Boulder. USA, summer 1996.

B- Member of the encouragement committee for gifted and intelligent students at King Saud University, Riyadh ( 1998- 2000).

C- Member of the academic accreditation and assessment  committee, which represent the mathematics  department  in the Science college for girls, at King Saud University, Riyadh, ( 2007).

D- Internal examiner of the student  '' Rabab Al -Yusof `` for her  masters degree,  2004.

  

E- Member of: 

      1- The American Mathematical Society (AMS) since 1992.

      2-  The Saudi Association for Mathematical Science.

F- Seminars:

       1- Delivered several seminars  at University of Colorado,  USA (1996-1997).

       2- Delivered a seminar on `` WHAT IS NONCOMMUTATIVE GEOMETRY '' at King Saud University, Riyadh (2005).

 

RESEARCH INTERESTS: 

Noncommutative geometry is a new and a very rich area in mathematics. It  combines geometry, analysis and topology together. It was started by Prof. Alain Connes in 1980, in an effort to relate the theory of algebras of operators on Hilbert spaces to differential geometry and algebraic topology.

My interest : equivariant cyclic homology and cohomology theories, equivariant  Chern - Connes Characters associated to the Dirac operator on spin manifolds, K-homology,  C* algebra and Frechet * algebra. 

Currently; I am trying to characterize the smooth Frechet * algebra, using the famous Gelfand-Naimark Theorem.

 

PUBLISHED PAPERS:  

1-   Azmi, F.  `` The Equivariant Dirac Cyclic Cocycle ".       Rocky Mountain J. of Math. Vol. 30, no. 4, (1171- 1206), 2000.   2 - Azmi, F.  `` The Chern- Connes Character Formula For Families Of Dirac                  Operators".  Publicationes Math. Debrecen, vol. 61, (47 - 73),  2002.   3-   Azmi, F.  ``Equivariant Bivariant Cyclic Theory and Equivariant Chern - Connes  Character". Rocky Mountain J. of Math. Vol. 34, no. 2, (391 - 412), 2004.   4-  Azmi, Fatima`` Characterization Of  Continuous  Functions On Open  Connected  Subsets Of Rn ". JP Journal of Geometry and Topology. Vol.7, (2), (235-248),2007.   5- Azmi, Fatima, `` On a Subclass of Meromorphic Close To Convex Functions Of Complex Order". Far East Journal of Mathematical Sciences (FJMS),Vol. 29, no. 2, (369 - 377) 2008. 6- Azmi, Fatima,  `` Differential Frechet * Algebras And Characterization Of Smooth Funtions on R, ".  Submitted. 7- Azmi, Fatima, "Characterization Of Special Cp* -Algebras and Special Differential p-Frechet * Algebras" Far East Journal of Mathematical Sciences (FJMS),Vol. 31, no. 1, (99 - 112) 2008. 8- Azmi, Fatima and  Ibtehal Al-Azman  “A note on K0-group and Cp* -algebras”. To appear in the JP Journal of Geometry and Topology. Vol.8, (3), (229-237),2009.

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