Ali Jararian's math pages

UNH Department of Mathematics and Physics

Greetings

Welcome to my webpages for 2016. You can contact me at

Profile

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

Background
Before joining UNH 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 levels at Sharif University of Technology, a highly selective university (MIT of Iran) in Tehran.

Research
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.  In the recent years I have been mostly working on determining the structure of linear preservers on spaces of matrices and operators. Also, I have been working on some problems about semigroups of operators. I have published about two dozen research papers in peer refereed mathematics journals.

Although I am a pure mathematician, in the past 15 years I have tried 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 topics from mathematics, and in particular some of the theoretical parts Functional Analysis and Operator Theory. It is used in CT scan machines, PET, MRI, and sonography, to name a few.