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Lutz Warnke, who is soon joining the School of Mathematics faculty, is receiving the 2016 Dénes König Prize. This award is awarded biennially by the SIAM Activity Group on Discrete Mathematics (SIAG/DM) to an early career researcher or early career researchers for outstanding research, as determined by the prize committee. Awards are given for research in an area of discrete mathematics, based on a publication by the candidate(s) in a peer-reviewed journal published in the three calendar years prior to the year of the award.
Lutz is being recognized for his contribution to the study of random graph processes and phase transitions. His impressive contributions include joint papers with (his advisor) Oliver Riordan.
- The Evolution of Subcritical Achlioptas Processes, Random Structures and Algorithms 47 (2015)
- Explosive Percolation Is Continuous, Science 333 (2011), 322-324.
Lutz Warnke will given this prize during the biennial SIAM Conference on Discrete Math, which happens to be at GSU in Atlanta this year, June 6-10, 2016.
School of Mathematics' graduate students Samantha Petti and Justin Lanier have been awarded NSF graduate research fellowships. They join Anna Kirkpatrick and JD Walsh as NSF fellows currently among the graduate students in the School. This year only 3 such fellowships were awarded to the entire College of Sciences. More infomation on this NSF program is available on the NSF Graduate Research Fellowships Program website.
April is Mathematics Awareness Month! In the first of a series of Q & A miniprofiles, The College of Sciences published Get to Know the Math Prof: Prasad Tetali.
In the article, Prasad explains his research, recalls highlights of his career, and shares personal insights.
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!
What is your research about?
I work in probability theory as it applies to physics. Here's an example: Imagine taking a city map, say the street grid of Atlanta, and placing random speed limits on the streets. Some streets may be set at 10 MPH, and others at, say, 20 MPH. Given these random assignments, what is the fastest route from one point in the city to another? How can we determine the fastest route? How different is this fastest route from the one obtained if all streets had the same speed limit?
Problems like travel times on street grids are related to social network connectivity, computer science problems, and even the behavior of magnets. Developing tools to attack theoretical problems often leads to advances in such applications. This ability is particularly relevant in the age of big data sets and the Internet.
What has been the most exciting time so far in your research life?
During my postdoc at Princeton University, a grad student and I developed a way to apply tools called Busemann functions to a different field. These functions have been used traditionally in a field called metric geometry, and our work, along with some from a professor at Washington, made them work in probability theory, which is very different. Our success led to several new results that unified many past works by others. Much of my current work focuses on exploring these functions and their applications.
How did you find your way to mathematics research?
As a child, I was encouraged to study and learn as much as possible. Even in preschool, I was working through second- and third-grade math workbooks. I learned very early that I enjoyed doing math problems.
When I started college at the University of Florida, I chose computer engineering because I heard it was a difficult major. It was indeed challenging, but also very interesting. During my second semester, I had a choice between theoretical or computational linear algebra. I heard that the theoretical course was harder, so I took it, hoping to learn more. Because I really enjoyed abstract reasoning, I decided to double major in computer engineering and math. But when the time came to choose what to study in grad school, it was clear to me that I liked math more.
In grad school, I was hugely influenced by my advisor. He taught me all about research, going to conferences, networking with people, and what problems are interesting. He also taught me research skills, such as how to reduce complex problems to simpler ones.
What advice would you give to a college freshman who wants to be a mathematician?
As early as possible, take a few pure math courses and a few applied math courses. It is good to know early whether you prefer applications and real computations over proofs and abstract reasoning. Take as many math courses as possible, and try to do some summer reading one-on-one with professors. Having a broad background will help you choose the right graduate school for your specific interests.
If you could not be a mathematician, in what line of work would you be now?
As I get older, I have become more motivated by the feeling I get when I appreciate the beauty of a mathematical argument or structure. I get this same feeling when listening to classical composers or reading profound books. In fact, nearly anything could bring me this feeling, as long as I take it seriously and pursue it with curiosity. Likely it is easiest to do this in an academic atmosphere, so I would try to be a professor of some other subject, maybe piano performance or literature.
What is the most exciting thing about being at Georgia Tech?
