Georgia Institute of Technology College of Sciences

What is your research about?

I've been all over the place in terms of research.  In fact, majority of my publications have been outside of mathematics proper - in electrical engineering (network theory), physics (quantum mechanics and fractals), operations research (optimization, games), education (cross-disciplinary learning, MOOCS), etc. My latest paper was with a student on nuclear engineering. What ties these research activities all together is that the problems involve a combination of discrete mathematics, matrices, and computers. I find much of mathematics all by itself to be sterile and too inward-looking. 

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

Working with really good students even before they get to Georgia Tech. Through the Distance Calculus Program I started teaching in 2005, high school students in the Georgia Public School System have been able to take college credits for courses in calculus. Using audio or video links, they take the courses at the time I teach them in Tech, and they take the same quizzes and tests that I give to on-campus students.

The program now serves close to 500 high school students per year. It enables public high schools to teach college-level courses at low cost. Almost all of the students in the program apply and are admitted to Georgia Tech, making up 6-7% of the freshman class when they get here. I'm very proud of that. (More information about the Distance Calculus Program is on pages 14-15 in Volume 8 of Proof Reader.)

How did you find your way to mathematics research?

It was either mathematics or music. I had a really great seventh-grade math teacher.  Also the wonderful math faculty at University of Maryland were incredibly helpful and supportive.

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

Do the mathematics that you enjoy and have fun with it.

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

A musician.

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

The students are really great. They are not just good at science and technology. They do wonderful things that are not graded or even required in class. Riding bicycles, making music, building things.

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

I play (in public) at least a dozen instruments. In college I was a piano player in a blues band; these days I play jazz standards on piano (from an ipad!). I play lots of "stringy things" - double bass, electric bass, guitar, mandolin, octave mandolin, mandocello, ukulele, etc. I play baroque and modern flute, and a whole bunch of renaissance woodwinds you've never heard of. Sometimes you can catch me on campus at the Wesley Foundation on Tuesday evenings. (For more of Tom Morley's musical interests, visit Tom Morley's facebook page.)

And I once taught an entire semester course on the Rubik's Cube.

What is your ideal way to relax?

Riding a bicycle with friends, and sprinting up some of the steep hills in the Atlanta area.

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

County Kerry Ireland, where I have some second cousins; Nepal, just for fun; and Spain for the architecture and food.

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

Commission a builder I really like to build a five-string double bass in the style of Abraham Prescott's 19th-century basses, build and equip a personal recording studio, and then give lots of it away.

What is your research about?

I am a probabilist, a mathematician studying probability theory - a specialist of the study of chance and randomness. Because we do not really have a definition of randomness, it might appear, at first, contradictory to try to have a mathematical theory dealing with something that is undefined. But everyone has some intuition about randomness.

When flipping a fair coin, the outcome cannot be predicted with certainty, but a couple of assumptions are reasonable. First, one expects to get on each flip either a head or a tail with equal probability. Second, one expects that when flipping this same coin a very large number of times (say 10,000 times) one would approximately get 5,000 heads and 5,000 tails.

Both assumptions are reasonable. The first is a case of the use of postulates. The second is based on a theorem now called The Law of Large Numbers. This general theorem was proved only in the 20th century, some 250 years after the proof of its first particular case. Nowadays in popular culture, aspects of something called the "wisdom of crowds" is nothing but a manifestation or application of The Law of Large Numbers.

There is a general level of misconception about probabilists. First and foremost, they are mathematicians whose goal is to prove theorems - and not to compute the odds of winning the lottery. These theorems might not be at all motivated by real-life problems. Probabilists are in that sense closer to "pure" mathematicians than to "applied" ones.

However, because randomness is part of life, some theorems are motivated by real-life applications or by physics, statistics, other sciences, or engineering. Moreover, probability theory is widely applicable: Former students of mine who are not university professors are designing mathematical models for finance in Wall Street, computing the odds and designing casino games, or trading energy options.

I have, myself, some interest in such applications. I have done research in mathematical finance and also proved theorems having potential consequences in bioinformatics. In each case, what was crucial was the unity, the power, and the reach of the mathematics of probability theory.

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

This is a unique time and opportunity for you, a time of freedom. Explore, learn as much as possible, take risks, follow your intuition, your passion, and do not worry about where it is going to lead you.

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

Maybe an oenologist, since I have throughout the years developed a knowledge of various aspects of viniculture.

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

I have judged high-level coffee/barista national championships.

What is your ideal way of relaxing?

Drinking some good wine with some good friends.

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

I do not have such a list.

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

I have never played the lottery.

What is your research about?

