Ali Jafarian, Ph.D.


Ph.D., Mathematics, University of Toronto, 1973 
M.S., Mathematics, Shiraz University, 1969
B.S., Mathematics, Tehran University, 1966

Research Statement

My main research areas of interest are Functional Analysis and the Theory of Bounded Linear Operators on Banach and Hilbert Spaces,  in particular its finite dimensional version,  which is Linear Algebra.  I have published about two dozen research papers in peer refereed mathematics journals.  Results of some of these papers have been presented at national and international mathematics conferences.  Although I am a pure mathematician by training, I have spent the past 15 years trying to find out how some of what I have learned applies to other disciplines.  One of the topics I have worked on is Wavelets (invented in 1987 by Ingrid Daubechies of Princeton), which now has a vast range of applications such as signal and image processing, data compression, seismology, speech recognition, stock market analysis and much more.  I have taught a wavelet course for our Electrical and Computer Engineering graduate students.  Another area that I have worked on is Mathematics of Medical Imaging, which uses advanced mathematics and is used in CT scan machines, PET, MRI, and Sonography, to name a few.

Before joining the University of New Haven in 1990, I was a visiting professor at the University of Victoria, Canada, for two years. Prior to that, I taught for 15 years at graduate and undergraduate level s at Sharif University of Technology, a highly selective university (MIT of Iran) in Tehran.

General Interests

I have a passion for music, art, Persian poetry and literature.  I also enjoy gardening and cooking.

Published Books and Articles

A. Articles :

1. Ali A. Jafarian, Alexey Popov, Mehdi Radjabalipour, and Heydar Radjavi, Cummutators of Small Rank and reducibility of Operator Semigroups, to appear in the Proc. Amer. Math. Soc.  (2014).

2. Ali A. Jafarian,   Linear Preservers on Strictly Upper Triangular Matrix Algebras, Oper. Matrices ,  7, No. 4, 947-953 (2013).

3. A. A. Jafarian, Mathematics of Computerized Tomography. (This is an article dedicated to Professor M. Radjabalipour on the occasion of his prestigious award from Farhangestan-e Uoloum, 2012, Iran.)

4.  J. Bernik,  … , A.A. Jafarian, …, Semigroups of Operators with Nonnegative Diadonals, Linear Alg. Appl., 433, 2080-2087 (2010).

5. A.A. Jafarian,  A Survey of Invertibility and Spectrum Preserving Linear Maps, Bull. Iranian Math. Soc.,35, No.2, 1-10 (2009). 

6. A.A. Jafarian, et. al, Semitransitive Subspaces of Operators, Electronic J. of Lin. Alg.,15, 225-.

7. A.A. Jafarian, L. Rodman, and P. Semrl, linear Maps Preserving the Isomorphism Class of   Lattices of Invariant Subspaces,Proc. of Amer. Math. Soc., 126, 3607-3617(1998).238(2006). 

8. A.A. Jafarian, H. Radjavi, P. Rosenthal, and A.R. Sourour, Simultaneous Triangularization, Near Commutativity, and Rota’s Theorem, Trans. of Amer. Math. Soc., 347, No. 6, 2191-2199 (1995).

9.  D. Hadwin, A.A. Jafarian, C. Laurie, E. Nordgren, H. Radjavi and P. Rosenthal,   Local Multiplications on Algebras Spanned by Idempotents, Lin. and Mult. Alg., 37,259-263 (1994).

10. A.A. Jafarian, and A. R. Sourour, Linear Maps that Preserve the Commutant, Double Commutant or the Lattice of Invariant Subspaces, Lin. and Mult. Alg., 38, 117-129 (1994).

11. A.A. Jafarian and A. R. Sourour, Continuity Properties of Hyperlat and Reducing Subspaces, Linear Alg. Appl. 141, 253-264 (1990).

12. M.D. Choi, A.A. Jafarian, and H. Radjavi, Linear Maps Preserving Commutativity, Linear Alg. Appl. 87, 227-241 (1987).

13. A.A. Jafarian and A. R. Sourour, Spectrum Preserving Linear Maps, J. Funct. Anal. 66, No. 2, 255-261 (1986).

14. A.A. Jafarian and M. Radjabalipour, Transitive Algebra Problem and Local Resolvent Techniques, J. Operator Theory, I, No. 2 (1979).

15. A.A. Jafarian, Algebras Intertwining Normal and Decomposable Operators, Can. J. of Math., XXXI, No. 6, 1339-1344 (1979).

16. A.A. Jafarian and A. G. Miamee, On Matrices Over the Ring of continuous Functions  and n-Normal Operators, Bull. Iranian Math. Soc., 6, No. 2, 69-78 (1979).

17. A.A. Jafarian and H. Radjavi, Compact Operator Ranges and Reductive Algebras, Acta. Sci. Math., 40, 73-79 (1978). 

18. A.A. Jafarian, Weak Contractions of Sz-Nagy and Foias are Decomposable, Rev. Roum. Math.  Pures et Appl., XXII, No. 4, 489-497 (1977).

19. A.A. Jafarian, Weak and Quasi-Decomposable Operators, Rev. Roum. Math. Pures et Appl., XXII, No. 2, 195-212 (1977).

20. A.A. Jafarian and F. H. Vasilescu, A Characterization of Two-Decomposable OperatorsRev.  Roum. Math. Pures et Appl., XIX, No. 6, 769-771 (1974).

21. A.A. Jafarian, Existence of Hyperinvariant Subspaces,Indiana University Math. J., 24,   No. 6, 565-575 (1974).

22. A.A. Jafarian, Some Results on A – Unitary, A – Self-Adjoint, and Decomposable OperatorsIndiana University Math. J., 23, No. 11, 975-979 (1974).

23. A.A. Jafarian, On Reductive Operators, Indiana University Math. J., 23, No. 7, 607-613 (1974).

24. A.A. Jafarian,  Spectral Decompositions of Operators on Banach Spaces,Ph.D. Dissertation, University of Toronto (June 1973).

25. A.A. Jafarian, On Differentiability of Continuous Functions, Proc. of the First Iranian Math.Conf.,49-56(1970).

B. Books:

1. Translation to Persian of the book: Calculus and Analytic Geometry, by G.B. Thomas, 1980.  (Co-translator: Dr. A.G. Miamee.)

2. English-Persian Dictionary of Mathematics and Statistics, Iranian Math. Society, 1991.  (This is the result of several years of work accomplished by a group of Iranian mathematicians.  I was one of the editors and a major contributor to this work.)

3.  Linear Algebra, under preparation.

Offices/Positions Held

Editorial Board, Bull. of the Iranian Mathematical Society, 1980 – 1988.

Chair, Department of Mathematics & Computer Science, Sharif University of Technology,  Tehran, Iran, 1981 – 1983. 

 President, Iranian Mathematical Society, 1978 – 1980.

Chair, Ph.D. Program in mathematics, Sharif Univ. of Tech., 1987 –1988.  

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