When I was in high school in Florida, many students who were interested in math or science tried to go to Georgia Tech, because it was the best school nearby. I was accepted, but ended up going to the University of Florida for financial reasons. So it is very exciting to be at Georgia Tech not as a student, but as a professor! The faculty are great researchers, often coming up with ground-breaking results. It is a great environment for my work.
What are you most surprised about in your encounters with Georgia Tech students?
I have been surprised by the diversity of student backgrounds and the variety of scientific perspectives here at Georgia Tech. I have not been at a technological institute before, and it is great to see so many people who are like me -- interested in engineering, math, and the sciences. Furthermore, students come from all possible backgrounds and ethnic groups. It is great that the student body seems to be less homogeneous than I expected.
What unusual skill, talent, or quality do you have that may not be obvious to your colleagues?
I have played classical piano since I was 9 years old. I'm out of practice now, but I was pretty serious in college. Most of the music I listen to now is classical, and lately I have been listening nonstop to the Mahler symphonies, which may be obvious to my colleagues, as they can hear it coming through my office door.
What is your ideal way of relaxing?
I love spending time with my wife and daughter, and I get to do this nearly every night. I used to come home and work all night, every night. But since having a child, I do not do that anymore. I am forced to slow down and play with my daughter and her toys. I also go to the gym every day and make sure I read a novel while doing cardio. This is not so much relaxing, but is it is not work related.
What three destinations are still in your travel to-do list?
I would like to go to Japan, Australia, and somewhere in Africa. I have heard many good things about Japan from a good friend who lives there. Australia is just so far away that I would like to be able to claim to have gone there. And Africa offers so few opportunities for conference-related travel, so this makes me even more interested.
If you won $10 million in a lottery, what would you do with it?
It is unlikely that I would ever play the lottery, as the expected gain is very low. It is a waste of money. However, if I were forced to play and I won, I would pay off my student debts. After that, I would buy a house, and then give a lot of money to my family. The rest I would save. There aren't too many items I really want to buy.
What is your research about?
I work in the field of arithmetic geometry. One type of fundamental problem is finding whole-number solutions to equations such as x⁵ + y⁵ = z⁵, or showing that no such solutions exist. This kind of problem goes back almost 2,000 years to the Greek mathematician Diophantus; hence they are called Diophantine equations.
The idea behind arithmetic geometry is to first consider the space of solutions to the equation in complex numbers x,y,z. This space is geometric in nature; for instance, if you squint hard enough, the space of solutions to x⁵ + y⁵ = z⁵ starts to look like a donut with six holes.
One then makes geometric arguments about this space and uses some very deep theorems to derive the properties of the set of whole-number solutions.
Math is worth doing for its own intrinsic beauty and for the subtle understanding about the world that it gives us. Although pure math is not concerned with practical applications, historically it has proved over and over again to be useful in the most surprising and important ways. A recent example is the use of elliptic curves defined over finite fields (an important player in arithmetic geometry) in some of the most advanced encryption algorithms in use today.
What has been the most exciting time so far in your research life?
I spend about 95% of my research time writing and revising papers, doing straightforward verifications, or just plain being stuck. The other 5% is where the "aha!" moments happen that make it all worth it.
So far the most memorable time was when I solved my Ph.D. thesis problem. For weeks, I had been thinking hard about the same thing. Then one day, just as I was spreading mayonnaise on my sandwich for lunch, I realized what to do to make the final step work. From there, the solution was like a cascade of dominoes, with everything falling exactly into place. That was not only extremely satisfying. It also launched my career: I was one of the first people to use so-called tropical geometry to solve a problem in arithmetic geometry, which strategy has become something of a cottage industry now.
How did you find your way to mathematics research?
My father has a Ph.D. in physics, so I grew up assuming I'd get a Ph.D. as well. I was always interested in thinking about math. For instance, in high school, when I realized I didn't know why the Pythagorean theorem was true, I spent one evening working out a nice geometric proof. Of course this proof had been known since Greek times, but it was satisfying to work something out on my own.
I didn’t get serious about studying math until freshman year of college, when I discovered that I enjoyed my math course more than my physics course.
What advice would you give to a college freshman who wants to be a mathematician?
