## Get to Know the Math Prof: Yao Yao

I work on partial differential equations that arise in biology and fluid dynamics.

Collective behavior is a phenomenon that is commonly observed for many animal species, such as a flock of birds in flight or bacteria aggregating and forming patterns. If we want to track the movement of each individual, the whole system would consist of thousands or millions of equations, which would be tough to analyze or simulate. However, if we treat the system as a cloud of particles and track how the density function evolves in time, then the whole system can be described much more easily using one or two partial differential equations.

Although fluid dynamics seem unrelated to animal swarming, both phenomena can be described by partial differential equations with some long-range interactions between the particles. I analyze these nonlocal equations from the mathematical aspect, such as studying whether the solution converges to some equilibrium pattern as the time goes to infinity.

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

For many fundamental equations of fluid dynamics, it is unknown whether their solutions exist globally in time or blow up in finite time. Last year I completed a paper with Alexander Kiselev, Lenya Ryzhik, and Andrej Zlatos, where we study how a "vortex patch" evolves in time for a fluid equation. We are excited to discover that when the parameters of the equation are within certain range, the vortex patches with initially smooth boundary can indeed develop a singularity in finite time. To the best of our knowledge, this is the first rigorous proof of finite time singularity formation in this class of fluid dynamics models.

### How did you find your way to mathematics research?

When I was a child, my grandfather shared many interesting math puzzles with me. Thus I always see math as a fun subject. Even though it was natural for me to major in math in college, I didn't expect to be a math professor.

When I got into UCLA for graduate school, my plan was to find an industry job after getting my PhD degree. My life took a turn when I met my future advisor, Inwon Kim, in my first-year graduate class. Through her guidance I started to do research in partial differential equations, and her style of doing mathematics had a great influence on me.

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

Take a variety of math classes in different areas, and see which area you like best. Do not feel frustrated if you do not do well in some classes. Many people think that one has to bloom early to succeed in math; I believe that everyone has their own pace of growth. Doing research in math is not about how quick you are, but more about how far you can go in a much longer time scale.

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

Maybe I will become a programmer. When I took my first programming class in college, I immediately fell in love with all the algorithms, especially analyzing their computational complexity. Later I did quite well in some college programming contests, so this is something that I am confident that I can do well.

However, if I can be granted any skill that I want to have, I wish I could become a dog trainer. Or a cat trainer, if there is such an occupation...

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

I am grateful for how kind and supportive my colleagues are. Throughout my eight months at Georgia Tech so far, I have received lots of helpful advice from so many of them. They made my first year experience very enjoyable.

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

I'm surprised - and very glad - to see so many female students at Georgia Tech who are passionate about engineering and science. When I went to college, the percentage of female students in the math department I attended was much lower.

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

I have played accordion for many years since I was a kid. Right now I play classical guitar more often, because it is quieter and thus less annoying to my neighbors, even though I'm still a beginner on this.

### What is your ideal way to relax?

To me, a perfect relaxing day in Atlanta would be a sunny weekend day when I can get up late, try some new restaurant on Buford Highway, then go for a short hike at Stone Mountain or along the Chattahoochee river with my husband. This can happen only when neither of us is writing papers or traveling to conferences, so we get to enjoy such a relaxing weekend only once or twice a month.

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

I want to visit Russia (hopefully not in winter though), and take the trans-Siberian railway that goes all the way to Beijing. Another destination on my to-do list is Japan. I am a big fan of anime and manga, and I also want to see whether I can survive there with what I know from my two-year Japanese language class. Finally, for many years I have dreamed to hike the Inca Trail to Machu Picchu.

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

In addition to buying a house and visiting the above travel destinations, I will probably start a cat rescue shelter, or open a cat cafĂ©.

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• Yao Yao