moori, jamshid, University of Natal, Pietermaritzburg

Jamshid Moori (SENIOR PROFESSOR OF MATHEMATICS)

School of Mathematical Sciences

University of KwaZulu-Natal

P Bag X01, Scottsville 3209, Pietermaritzburg, SOUTH AFRICA

Phone (W): +27 33 260 5649, Phone (H): +27 33 3473 265

Fax: +27 33 260 5648, Cell: 0828725674 Email: moori@ukzn.ac.za

RESEARCH INTERESTS: I do research in the areas of Finite Simple Groups, Representation Theory of Finite Groups and Applications of Finite Groups to Codes, Combinatorial Designs and Geometries. My contributions began with my MSc and PhD work. Most of my refereed papers are published in the Journal of Algebra, Journal of London Mathematical Society, Communications in Algebra, Journal of Group Theory, European Journal of Combinatorics and Discrete Mathematics. All these papers are reviewed (or are in the waiting list to be reviewed) by the Mathematical Reviews. Presently I have two PhD students working with me on Codes and Designs from Finite Groups and Representation Theory. I have acted as an external examiner for various PhD and MSc dissertations, and as a referee for various international journals. I have been acting as a reviewer for the Mathematical Reviews since 1990.

My Erdos Number is 3: Moori - J D Key - N J Calkin - Erdos.

My Mathematics Genealogy: Moori - D Livingstone - A Aitken - E Whittaker - A R Forsyth - A Cayley.

TEACHING EXPERIENCE: I have taught various courses at under-graduate, honours and post-graduate levels in Iran, UK, USA and South Africa. For under-graduate and service courses, class sizes varied from less than ten to large classes of up to 350 students.

	Under-graduate Courses: Abstract Algebra; Advanced Calculus; Calculus; Complex Analysis; Discrete Mathematics; Galois Theory; Group Theory; Linear Algebra; Linear Transformations and Functions of Several Variables; Number Theory; Real Analysis; Ring Theory; Theory of Differential Equations.
	Honours and Post-graduate Courses: Finite Simple Groups; Further Linear Algebra; Group Theory; Permutation and Linear Groups; Representation Theory of Finite Groups; Rings and Modules.
	Service Courses : Linear Algebra; General Mathematics; Differential and Integral Calculus for Engineers; Differential and Integral Calculus for Life Sciences; Algebra and Number Theory, and Discrete Mathematics for Computer Sciences; Quantitative Methods for Commerce and Finance.

CURRENT RESEARCH PROJECTS: The following are my current research projects, which are supported by the NRF (National Research foundation of South Africa) and University of KwaZulu-Natal Research Funds.

1. Computerised Documentation of the Finite Groups and Combinatorial Structures: The use of computing machines is influencing the current trends in a wide variety of fields of modern algebra. The utilization of ideas from modern algebra in other branches of pure mathematics together with their application to areas of modern applied mathematics (e.g. coding theory, graph theory ) has generated a demand for efficient computation in Finite Groups, Rings, Modules and Algebraic Number Fields. GAP and MAGMA are systems that support convenient and efficient computation with groups and other structures. They have already made significant contributions to the solution of problems in many areas of mathematics.

2. Clifford-Fischer Matrices and Group Extensions: In this area we are continuing our research on the method of Clifford-Fischer Matrices and its applications for computing the character tables of group extensions (split and non-split cases). Research students registered for masters and doctoral degrees are contributing to this project.

3. Generations and Spread of Finite Simple Groups: This will be the continuation of my earlier work and work with Dr M S Ganief. The research presently carried out in collaboration with Dr F Ali and Dr J Bradley (postdoctoral fellow)..

4. Codes and Designs Related to Finite Simple Groups: Research is carried out in collaborations with Professor J D Key (Clemson, USA) and Dr B Rodrigues (UKZN-Durban).

MOST RECENT PUBLICATIONS:

1. Some binary codes from symplectic geometry of odd characteristic, Utilitas Mathematica, 67 (2005), 121-128. (With J D Key and B Rodrigues). MR2137926 (2006e:94072)

2. A self-orthogonal doubly even code invariant under the M^{c}L:2 group, J. Comb. Theory, Series A, 110 (2005), 53--69. (With B Rodrigues). MR2128966 (2006a:05174)

3. The permutation actions of the symmetric groups S_{n} on the groups Z_{m}ⁿand \overline {Z_{m}ⁿ}, Quaestiones Mathematicae, 28 (2005), 179--193. (With K. Zimba). MR2146388 (2006c:20020)

4. Fischer-Clifford matrices of B(2,n), Quaestiones Mathematicae, 29 (2006), 9--37. (With K Zimba). MR2209789 (2006m:20014)

5. Binary codes from graphs on triples and permutation decoding, Ars Combinatoria, 79 (2006), 11--19. (With J D Key and B Rodrigues). MR2218255 (2006k:94181)
6. On the exact spread of the sporadic simple groups, Communications in Algebra, 35(8) (2007), 2588--2599. (With J Bradley). MR2345803 (2008g:20029)
7. Some designs and codes invariant under the simple group Co_2, J. of Algerbra, 316 (2007), 649--661. (With B Rodrigues). MR2358607

8. Fischer-Clifford matrices of the non-split group extension 2^6.U4(2), Quaestiones Mathematicae, 31 (2008), 27--36. (With F Ali). MR2404644 (2008m:20013)

9. On the ranks of the Janko simple groups J1, J2, J3 and J4, Quaestiones Mathematicae, 31 (2008), 37--44. (With F Ali). MR2404645 (2009a:20026)
10. On the affine subgroup of the symplectic group, Far East J. Math. Sci, to appear. (With B Rodrigues).
11. A self-orthogonal doubly even code invariant under the M^{c}L group, Ars Combinatoria, to appear. (With B Rodrigues).
12. Partial permutation decoding for some binary codes from graphs on triples, Ars Combinatoria, to appear. (With J D Key and B Rodrigues).
13. ome ternary codes invariant under the simple group M^{c}L:2, Ars Combinatoria, to appear. (With B Rodrigues).