Being a mathematician is both an extremely solitary and a very social activity. Learning, understanding, or communicating mathematics takes a large amount of care and rigor. It is best done alone, with no distractions and with long periods of concentration. But you should also interact with a community of peers, to chat about the most compelling things you’ve learned or thought about recently and to work together when you get stuck, which happens daily.
Take intellectual risks. Sign up for a graduate course even if you’re not sure you'll get an A in it. Go to seminars and expose yourself to concepts you might not understand. Try undergraduate research programs. Never be afraid to tell someone that you’re confused, and ask them to explain something more slowly.
If you could not be a mathematician, in what line of work would you be now?
I'd probably be a computer programmer. I've always been good with computers. I learned Basic programming when I was around 12.
What is the most exciting thing about being a part of Georgia Tech?
The students. I really enjoy teaching upper-level undergraduate math classes. Some students are extremely hard-working and talented. I derive a lot of pleasure from interactions in class and office hours.
What are you most surprised about in your encounters with Georgia Tech students?
Individual students often surprise me greatly. I've had very good students who participate in activities such as professional cage fighting, EMT work in ambulances, cheerleading for a major professional sports team, and serious bodybuilding. I never know what to expect when a new student walks into my office.
What is an unusual skill, talent, or quality you have now that is not obvious to your colleagues?
I used to be a very good lindy hop dancer. You can find videos on YouTube. Start by searching for the Rock Step Lobstahs.
What is your ideal way of relaxation?
The real answer is a movie and a beer, but I’m going to go with jogging. I run about 4.5 miles almost every day, a great way to clear my head. My wife and I just had a baby, though, so all of my routines are up in the air at the moment.
What three destinations are still in your travel to-do list?
I have to do a lot of traveling for work, 5-10 conferences all over the world each year. But I would always prefer it if the conference were at Georgia Tech and I could stay at home. So instead of listing places I wish I could visit, I'll mention the three most interesting places where I've attended a conference since I came to Georgia Tech: Fukuoka, Japan; Papeete, French Polynesia; Rio de Janeiro, Brazil.
If you won $10 million in a lottery, what would you with it?
I'd put it in low-risk investments and live off the interest. I never particularly wanted to be rich. I'd much rather have stability than wealth, thus my choice to become a tenured professor. That said, with $10 million, I’d have enough income to build an obscenely powerful personal computer, just for kicks.
What is your research about?
I work on theory and algorithms of graphs. A graph consists of nodes and links joining nodes. Many real-world situations, including social networks and communication networks, can be modeled by graphs.
My current research has two components: basic mathematics research in graph theory and application of graph theory to other areas of mathematics and engineering.
Examples of basic research in graph theory are problems related to the Four Color Theorem, which states: Given a map of countries, one can always color the countries with at most four colors such that countries sharing borders always have different colors. Techniques we developed may be used to solve other problems in graph theory, as well as related problems in theoretical computer science and engineering.
An example of applications of graph theory is a project I'm working on with engineering colleagues about radio-frequency, or spectrum, allocations for wireless communications. We use graph theory techniques to find good solutions to resource allocation problems formulated by engineering colleagues to address the technological challenges in spectrum trading.
Basic math research often leads to results and tools that can be used to solve practical problems or improve the known solutions to practical problems, which could benefit society. For example, our work on spectrum trading took advantage of underutilized communication spectra to make wireless networks more agile and efficient.
What has been the most exciting time so far in your research life?
In the past several years, I and several graduate students have been working on an old conjecture in graph theory, called the Kelmans-Seymour conjecture. We recently solved it. The work required some new techniques that will likely be useful for other problems. It will lead to PhD theses for the graduate students involved.
How did you find your way to mathematics research?
When I was in high school, I started participating in mathematics competitions and did well in them. So I gradually developed an interest in mathematics.
What advice would you give to a college freshman who wants to be a mathematician?
Build a good foundation of mathematics. Try to understand every bit of the details of what you see. Be patient; you may spend several hours (or even days) on a homework problem and not solve it. However, the thinking process itself is a very good mathematical training.
If you could not be a mathematician, in what line of work would you be now?
I honestly do not know. Maybe a musician, but I am not sure if I have the talent.