I work closely with biologists to combine mathematical modeling with experiments. We study how populations of bacteria grow and evolve, as well as the dynamics of bacterial killing by antibiotics and viruses, especially in physically structured environments such as biofilms.

Physically structured habitats are particularly critical for treatment of surface-associated infections, such as endocarditis, osteomyelitis, and infections of prosthetic heart valves and joints. Our goal is to improve the efficacy of antimicrobial therapy.

I am also the principal investigator of the Boeing-sponsored FlyHealthy™ research study, whose goal is to understand the rates and routes of transmission of infectious diseases in an airplane cabin during flight and to find strategies to mitigate transmission.

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

Do a minor in an exciting area of science, engineering, or finance. A minor will help you develop a foundation of knowledge in another field, to see how mathematics is used in applications and to learn new mathematical methods. Almost everything I know about numerical approximations and special functions I learned in physics classes.

The minor would also provide a basis for future multidisciplinary collaborations, which I enjoy immensely. Also learn to program well in at least one computer language, and take at least one intensive writing class.

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

A huge amount of exciting research goes on at Tech, and almost everybody uses, or at least appreciates, mathematics. This environment leads to many exciting collaboration opportunities across campus.

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

I am continually surprised by their cleverness and excellent work ethic.

Just yesterday I met with an undergraduate who started a research project with me on animal movement. Two weeks ago I sent him a video of the movement of a deer that a wildlife biologist colleague created from GPS tracking. On his own initiative, the student extracted the essential data from the video, taught himself the basics of Markov chains, and constructed a Markov chain model. Wow!

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

I hated biology in high school and college, because it was taught to me as completely descriptive, with no quantitative element. Biology has since become much more quantitative, and mathematical models have provided many important insights to biological phenomena. If I could not be a mathematician, I would probably enjoy being a microbiologist, a geneticist, or a virologist.

Shown on the right is a competition robot built by robotics team that Howie Weiss mentors.

What unique skill, talent, or quality do you have that your colleagues may not know about?

I have a robot shop in my basement.

Members of my entire family are big supporters of FIRST Robotics Competition (FRC) in Dekalb County schools. When my older daughter, Kristin, was in high school, she competed in FRC, which involves building and programming robots up to 120 pounds. Now a Georgia Tech sophomore, she mentors Dekalb County's only FRC team.

My younger daughter, Zoe, has competed on Dekalb County's only FTC (FIRST Tech Challenge) team these past three years. We have been hosting her team in our basement, complete with a 12 ft x 12 ft playing field. Previously, she participated in FIRST LEGO League (FLL) robotics. In FLL, children in grades 4-8 build and program autonomous robots using LEGO Mindstorms components and compete in a yearly themed playing field.

Most Dekalb County elementary schools have an FLL team, but very few teacher-coaches have any technical background. My wife, Lora; Zoe; and I spend Friday evenings in the fall traveling around to Dekalb County schools to help run hands-on FLL workshops. We also judge at the local and state tournaments.

What is your ideal way to relax?

I enjoy outdoor activities: paddling along local rivers, hiking, and biking with my family. I also ran for much of my life, and after a (too) long hiatus, I have resumed running.

What three places would you like to visit?

Certainly the Galapagos Islands.

Several years ago I wrote a paper on inverted biomass pyramids at some pristine coral reefs in the middle of the Pacific, and in principle, I would love to explore one or two of these reefs. In practice, this would likely require weeks on a boat in the open ocean - I get queasy just thinking about this - and then diving with aggressive sharks.

Finally, I would like visit Tromsø, located above the Arctic circle, to observe the Northern Lights and give a talk in the world's northernmost university. I know a few excellent scientists who work there.

Georgia Tech's BS DMTH alumna (2011) Michelle Delcourt is now a graduate student at the University of Illinois at Urbana-Champaign. She recently received the Graduate Student Leadership Award from the university's Graduate College. This award is sponsored by The Graduate College and its student advisory group, SAGE (Students Advising on Graduate Education). It was created to recognize graduate students who have exhibited outstanding service that has positively impacted the campus or wider Urbana-Champaign community.

Through her work with two math department organizations – Illinois Geometry Lab and Association for Women in Mathematics, Michelle has demonstrated exceptional leadership skills. She single-handedly pioneered and raised over $25,000 for the Sonia Math Days for Girls and Girls Engaged in Mathematics and Science (GEMS), wherein she created extremely successful workshops that have affected the lives of many young girls by introducing them to beauty within deep mathematics. Her work has led to ongoing partnership with Chicago Preparatory Science and Engineering Program that provides non-traditional learning opportunities in math and science to some of Chicago’s most underserved populations.

