Interview with Dr. Narendra Govil

Dr. Narendra Govil retired from DMS and became an Emeritus Professor in June 2020. Luke Oeding (virtually) sat down with him to learn about his long and distinguished career.

Q1: What was your trajectory that brought you to Auburn?

I was born in a village in my grandfather’s house when my father was a student and grew up in Aligarh, a town about 100 miles east of Delhi, India, where my father settled to work as an attorney. I earned my M.S. in Mathematics at Aligarh Muslim University. I then started working for my Ph.D. in Mathematics there with a research scholarship from the Government of India, but before I completed my Ph.D., I joined as a Lecturer in Mathematics at the College of Engineering and Technology in the same university.

In 1964, I left India and moved to Canada where I attended the University of Montreal, ultimately earning my Ph.D. there in 1967/68. After a short stay at Concordia University, Loyola Campus, Montreal (1967-1970), I moved and became an Assistant Professor at Indian Institute of Technology (IIT), New Delhi, India, where I was promoted to Associate Professor in 1978 and to Full professor in 1980.  During that my stay at IIT, I also held visiting positions at the University of Montreal; Tata Institute of Fundamental Research (TIFR), Mumbai, India; Dalhousie University, Halifax, Canada; and University of Alberta, Edmonton, Canada. Also, while at IIT, I was elected a Fellow of the National Academy of Sciences, India.

In 1983, I received an offer of Visiting Professor at Auburn University, which I accepted. This offer came at the initiative of Professor Richard Zalik and on the recommendation of Professor Charles Micchelli (IBM Research), a well-known mathematician in the field of Approximation Theory.

Soon after starting work at Auburn, I, along with Dr. Richard Zalik, Dr. Geraldo de Souza, and others developed an active research group in Analysis and started having research seminars every week.  I found the department to be a very congenial place. After considering many other factors, I found Auburn to be a very nice and, in fact, a perfect place to raise my family and, in particular, to educate my two sons who were at that time studying in a high school in Delhi, India.  

In November 1983, I expressed to Department Chair Professor Jack Brown my interest in extending my visiting professorship for another year, and he encouraged me to apply.  Assuming that my visiting professorship would be extended, I sent visa papers to my wife and children who were in India and they joined me in January 1984.  As expected, I received a Visiting Professorship for another year, but then, sometime during 1984-85, a tenure-track faculty position in Analysis became available; I applied and was selected, joining as Associate Professor in September 1985. In March 1986, I met Dr. Zalik in Parker Hall who told me, “Narendra you probably do not know that you have been promoted to Full Professor and the letter of promotion is in your mail box.” In that same year my green card application for permanent residency was approved.  

The year 1987 proved to be a banner year for us: we built a house in June; my older son, Sanjay, who had begun his studies in electrical engineering in Fall 1984, completed his degree with honors and began working for IBM; in August, my younger son, Sandeep, enrolled at Auburn University, eventually earning his degree in electrical engineering with honors, followed in 2000 with a Doctor of Medicine from the University of Alabama at Birmingham (UAB) Medical School.  We got well set in Auburn in terms of job, green card, home, and children.

All this was possible only due to the help, guidance, and support I received from Auburn University and everyone in the Department, in particular, Dr. Richard Zalik and Chairs Dr. Jack Brown and Dr. Jim Wall during that period.

Q2: What is your favorite Mathematical Theorem (and why)?

Although there are many theorems that I consider to be my favorite, I will give the following two because even though their statements look so simple, they have wide ranging applications, due to which whole subjects have developed around them.

Bernstein Theorem states that if \(p(z)\) is a polynomial of degree \(n\) then \(\max_{|z|=1}|p’(z)| \le n \max_{|z|=1}|p(z)|\).

This theorem has its generalization for Functions of Exponential Type, also proved by Bernstein.

Eneström-Kakeya Theorem states that if \(p(z)=\sum_{k=0}^n a_k z^k\) is a polynomial of degree \(n\) with real coefficients satisfying \(0 \le a_0 \le a_1 \le ….\le a_n\), then \(p(z)\) has all its zeros in \(|z| \le 1\).

Q3: What's your favorite experience teaching Math?

My favorite experience has been to interact with extremely nice and good students who are always polite and eager to learn in the very conducive classrooms of Parker Hall and the SCC building. Although I enjoyed teaching graduate courses in Complex Analysis the most, I must say that I love teaching and so, to be honest, I loved every course that was assigned to me. During my career at Auburn and other institutions, I taught a variety of undergraduate and graduate courses including College Algebra and enjoyed teaching almost every course. The best part was when I entered the classroom and saw happy faces of students looking forward to the class to begin.

Q4: Which of your research results are you most proud?