What is the most exciting thing about being a part of Georgia Tech?
I am surrounded by outstanding colleagues in mathematics. I can collaborate with engineering colleagues so that what I do in my basic research could be applied to more practical problems.
What are you most surprised about in your encounters with Georgia Tech students?
Most Tech students are good at math, want to learn math, and study very hard. I have taught at different places, where most students were not like this.
What is an unusual skill, talent, or quality you have that is not obvious to your colleagues?
I play table tennis reasonably well. Some of my colleagues know, some do not.
What is your ideal way of relaxing?
Listening to music, reading, and hiking, but I am unable to do so very often.
What three destinations are still in your travel to-do list?
Tibet is definitely one of them, but I have not seriously thought about this. Perhaps, I will wait until I retire.
If you won $10 Million in a lottery, what would you do with it?
I do not know. I've never thought about it.
Thomas is now the recipient of Georgia Tech's highest award given to a faculty member: the Class of 1934 Distinguished Professor Award.
"This award is special because it's from Georgia Tech," Thomas said. "I've been at Georgia Tech for over 25 years, so receiving this award means a lot to me."
The Class of 1934 Distinguished Professor Award recognizes outstanding achievement in teaching, research, and service. Instituted in 1984 by the Class of 1934 in observance of its 50th reunion, the award is presented to an active professor who has made significant, long-term contributions - contributions that would have brought widespread recognition to the professor, to his or her school, and to the Institute. The award includes a stipend of $20,000.
Letters of support for Thomas' nomination came from world-renowned senior researchers familiar with the significance of his work, former Ph.D. students who wrote of his record as a teacher and mentor, and former postdoctoral fellows who praised his ability to develop young talent.
Dean of Tech's College of Sciences Paul Goldbart said, "Robin is a shining star in the international firmament of modern mathematics - a brilliant researcher, inspiring mentor, superb instructor, and treasured colleague. Just today, I had the pleasure of hearing from one of our mathematics graduate students about a glorious contribution of Robin's to the famous four-color problem of map and graph theory."
Research in Discrete Mathematics
Before coming to Tech in 1989, Thomas worked at Bellcore, a telecommunication research and development company.
"The reason I came here is because Georgia Tech made me an offer I could not refuse," he said. "I was technically working in industry, but, in reality, I was also doing my own research. So, in that sense, the research part was not that different."
Thomas' research in discrete mathematics is concentrated in the fields of graph theory and combinatorics, areas with applications across a wide span, from engineering and computer science to economics, biology, and social science. The issues being researched are often motivated by real-world problems in telephone network design, airline scheduling, online auctions, and Internet design and searching. Many of the problems solved by Thomas and his collaborators were open for several decades and had successfully resisted the best efforts of the world's leading researchers.
Thomas also is director of Tech's Algorithms, Combinatorics, and Optimization (ACO) program, an interdisciplinary Ph.D. program linking the College of Computing, the School of Mathematics, and the H. Milton Stewart School of Industrial and Systems Engineering. About half of ACO's Ph.D. students go into academia and the others go into industry.
Thomas has graduated 16 Ph.D. students at Tech, and he has been an informal advisor to many others.
In receiving the Class of 1934 Distinguished Faculty Award, he joins ACO colleagues Dick Lipton (Computer Science) and George Nemhauser (Industrial and Systems Engineering), who were honored with the award in 2012 and 2015, respectively.
Persevering with ALS
In 2008, Thomas was diagnosed with amyotrophic lateral sclerosis, also known as ALS or Lou Gehrig's disease. The disease is characterized by stiff muscles, twitching, and a gradual decrease in muscle strength, resulting in difficulty speaking, swallowing, and eventually breathing.
"It's a progressive disease, where I'm gradually losing the use of my legs and other functions," said Thomas, who uses a motorized wheelchair to get around.
"I had to completely change the way I deliver lectures," said Thomas, who is on faculty development leave this semester, but usually teaches Applied Combinatorics (Math 3012) and Graph Theory (Math 6014). "I can no longer stand in front of a whiteboard. At first, I was writing my lectures on paper and using a document camera to project it onto a screen. But that's no longer possible."
Now, Thomas prepares his lectures in advance, which he says is both good and bad.
