Part of a Series of Q&A Miniprofiles for Math Awareness Month
Apr 4, 2016 | Atlanta, GA
What is your research about?
I work in discrete mathematics with connections to theoretical computer science and optimization. Discrete mathematics refers to objects such as integers, graphs, biological units, computers, and social networks. It can involve a finite or an infinite number of objects. It deals with counting techniques that are more sophisticated than basic permutations and combinations.
Discrete mathematics also deals with probability models and algorithms that involve (and benefit from) tossing a coin or rolling a die, while making decisions. The results are often simple and very efficient. For example, given a very large whole number, a probabilistic algorithm can very quickly tell whether the number is prime or not. However, explaining why the algorithms work well can be tricky.
This field is useful in modeling and understanding digital computation, computer security, and optimization. It helps solve problems such as how to schedule airplanes to maximize capacity and minimize cost. Discrete math also can be used to understand genetic networks and the secondary structures of biological macromolecules.
In the past few decades, discrete mathematics has received much attention and support from the computer science community, thanks to everyone’s attempts to understand and classify many useful, everyday optimization problems as computationally easy, tractable, or intractable.
What has been the most exciting time so far in your research life?
I’ve had a few exciting times. The earliest was publishing my first research paper as a graduate student working with the Hungarian mathematician Paul Erdos, the most prolific mathematician of all times and one of the best-known 20th-century mathematicians. My work with Erdos perhaps was one factor that helped me get the job at Tech!
Another time was when my 2008 research paper in number theory and cryptography, written with my former postdoc Ravi Montenegro, got noticed by a French popular science writer, who then wrote about it in the French science magazine La Recherche. The title of our paper -- “How long does it take to catch a wild kangaroo?” – may have had something to do with the popular attention.
The third would be when the paper I coauthored with my Georgia Tech colleague Ernie Croot and Andrew Granville (University of Montreal), and Robin Pemantle (University of Pennsylvania) was published in 2012 in the Annals of Mathematics, the top journal in the field.
The problem the paper addresses had been around for a while. It was brought to my attention in 1996 by Carl Pomerance, and in 2006, Ernie and I made the first breakthrough. And just recently, a conjecture we had raised and left open in the paper got settled in a preprint by three mathematicians. It is a 20-year story, which can be typical in math!
How did you find your way to mathematics research?
At some point in college, I realized that math has permanence. A theorem with a correct proof is a theorem forever.
Math appealed to me in high school, because it involved little memorization. Out of laziness, I went into engineering, a path that’s common to my generation in India. In graduate school, I went into computer science, because it was becoming popular. Finally, the computational aspects of number theory inspired me to pursue math. Taking a course with Joel Spencer at New York University on a different topic and meeting Erdos sealed the deal!
What advice would you give to a college freshman who wants to be a mathematician?
Develop a thorough and broad background in mathematics, before settling for and specializing in what might be more readily appealing.
If you were not a mathematician, in what line of work would you be now?
Music or ornithology. I discovered my passion for these too late.
What is the most exciting thing about being a part of Georgia Tech?
The colleagues who are excited about research and the hard-working students. It’s a pleasure to work with both.
What are you most surprised about in your encounters with Georgia Tech students?
How well behaved they are. The most trouble some of them get into is not showing up to class. Unfortunately, the omnipresence of the Internet might be affecting the behavior of all of us.
What is an unusual skill, talent, or quality you have that is not obvious to your colleagues?
I have been serving as the Interim Chair of the School of Mathematics since April 15, 2015. I’ll let my colleagues judge whether I am any good at it, but I certainly have gained new experience and have more appreciation for those who do a terrific job!
Also, I am an avid bird watcher, which might come as news to most of my colleagues.
What is the best way you want to relax?
Without a doubt, being at the beach, having grown up next to it. Sadly, I go only once a year.
What three destinations are still in your travel to-do list?
Costa Rica, for the birds. Africa and Australia, because they seem as close to experiencing “another planet” as I might ever get to!
If you won $10 Million in a lottery, what would you do with it?
Use it as seed to generate more, through investment and fund-raising, for the following:
- Acquire space for the School of Mathematics and provide scholarships for talented students to pursue their passion.
- Support services and initiatives related to mental health and physical disability.
- Pay for our daughter’s college and a beachfront property!