Now, a 5th year PhD candidate, she uses her love of math and art to engage young girls and underrepresented minority students in math through community outreach programs. She hopes that her approach could help attract students who might not otherwise choose mathematics. The Graduate Life blog has a nice article about Michelle.

What is your research about?

My research is in a general area called applied and computational mathematics. The primary goal is developing efficient and accurate methodologies, based on modern mathematics, to improve computer simulations for a wide range of problems in science, engineering, and even social sciences. For example: How to find the best path for a robot to travel from one place to another with the least energy cost while avoiding collisions with possibly moving obstacles? How to predict viral news propagation on social media, such as Facebook or Twitter?

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

My research career has brought many exciting times, including having my first paper accepted, receiving an offer from Caltech as a postdoc, and coming to Georgia Tech as an assistant professor. The happiest times were when I collaborated with engineering colleagues, including Ali Adibi and Magnus Egerstedt of the School of Electrical and Computer Engineering. Together we developed methodologies that are now being applied to optical devices for medical imaging, and to robotics.  It is very rewarding to see my research in action, and it is even more exciting to discover new challenging mathematical problems emerging from practical problems.

How did you find your way to mathematics research?

I started to like mathematics since I was a kid in elementary school. Having been influenced by my father, who is a high school math teacher, selecting math as my college major was one of the easiest decisions for me. While in college, I wanted to become a high school math teacher after graduation. That changed when I met my Ph.D advisor, UCLA's Tony Chan, in Hong Kong in 1994. He convinced me to pursue a research career in applied and computational mathematics. I still appreciate his advice, and I am very happy with the selection I made.

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

Keep your curiosity in math as well as other disciplines, such as engineering or science. You will often find that math is essential in other disciplines, and that may motivate you to learn more in mathematics.

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

I may want to be an engineer. I am always fascinated by the infinite possibilities in engineering designs, and I am interested in space explorations.

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

I like Georgia Tech students very much. I especially like our students’ attitude of working hard and seeking opportunities to explore challenging problems in academia. I also enjoy the opportunities to work directly with the top engineers in the world.

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

I am very impressed by our students’ eagerness to learn. On various occasions, students have asked me to lecture on topics beyond the course syllabi.

What is your ideal way to relax?

The best way for me to relax is to be half asleep while watching basketball games on TV. Unfortunately, I haven't watched TV for several years.

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

Rome, Seoul, and Demark. Rome for the history and food, Seoul to observe the Gangnam life style, and Demark for the fairy tales.

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

This will not happen because I have never played in a lottery. However, if I won this large sum of money, I will probably set up a scholarship to help qualified graduate students and postdocs to pursue a research life in mathematics. 

What is your research about?

I work in an area of mathematics called harmonic analysis. This field grew from the fundamental fact that many functions defined over an interval can be decomposed as sums of the simple sine and cosine functions.

I study cases where the above decomposition does not hold - or holds but is not efficient enough - say, because the functions are no longer defined over an interval. The question is whether similar decompositions are possible also in such cases, with the sines and cosines being replaced by other functions with a simple structure.

Usually, the goal is to use functions which mimic the structure of the sines and cosines, in one way or another. By finding good replacements for the trigonometric functions, one obtains a good way to understand the behavior of functions and the interrelationships between them. With this we get an excellent tool to study the mathematical aspect of the way the world around us behaves.

This area is of much interest in natural sciences and engineering, including in sound and image processing, wireless communications and data transmission, methods in quantum mechanics and quantum computing, and the analysis of signals in geophysics and medicine.

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

Don't be afraid of making mistakes and of asking "stupid questions." The only way to be a scientist is by having the courage to do both.

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

I joined the faculty in Georgia Tech only recently and was pleasantly surprised by how kind and warm everyone is. I am most excited by the opportunity to be a part of a community that does outstanding science while maintaining the sense of "community."

What is an example of a fun mathematical puzzle?

While going on a walk with your monkey, you encounter a long (though finite) row of poles. The poles are so high that you cannot see the top of any of them. Suddenly, your monkey escapes and jumps to the top of one of the poles. You don't know which one.

The only thing you can do is throw rocks at the poles. If the rock hits at the precise pole your monkey is sitting on, he will jump back to your arms and you could both go home to eat ice cream. However, if you miss, and the rock hits any other pole, then the monkey will jump from the pole he is sitting on to a pole just next to it. So the monkey has two options for where to jump, unless it is at the end of the line of poles.

Find a deterministic tactic that will ensure your success in getting your monkey back and going home to eat your ice cream.

