Mathematician’s research is known worldwide

May 19th, 2010

There is always work for Mort Seddighin. A student calls to ask about a textbook for an online class. On his desk, there are dozens of papers laying nearby.

He picks up a bundle of stapled papers between his pointer finger and thumb to show that even though classes have just started for the semester, he has work to do.  “I have this stack of papers to referee for journals,” Seddighin said.

Seddighin is an operator theorist but he also works with theoretical aspects of statistics, semi-groups and quantum theory. As a professor of mathematics at Indiana University East, he teaches calculus, mathematical modeling, linear algebra, and statistics to students at the undergraduate level.

The papers he is reading have been submitted by other mathematicians for national and international mathematics journals and is on the editorial board of the Journal of Mathematical Sciences: Advances and Applications. This is a journal of international scope whose editorial board members are from major universities such as University of Tokyo and University of Alberta.

Neatly organized stacks of his own published papers are filed in a wooden bookcase next to his uncluttered desk. Several of the papers are on a theory that he has worked on for almost 30 years.

Since he was a Ph.D. candidate at the University of Colorado in 1981, Seddighin has become a known name in mathematics. While a doctorate candidate, he worked with his advisor, Karl Gustafson, a professor of mathematics at the University of Colorado at Boulder. They began work on what would eventually be known as “the Theory of Antieigenvalues.”

“I was really interested in physics but to really understand physics and topics such as relativity and quantum theory, you have to understand higher mathematics,” Seddighin said.

Throughout the past three decades Seddighin and Gustafson have written a large number of papers on the antieigenvalue theory and advanced the theory. Recently they have expanded the theory and created the “Slant Antieigenvalue Theory.”

“There was a need to generalize the theory,” Seddighin said. “My work is a new type of concept. Antieigenvalues are a quantity that show the maximum turning capability of mathematical objects such as operators, matrices, and differential equations.

Seddighin has also discovered a mathematical Lemma – the Seddighin’s Lemma – and proven it. Seddighin’s Lemma, “Two Nonzero Component Lemma” (TNCL), has applications in fields including economics. According to Seddighin, for certain objective functions, the TNCL creates a paradox in a portfolio theory by Harry M. Markowitz who received a Nobel Prize in 1990 for mathematically showing diversification was necessary to maximize profit.

Seddighin’s Lemma implies that, for certain formulations of the portfolio objective functions, it’s possible to maximize the objective function using only two non-zero decision variables. Markowitz would advise that gain is maximized by diversifying a Stock Portfolio in a given market. Seddighin’s Lemma shows that, for certain objective functions, choosing two stocks will maximize gain.

Seddighin is also currently investigating the application of TNCL in certain resource allocation problems such as Distribution of the Search Effort.

When Seddighin is not conducting research, or teaching undergraduates, he is refereeing and reviewing articles and books for mathematics journals and professional organizations.

He frequently referees for journals such as Journal of Mathematical Analysis and Applications, Journal of Inequalities, Journal of Pure and Applied Analysis, and Mathematica Slovaca. He is the local representative of Mathematical Association of America.

He is a reviewer for the Mathematics Association of America, Mathematical Reviews (MR), American Mathematical Society, and  Journal of Research in Mathematics Education.

Seddighin is well-known among mathematicians in his field of specialization worldwide. He frequently receives personal invitations to present plenary talks at international conferences or organize international conferences and symposiums.

In 2007 by an invitation from the organizing committee, he presented a plenary talk, “Antieigenvalue Techniques in Statistics” at the 16th International Workshop on Matrices and Statistics. He was recently invited to organize an international symposium in September 2010 in Greece.

In April 2010, Seddighin received the IU East Award for Excellence in Research. This award recognizes excellence in research and/or creative work by a full-time faculty member over a sustained period of time.

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