"It's good because students get to see the material ahead of time. They can print it and bring it to class. The bad thing is that I have to anticipate the students' questions. So I design my lectures where I ask the questions for them and then reveal the answers."
Of course, Thomas cannot anticipate every question. When a student asks a question that he did not expect, he answers it and asks for a student volunteer to write the answer on the white board. He also has a teaching assistant to help him prepare for class.
Although Thomas' body is failing him, his mind remains sharp and focused.
"There are lots of ongoing research projects that I would like to finish," he said. "In terms of career moves, I don't have any aspirations to be a department chair or anything similar. I'm quite happy with running the ACO Program."
Thomas, center, is pictured with his advisor and some of his former students at a conference held in his honor in 2012. The Conference on Graph Theory took place at Georgia Tech to ce
What is your research about?
My research involves using mathematics to understand human behavior and has largely focused on criminal behavior. I try to use math to help predict, solve, and defend against crimes. This research has led to tangible societal benefits, including a software program now in use by several police departments, including Atlanta's, that helps police better predict where crimes may occur today
What has been the most exciting time so far in your research life?
The most exciting time was probably when I was still a young graduate student and everything was so new. I still remember when my first paper was accepted for publication: It gave me a huge sense of validation and served as a tangible symbol of my entrance into academia as a researcher.
How did you find your way to mathematics research?
My path to mathematics research was not direct, as my degrees are all in physics. But the division between physics and applied math is a bit blurry, and given my own research interests, math made a bit more sense. So after obtaining my PhD, I went to the UCLA math department for my postdoc, and have been in math since then.
One early influence that led me on this winding path was watching Carl Sagan's Cosmos when I was a child. I still remember being in awe of the idea that you could explain the universe through equations. I knew at that time that I had to be a part of that.
What advice would you give to a college freshman who wants to be a mathematician?
I would advise them that mathematics is a huge field and that they should explore all the possibilities that being a mathematician can bring. They might end up really liking very pure, abstract math, or more applied topics. And they should explore all the future careers that can be had with a mathematics degree, outside of the obvious track into academia.
If you could not be a mathematician, in what line of work would you be now?
The answer depends on whether we are constrained to reality, or I'm allowed to give a more fanciful answer. I could simply say that I'd be a physicist, and my job would not be much different. If I'm allowed to dream, I would probably choose to be an author, as I've always loved reading and writing creatively. Or maybe a chef, because I love food and cooking.
What is the most exciting thing about being a part of Georgia Tech?
Just the atmosphere at Tech is so exciting. The students are all so great and motivated, and the research here is really cutting edge. Georgia Tech is a really positive place.
What are you most surprised about in your encounters with Georgia Tech students?
The students here have really great attitudes toward learning and take that with them to the classroom. This always surprises me, pleasantly, as it is not generally true across all campuses.
What is an unusual skill, talent, or quality you have that is not obvious to your colleagues?
I enjoy working with my hands, and I am a competent handy man around the house. I've done various things around our home, from re-plumbing our swimming pool, to installing a top-mounted chimney damper, to building raised garden beds.
What is your ideal way of relaxing?
I enjoy just lying on a raft in my aforementioned pool on a warm summer day, listening to the breeze whistling through the trees and the chirping of birds. Throw in a nice cold beverage and I'm all set. For me, relaxing often means turning off my brain for a while so that it can recharge. I think I have been able to strike a healthy balance between work and leisure, so that I don't feel starved for relaxation.
What three destinations are still in your travel to-do list?
One nice perk of being an academic is that you get to travel a lot, so that many places that were on my list have been crossed off by now. I would like to visit a South Pacific island, like Tahiti, for obvious reasons. I love trying new foods that are unconventional, at least to a Western palate, so enjoying some food tourism in a country like Thailand or Vietnam would be great. Finally, I'd really like to visit Ireland, for the beautiful green countryside and the pubs.
If you won $10 Million in a lottery, what would you do with it?
I'm not really into possessions as much as experiences, so I don't think I would go nuts buying huge homes or elaborate automobiles. After setting aside money for my daughter's future and for retirement purposes, I'd use the rest to fund travel and dinners at amazing restaurants, things of that nature. I'm somewhat miserly, so I doubt I would run through all of that money in my lifetime.
