Get to Know the Math Prof: Zaher Hani

What is your research about?

My research is in a field of mathematics called partial differential equations. These equations describe the evolution with time of various physical systems, ranging from the motion of water in the ocean or of air in the atmosphere, to the strength of an electromagnetic signal, and all the way to the motion of galaxies according to Einstein's equations of general relativity.

Partial differential equations have fundamental importance in everyday applications. For example, they have allowed us over the past 50 years to make more accurate weather predictions, improve how we handle turbulence in the atmosphere in relation to air travel, and invent faster ways to transfer information by electromagnetic signals (like using fiber optics for fast speed internet communication). Partial differential equations also appear in finance, where they are used to model changes in stock prices.

The study of partial differential equations is broad because of the various applications. I work on a particular class called nonlinear dispersive equations. This class includes equations governing ocean and atmospheric sciences, plasma physics, nonlinear optics (including fiber optics), and Einstein's equations of general relativity.

The first question when analyzing such equations is whether a solution exists, or not. The second question is whether we can describe the properties of this solution. In most cases, this solution cannot be written explicitly, so we have little to no way of inspecting its properties beyond analyzing the equation itself. This leads to a very nice and delicate study, in which we try to figure out the properties of the solution without having a formula for it, but only by looking at the equation that it solves.

What has been the most exciting time so far in your research life?

I get a lot of satisfaction from learning new concepts and ideas, even if they weren't my own, or if they don't lead me directly to new theorems. Understanding the "smartness" of a new idea brings a lot of gratification by itself.

In my own research, some of the most exciting moments have happened when I had been working on a certain problem, and I suddenly realized that I could solve something more complex that didn't seem related at first, or prove something stronger that I didn't expect to be able to do at the start. These research surprises have happened twice to me, and they have led to two of my best works.

Of course, in many cases, those bursts of optimism aren't always well-founded, and I end up realizing that I'm still at square one.

How did you find your way to mathematics research?

I was always good in math at school. I was also excited about it, and felt that it made perfect sense. Being the youngest in the family, I also had the chance to look at my brother's or sister's more advanced science and math textbooks whenever I was intrigued to know more about a particular concept. This happened a lot in high school, and I often read through my sister's university-level calculus and analysis books.

I started my undergraduate degree in physics. Soon enough, I started realizing that I need a stronger math background to properly understand the physics that I was excited about. Upon trying to form this background, I started to appreciate the depth and beauty of mathematical ideas in their own right.

I still find myself walking back and forth on the bridge between mathematics and physics, and I often do the backward journey towards physics to properly understand the underlying phenomena and properties of the equations I study from a mathematical viewpoint.

What advice would you give to a college freshman who wants to be a mathematician?

A mathematics degree is one of the most versatile degrees one can get these days. So first of all, congratulations on the wise choice of a major!

Take the foundational courses in mathematics and try to go a bit deeply into several topics. Foundational courses, including calculus and linear algebra, sometimes give a misleading idea about what real mathematics is.

If you feel you're more inclined towards the applications, take one of the many application-oriented courses that the School of Mathematics offers. If you feel particularly intrigued by a particular mathematical topic and think you might want to pursue a higher degree in mathematics, try to take even some introductory graduate courses on that topic.

One last piece of advice: Take some time to appreciate the depth of certain mathematics theorems. Taking a walk and pondering at a particular concept or theorem carries a lot of joy and benefit to it.

If you could not be a mathematician, in what line of work would you be now?

I like academic life, so if I had to choose something other than math, I would probably like to be a historian. My brother is an engineer, and my sister is a medical doctor; sometimes I like the kind of interaction they get to have with very different kinds of people on a daily basis, at a scale larger than is possible in academia. 

What is the most exciting thing about being a part of Georgia Tech?

I moved to Georgia Tech last year, and I was positively surprised by the atmosphere at the School of Math when it comes to encouraging young faculty to advance in their research career. I also like interacting with motivated students, especially when I see them excited about mathematics.

What are you most surprised about in your encounters with Georgia Tech students?

Georgia Tech students are very motivated, and they often have excellent background to excel in their studies, and hopefully careers afterwards. I also think they are delightfully nice.

What unusual skill, talent, or quality do you have that is not obvious to your colleagues?

I like listening to various kinds of music, including some contemporary pieces.

I enjoy reading history and thinking about how big historical events affected normal people, and not just big political figures.

I also keep on trying to adopt new hobbies. Even though I don't always stick to them, I always enjoy learning something new. For example, I did yoga for two years, and I enjoyed it a lot, but I haven't done it in a while now. I hope to start again soon.

What is your ideal way of relaxing?

I like hiking a lot. I haven't done much hiking here in Atlanta yet, but I look forward to it. I also enjoy spending time on a beach.

What three destinations are still in your travel to-do list?

I would like to go to South America, which I've never visited, particularly Brazil and Argentina. I was recently invited to a conference in Chile this year, so I'm quite excited about that. Africa is another very interesting place for me to discover. Southeast Asia and Cuba are also interesting destinations.

If you won $10 Million in a lottery, what would you do with it?

Winning a lottery is not really something that is probabilistically significant to invest time or money on. But, for the sake of argument, I would probably buy two houses, one in a big city, and another in a more quiet and scenic place with nice nature around. I would probably spend most of my time between those two places doing research. I'll probably travel a bit too, including visits to my collaborators. 

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  • Zaher Hani