Due to my long research career and having published more than 100 research papers, I would consider quite a few of my results of some importance, particularly where we attempted to solve an open problem or generalized/sharpened some well-known results. Also, I consider them of some importance, because they have given (or likely to give) rise to quite a few papers in the field. Here is just a sampling:

1. On the Eneström-Kakeya Theorem, Tôhoku Mathematical Journal 20 (1968), 126-136 (with Q. I. Rahman).
2. Functions of Exponential Type not vanishing in a Half-Plane and Related Polynomials, Transactions of the American Mathematical Society 137 (1969), 501-517 (with Q. I. Rahman).
3. On the Derivative of a Polynomial, Proceedings of the American Mathematical Society 41 (1973), 543-546.
4. Inequalities for Polynomials Satisfying \(p(z) \equiv z^np(1/z)\), Proceedings of the American Mathematical Society 57 (1976), 238-242 (with V. K. Jain and G. Labelle).
5. On the Location of the Zeros of a Polynomial, Journal of the Approximation Theory 24 (1978), 78-82 (with B. Datt).
6. On the Derivative of a Polynomial, Illinois Journal of Mathematics 23 (1979), 319-329 (with Q. I. Rahman and G. Schmeisser).
7. Some Inequalities for Entire Functions of Exponential Type, Proceedings of the American Mathematical Society 123 (1995), 2757-2761 (with Robert B. Gardner).
8. Perturbations of the Haar Wavelet, Proceedings of the American Mathematical Society 125 (1997), 3363-3370 (with R. A. Zalik).
9. On comparison of annuli containing all the zeros of a polynomial, Applicable Analysis and Discrete Mathematics 11 (2017), 232-241 (with Aseem Dalal).

Q5: Which of your many accomplishments at Auburn has brought you the greatest joy?

In fact, I enjoyed all three of the major aspects of my job as a professor -- teaching, research and service, which includes advising graduate or undergraduate students. In particular, I enjoyed working as Undergraduate Program Officer and Associate Chair in the Department where I got opportunities to organize events for students, meet and know students and their parents, and attend meetings in my capacity as UPO and Associate Chair or on behalf of Chair.

Q6: What do you want to do when you grow up (AKA Retire)?  

Presently, I am busy with two books which I hope should come out in about six months.  After the books have appeared, I plan to continue my research interests, read more in history and related subjects. Also, after the COVID-19 problem is better, I may work as a volunteer in some hospital or teach somewhere on a volunteer basis, preferably in an underprivileged church.

Q7: If I might be so bold to ask, what do you hope will be your legacy?

Someone who tried to do his best with full devotion and sincerity in teaching, research, service, or whatever job was assigned to him. Also, his efforts were duly recognized through awards bestowed by the University and students, such as the Alumni Professorship, Outstanding Advisor Award, Outstanding Graduate Teaching Award, #1 Professor Award of Honors Calculus IV, and Top Teacher Award of Kappa Delta.

Q8: Any advice for a young mathematician / statistician?

I believe that the younger generation hardly needs any advice from a person like me of the old generation, because the younger generation is much smarter than me. However, since you asked me, based on my experience, I can suggest the following, which to some might be useful.

1. Teaching is our number one job in any educational institution, so never think of ignoring it. Note that we are here for students who need teaching from good and dedicated teachers.  Long ago in this regard, I read a quote of Mahatma Gandhi written on a wall at the reception desk of a hospital in Delhi.

“The most important people in this organization are patients because it is due to them that we are here.”

Although the above quote was in a hospital, I believe that this perfectly fits in an educational institution as well, because the existence of an educational institution is only for students. I feel that no one can ever become a perfect teacher; therefore, it does not matter how good a teacher one is, there is always room for improvement.  Also, there is no age when one can stop striving to be a better teacher.  Learn from your weaknesses every day while teaching a class and try to overcome those weaknesses in the next class. Note that our prestige and respect among the students, and thus in the department, depends on how sincere we are towards our duties as teachers.

2. Research is a very important component of our job as a faculty. If we are not doing research, then we are not doing our job full time, but rather we are paid full time for doing a part-time job. Research in mathematics, besides being of importance for the development of science and technology, is equally important for becoming a better teacher.  In this regard, I give below a famous quote from the Nobel laureate Dr. Rabindranath Tagore.

“A lamp can never light another lamp unless it continues to burn its own flame. The teacher who has come to the end of his subject, who has no living traffic with his knowledge, but merely repeats his lesson to his students, can only load their minds, he cannot quicken them.”

3. Service and Outreach I also consider equally important for any institution because no institution or even a department can function efficiently just by the efforts of the Chair and his/her administrative team. The more people that put in their efforts, the better the department will function. Moreover, service and outreach give you opportunities to grow your leadership qualities, and to learn and test your skills and to find where you can be most successful. Do not wait for the Chair or any administrative team member to ask you for help but instead take initiative to volunteer for any job in the department/institution you feel you can handle.  Even in terms of rewards, my experience has shown that, in the beginning one may feel like the job is thankless, but ultimately it pays off in terms of rewards, and if nothing else, then you surely get the satisfaction for what you have done for the students and your institution.
4. There is nothing better than being motivated, positive, patient, optimistic, and helpful. Believe that whatever is happening is happening only for good. Always love yourself and others and try to stay happy!