What is your research about?
I am fascinated by analogies. Much of my work involves so-called "p-adic" numbers, which are analogous to real numbers like 2 or π, but with important differences. For example, in p-adic geometry, every triangle is isosceles! This world might sound exotic and useless, but p-adic numbers play an important role in modern life, including cryptography, which is the making and breaking of secret codes.
A lot of things in mathematics appear to have no applications, but in fact, down the road, they turn out to be incredibly useful.
What has been the most exciting time so far in your research life?
In 2006, Georgia Tech postdoc Sergey Norin found a clever solution to a problem one of my undergraduate research students had been working on. Building on Norin's solution, he and I soon proved a Riemann-Roch theorem for graphs. This theorem is another mathematical analogy, between graphs, which you can imagine as being like websites and the hyperlinks between them, and "Riemann surfaces," which are classic geometric objects from the 19th century.
The Riemann-Roch theorem is used widely, from error-correcting codes to string theory. Norin and I were the first mathematicians to realize that it has an avatar in the world of graphs. The resulting paper is now my most cited work.
How did you find your way to mathematics research?
In middle and high school, I loved reading recreational math books by Martin Gardner. Many mathematicians of my generation got interested in the subject from his writings. A conference called Gathering for Gardner takes place every two years in Atlanta.
During my senior year in high school, my first-ever mathematics research project placed third place in the 1990 International Science and Engineering Fair. The project helped get me a full scholarship to the University of Maryland, College Park, where my professors encouraged me to pursue mathematics as a career.
Although I wanted to be a math major, for a while I considered double majoring in physics, history of science, or poetry. I decided to focus on math. It was actually difficult for me to make the transition from being a "polymath" to a "mathematician."
What advice would you give to a college freshman who wants to be a mathematician?
Master the fundamentals. You have to be able to understand and write rigorous proofs to be a mathematician, and it takes a lot of discipline to do this. Expose yourself to different kinds of mathematics, and try to get some research experience as an undergraduate.
If you could not be a mathematician, in what line of work would you be now?
I'd be a professional magician. I've been interested in magic my whole life, but I never seriously considered doing it as a full-time job. I doubt I'd be good at the business end of it.
What is the most exciting thing about being at Georgia Tech?
I love the fact that the overwhelming majority of students are not only really good at math, but they appreciate its value for whatever they're studying. Students want to be in my class to learn, rather than attending only because it's a requirement. That's a great position to be in as a professor. When students want to learn from me, I'm much more motivated to give them something really valuable.
What are you most surprised about in your encounters with Georgia Tech students?
I'm surprised that those who are so good at mathematics resist the temptation to major in it. Seriously, math just literally sucked me in -- I was so fascinated by its elegance and mystery.
What unusual skill, talent, or quality do you have that may not be obvious to your colleagues?
My colleagues know about the magic. They may not know that I sang in a highly regarded a cappella group in the University of Maryland, College Park; or that in 1990 I won a national poetry contest sponsored by the National Holocaust Foundation; or that in 1995 I was a contestant on Jeopardy! I came in second, but the guy who beat me went on to win the Tournament of Champions that year.
How do you like to relax?
Hmm, I'm not sure what you're talking about.
Seriously, most of my downtime now I spend with our 6-week-old baby. That's not always relaxing, but it's what I want to do when I'm not working. It's great for taking my mind off work.
What three destinations are still in your travel to-do list?
I'd like to visit southeast Asia (Vietnam, Cambodia, Thailand). I love the food, and I admire the politeness and respect for tradition in their culture. I'd also like to see Iguazu Falls, on the border between Brazil and Argentina, and Victoria Falls, on the border between Zambia and Zimbabwe. I'd explore the Amazon as well, but I hate mosquitoes. And I'm afraid of crocodiles.
If you won $10 Million in a lottery, what would you do with it?
Put it toward my kids' college education. I'd also buy my wife some really nice jewelry, as a gesture of thanks for reviewing my responses to these questions.
Note: the image above was taken in June 2015, when Matt Baker brought his "Mathemagical Mystery Tour" to more than 100 members of the Atlanta Science Tavern in Manuel's Tavern.