Look for the answer next week in the College of Sciences Facebook page.

What math book would you recommend to an undergraduate student interested in mathematics?

When I was an undergraduate student, I very much enjoyed "Proofs from THE BOOK." by Martin Aigner and Günter M. Ziegler. It provides a collection of beautiful mathematical proofs obtained with rather basic tools. Readers would need some basic undergrad knowledge to understand many of these proofs.

The book is dedicated to the famous mathematician Paul Erdos (also referenced by Prasad Tetali).

Here's an excerpt from the preface: "Paul Erdos liked to talk about THE BOOK, in which God maintains the perfect proofs for mathematical theorems... Erdos also said that you need not believe in God but, as a mathematician, you should believe in THE BOOK."

What is an example of an event in math history that resonates with you?

In 1822, Joseph Fourier published his paper regarding the heat equation. The paper includes Fourier's observation that every function can be decomposed into a sum of sines and cosines. (We now know that this is true for many functions but not for every function). This work had a significant impact on the development of mathematics in general and the area of harmonic analysis in particular.

It might be surprising to learn that Fourier wrote a first version of this paper in 1807, and it took him 15 years to succeed in publishing this work. The part of the work regarding the evolution of heat was recognized as significant earlier, but the part regarding the decomposition of functions was considered a disgrace. For this reason, the paper was not published for many years.

Human history has many similar stories of belated recognition, and I think there is a moral in them, although the precise lesson to be learned should be thought of carefully.

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. 

What is your research about?

I work at the interface of discrete mathematics and molecular biology. For instance, most viruses code their genomes in RNA rather than DNA, which is then packaged into a protein capsid. Understanding how this happens is a fundamental biomedical problem with important therapeutic applications. The "branching" of these large RNA molecules (much like a tree in nature) is a critical characteristic that I've studied using techniques from analytic, geometric, and probabilistic combinatorics. 

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

The most recent breakthrough always seems the most exciting. As one of my undergraduate researchers, who is now a PhD student in the School of Electrical and Computer Engineering and works at the Georgia Tech Research Institute, said: "It's hard but rewarding. Half the time it feels like you are banging your head against the wall, but every now and then you get something to work, and it's such a rush."

How did you find your way to mathematics research?

My father is also a mathematician, so by becoming an academic I was just going into the family business. However, I majored in both biology and physics before settling on mathematics as the common denominator among all my interests.

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

A degree in mathematics can be the gateway to any number of great career options - basically anything that values problem-solving and analytical skills including medicine, law, and business, as well as statistics, actuarial science, and computing. And of course, teaching, industrial research, or academia.

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

Recently, I've become interested in architecture, urban planning, and the physical environment's effect on our psyches. It's fascinating to be in downtown Atlanta and realize that it's more obvious how to enter a building from a vehicle than on foot.

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

The School of Math is on an amazing trajectory; the list of top math departments has been relatively static for decades, but we're one of the few newcomers. That's a testament to the value of investing in mathematics at one of the premier engineering schools in the world.

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

The students here are very smart and highly motivated, yet retain a sense of humor about the campus culture that resonates with my own geekiness.

How many official bookstores sell the equivalent of our "North Avenue Trade School" T-shirts?  I gave my father one a couple of years ago, and he's worn it so much that I had to buy a replacement.

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

As an undergraduate in Urbana, I took the opportunity to study Japanese tea ceremony.  Setting aside time each week to focus on the ritual of preparing and serving a bowl of matcha tea was a wonderful way to clear my mind.

What is your ideal way of relaxing?

Since I have two young children, I'm quite fuzzy on the concept of "leisure." However, it's great fun to do simple things with them, like going for a walk to see the outdoor sculptures around Midtown. 

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

My husband is from Australia, and we travel there to visit his family, but I have yet to see notable places like the Great Barrier Reef or Uluru/Ayers Rock. Conversely, he's seen relatively little of the United States, and there are so many natural wonders closer to home. This just means that we're really looking forward to exploring the world with our daughters as they grow up.

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

What I really need is more hours in the day, but that's not something you can buy.  

What is your research about?

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 café.

This may sound like a familiar kind of riddle: How many brilliant mathematicians does it take to come up with and prove the Kelmans-Seymour Conjecture?

But the answer is no joke, because arriving at it took mental toil that spanned four decades until this year, when mathematicians at the Georgia Institute of Technology finally announced a proof of that conjecture in Graph Theory. Their research was funded by the National Science Foundation.

Graph Theory is a field of mathematics that's instrumental in complex tangles. It helps you make more connecting flights, helps get your GPS unstuck in traffic, and helps manage your Facebook posts.