What is your research about?
The world intrinsically contains multiple scales, and one theme of my research is to develop theories and algorithms that help us understand how different scales interact.
One classic example is the following astronomical problem. It is well known that planets rotate around their host star due to mutual gravitational attraction. For instance, Earth finishes one period of rotation around the Sun in exactly one year. Pairs of planets also experience mutual gravitational attractions, but such interactions are much weaker and the immediate effects are not obvious, especially if one considers only hundreds of years in the stellar system.
Nevertheless, the sun burns for billions of years, and over this much larger timescale, microscopic planet-planet interactions do accumulate. The question is, Will this accumulation lead to large changes of the planet orbits? Or more generally: How do small-scale details cascade to large scales?
Quantifying such cascades across scales is critical for many important questions, such as, Will Earth keep its current distance from the Sun and maintain its nearly circular orbit, both which are essential for sustaining the climate that fosters current life forms? Where was Earth when it formed billions of years ago? Can we predict the existences of planets outside the solar system, given that we can only see stars but not planets, due to planets' small sizes and faint luminosities? Will these so-called exoplanets be habitable?
Applications are not limited to the sciences. For instance, we have been using fast oscillations (e.g., laser) to control slower engineering systems. In this sense, my group addresses both scientific curiosity and engineering practicality, and that is one thing I enjoy about developing general methodologies.
What has been the most exciting time so far in your research life?
When scientists, engineers, and I collaborate, we always iterate many times to carefully formulate the problems, solve the core difficulties, and interpret the results. It is also the case when I work on mathematical proofs. Serendipity seldom happens to me; what happens more often is many solid little steps. All I do is prepare myself by thinking constantly, so that whenever good things happen they will not be missed.
How did you find your way to mathematics research?
Like many kids, I participated in informatics and mathematics Olympiads, which I found enjoyable. Such enjoyment may not be practical, as the competitions are serious and require significant training. I never qualified for the national teams to compete internationally, but my life has been positively changed.
In addition, my father, even though he was working in a non-STEM discipline, had an amazing curiosity about physics, and he motivated me by asking questions – such as, What are quarks made of? – when I had just learned to spell my name. Those questions sparked my life-long interest in how things work at microscopic and macroscopic levels. Therefore, it is a great pleasure to work in applied and computational math, as it provides a good blend of mathematics, informatics, and physics.
What advice would you give a college freshman who wants to be a mathematician?
Behind abstractness, there is almost always intuition.
If you could not be a mathematician, in what line of work would you be now?
In the financial industry, because of my interests in probability and differential equations; a programmer because of my experiences with algorithms; a professional gamer because of my playful nature; or house husband because of my ever-expanding to-do list of house work.
What is the most exciting thing about being a part of Georgia Tech?
Everyday Im discovering new exciting things, but so far what I have enjoyed the most is that Georgia Tech is one of the best technology schools, where stellar scientists, engineers, and mathematicians are just doors away, open to engaging discussions. I have equally enjoyed working with the wonderful students, who are positive, modest, eager to learn, and contributing to a lively campus life.
What are you most surprised about in your encounters with Georgia Tech students?
Given how good a university Georgia Tech is, the students are really modest and objective. Teachers should of course always try to teach as well as they can. But sometimes students do not try hard enough to learn, and whatever they cannot learn is the teacher's fault. This blaming of the teacher seldom happens here; instead, the relationship between students and teachers is generally healthy, with objective mutual feedbacks promoting quality education.
Tell me about an unusual skill, talent, or quality you have now or in the past that is not obvious to your colleagues.
I normally don't sing out of tune.
What is your ideal way of relaxing?
I enjoy many common ways of relaxing, except for drinking alcoholic beverages. Because I cannot work more than 10 hours per day in a sustainable way, I do relax quite often.
If you won $10 Million in a lottery, what would you do it?
One part of my research is on rare events modeling and simulation. I, like many others, claim that small- or zero-probability events will never happen. Consequently, to characterize these nevertheless important events, it is necessary to conduct extra analysis and design biased algorithms. Winning the lottery would shatter my research premise, and therefore I would mourn for a while. Then I will secretly invest the money.
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