Back to the question. How many? Six (at least).

One made the conjecture. One tried for years to prove it and failed but passed on his insights. One advanced the mathematical basis for 10 more years. One helped that person solve part of the proof. And two more finally helped him complete the rest of the proof.

Elapsed time: 39 years.

So, what is the Kelmans-Seymour Conjecture, anyway? Its name comes from Paul Seymour from Princeton University, who came up with the notion in 1977. Then another mathematician named Alexander Kelmans, arrived at the same conjecture in 1979.

And though the Georgia Tech proof fills some 120 pages of math reasoning, the conjecture itself is only one short sentence:

If a graph G is 5-connected and non-planar, then G has a TK5.

The devil called 'TK5'

You could call a TK5 the devil in the details. TK5s are larger relatives of K5, a very simple formation that looks like a 5-point star fenced in by a pentagon. It resembles an occult or anarchy symbol, and that's fitting. A TK5 in a "graph" is guaranteed to thwart any nice, neat "planar" status.

Graph Theory. Planar. Non-planar. TK5. Let's go to the real world to understand them better.

"Graph Theory is used, for example, in designing microprocessors and the logic behind computer programs," said Georgia Tech mathematician Xingxing Yu, who has shepherded the Kelmans-Seymour Conjecture's proof to completion. "It's helpful in detailed networks to get quick solutions that are reasonable and require low computational complexity."

To picture a graph, draw some cities as points on a whiteboard and lines representing interstate highways connecting them.

But the resulting drawings are not geometrical figures like squares and trapezoids. Instead, the lines, called "edges," are like wires connecting points called "vertices." For a planar graph, there is always some way to draw it so that the lines from point to point do not cross.

In the real world, a microprocessor is sending electrons from point to point down myriad conductive paths. Get them crossed, and the processor shorts out.

In such intricate scenarios, optimizing connections is key. Graphs and graph algorithms play a role in modeling them. "You want to get as close to planar as you can in these situations," Yu said.

In Graph Theory, wherever K5 or its sprawling relatives TK5's show up, you can forget planar. That's why it's important to know where one may be hiding in a very large graph.

The human connections

The human connections that led to the proof of the Kelmans-Seymour Conjecture are equally interesting, if less complicated.

Seymour had a collaborator, Robin Thomas, a Regent's Professor at Georgia Tech who heads a program that includes a concentration on Graph Theory. His team has a track record of cracking decades-old math problems. One was even more than a century old.

"I tried moderately hard to prove the Kelmans-Seymour conjecture in the 1990s, but failed," Thomas said. "Yu is a rare mathematician, and this shows it. I'm delighted that he pushed the proof to completion."

Yu, once Thomas' postdoc and now a professor at the School of Mathematics, picked up on the conjecture many years later.

"Around 2000, I was working on related concepts and around 2007, I became convinced that I was ready to work on that conjecture," Yu said. He planned to involve graduate students but waited a year. "I needed to have a clearer plan of how to proceed. Otherwise, it would have been too risky," Yu said.

Then he brought in graduate student Jie Ma in 2008, and together they proved the conjecture part of the way.

Two years later, Yu brought graduate students Yan Wang and Dawei He into the picture. "Wang worked very hard and efficiently full time on the problem, Yu said. The team delivered the rest of the proof quicker than anticipated and currently have two submitted papers and two more in the works.

In addition to the six mathematicians who made and proved the conjecture, others tried but didn't complete the proof but left behind useful cues.

Nearly four decades after Seymour had his idea, the fight for its proof is still not over. Other researchers are now called to tear at it for about two years like an invading mob. Not until they've thoroughly failed to destroy it, will the proof officially stand.

Seymour's first reaction to news of the proof reflected that reality. "Congratulations! (If it's true ...)," he wrote.

Graduate student Wang is not terribly worried. "We spent lots and lots of our time trying to wreck it ourselves and couldn't, so I hope things will be fine," he said.

If so, the conjecture will get a new name: Kelmans-Seymour Conjecture Proved by He, Wang and Yu.

And it will trigger a mathematical chain reaction, automatically confirming a past conjecture, Dirac's Conjecture Proved by Mader, and also putting within reach proof of another conjecture, Hajos' Conjecture.

For Princeton mathematician Seymour, it's nice to see an intuition he held so strongly is now likely to enter into the realm of proven mathematics.

"Sometimes you conjecture some pretty thing, and it's just wrong, and the truth is just a mess," he wrote in a message. "But sometimes, the pretty thing is also the truth; that that does happen sometimes is basically what keeps math going I suppose. There's a profound thought."

Article by Ben Brumfield