Our Communications, Development and Outreach committee and editorial staff invite you to take a look at the 9th edition of our newsletter, the ProofReader. This edition covers events in School of Mathematics from September 2015 through July 2016.
In this issue, we discuss the vast efforts made by the School and its members towards improving diversity, both inside the School and in the fields of mathematical sciences. As before, you will also find articles about the School's graduate and undergraduate academic programs, faculty news and events, mathematical history and research.
School of Mathematics Professor Haomin Zhou will receive the Georgia Power Professor of Excellence Award during the men's basketball game between Georgia Tech and Notre Dame University, this coming Saturday (January 28, 2017) during the half-time show at noon. The award recognizes one selected professor from each of Georgia Tech's six colleges, and aims to bridge academics and athletics.
Rachel A. Kuske took over as chair of the School of Mathematics on Jan. 3, 2017. The first woman to lead the school, she arrives at a time when the school is poised to take the next steps toward greater leadership in mathematics and expanding opportunities for students, postdocs, and faculty.
Kuske was most recently a professor of mathematics at the University of British Columbia (UBC). She was chair of the UBC Department of Mathematics in 2007-11. Since 2011, she served as a senior advisor to the provost on women faculty.
“Rachel is a highly accomplished leader as university researcher, educator, and administrator and is renowned for her expertise, energy, experience, and expectations for excellence,” says College of Sciences Dean Paul M. Goldbart. “Not only does she bring to Georgia Tech valuable domain leadership, but she also has a record of commitment to building bridges to related disciplines, especially engineering and the sciences, and she understands well the value of such bridges in the setting of the modern technological university.”
In a wide-ranging conversation, Kuske discussed her research, what drew her to Georgia Tech, what’s next for the School of Mathematics, and diversity as part of strategy.
"I work in applied stochastic dynamics, understanding the dynamical processes of phenomena that evolve over time in some complex way, but with some randomness. This area has a range of applications, including optics, neuron signaling, disease cycling, and climate dynamics.
"Mathematics is a great unifier. Mathematicians can look at some behavior, understand the models of that behavior, and boil it down to an abstract framework. Then they modify the framework depending on what they observe.
"They can apply that framework to other phenomena. What’s common with all mathematics is that certain structures to explain certain behaviors in one field can be brought to other fields. As soon as you can reduce something to an abstract framework, you can start look around for things that might fit in the same framework. In this way, mathematics connects fields that otherwise might never speak to each other."
GEORGIA TECH’S APPEAL
"So many things going on at Georgia Tech are of interest to a mathematician, from the viewpoints of applications and the strong quantitative angle. Georgia Tech has a lot of mathematically oriented people across campus.
"I had a job offer here 20 years ago. Although the School of Math and Georgia Tech were already very good then, I turned down the offer. Atlanta was not an attractive city for me at the time. Twenty years hence, Atlanta has transformed.
"Another big draw is the people in the school. In the end they were the ones who really recruited me. They basically said, we’re ambitious, there’s lots of things we want to do, and we hear you’re the person who will help us make it happen. The faculty saying we have a great trajectory and we want you to run with us—that is much more attractive than a head hunter’s call."
"Our faculty members are already leaders in research and education. Their visibility is already very good. The school is on a good trajectory for greater leadership globally. As we continue to hire strongly, recruit top-notch people, and expand our graduate program and our postdoc program, consistent high quality as a global player will naturally follow.
"We can be better in leading at Georgia Tech. Many Georgia Tech units are just hungry for it. We need to figure out how faculty, postdocs, and graduate students can engage fully in opportunities between schools and in other places. In a number of interdisciplinary programs where we play a key role, we can play an even bigger role.
"We should bring more people and resources to Georgia Tech rather than researchers going elsewhere. We want to make Georgia Tech a hub for mathematical activity. Georgia Tech as a hub will put us on the map in terms of recruiting. People will want to be here because great things are happening here.
"We want to transform undergraduate education so that the mathematics major generates options for students, including connections to other academic programs. We want students to know that if they come to the school, they will get a solid quantitative foundation from which they could pursue a variety of paths, at Georgia Tech or elsewhere.
"I’d like to hear from our majors. We have hopes and dreams for the school to support the hopes and dreams of students. We like to make sure those align."
"Generally, diversity is valuable. Strategically, organizations tend to do better when they are diverse and inclusive.
"Diversity is a thread that permeates across and holds up the pillars of research, education, and leadership, just like good governance, effective communications, or robust development activities. Viewed in this way, diversity gets built in everything you do.
"I would like diversity to just be a normal part of operations, without having to think about it. In many cases, however, we have to highlight efforts to help normalize inclusive practices and remind people that diversity is a part of what we do. Recognizing that it can appear in different scenarios, we need to make sure our processes are adapting for it."
Congratulations to Zaher Hani, the School of Mathematics most recent recipient of an NSF CAREER award! Zaher continues the School of Math’s success in this program, with 5 awards in recent years.
The Faculty Early Career Development (CAREER) Program is a Foundation-wide activity that offers the National Science Foundation's most prestigious awards in support of early-career faculty who have the potential to serve as academic role models in research and education and to lead advances in the mission of their department or organization. A CAREER award is viewed by DMS as the highest distinction that NSF can provide to junior researchers in the mathematical sciences.
NOTE FROM THE EDITOR: This blog post was first published on the Georgia Tech Lorraine blog on March 8, 2017, by Samuel Burke.
Last week I had the wonderful opportunity to sit down with Dr. Wing Li, the mathematics professor at GTL for this semester. I attend the class she is teaching for undergraduates this time around, differential equations, twice a week and can personally attest to the fact that she is one of the most genuinely nice professors currently teaching at Georgia Tech, and someone who really does care about her students learning.
I learned from Dr. Li that she attended high school in Hong Kong, which is where she first realized that mathematics was the subject she wanted to pursue into college and beyond. After graduating from high school, she moved to the United States by herself to attend an American college, first receiving her B.S. from the University of Iowa, and then her Ph.D. from the University of Michigan, both in mathematics. Now Dr. Li teaches at Georgia Tech and is currently in her 3rd semester at our French campus.
Dr. Li told me that she believes that many professors are reluctant to volunteer to teach at GTL, often due to having kids who are currently enrolled in primary or secondary school in the Atlanta area. However, Dr. Li is in the unique position of being married to a native of France and having kids who are fluent in the language. She told me: “it was an excellent experience for the children, not only did they get to learn subjects in French, but they also got to really see the differences between the American and French school systems.” Because of this, Dr. Li was more than happy to volunteer for the position multiple times.
Currently Dr. Li is involved in research related to a subject called operator theory, which she described to me as basically being linear algebra (matrices, subspaces, etc.) but with infinite dimensions. She says it is an extremely interesting subject since: “you can’t just use a calculator or a computer to solve for the answer when you’re working with infinite dimensions. You have to really break everything down to pure theory instead of solving for specific examples.” Also, “if you can understand how things work with infinite dimensions, working with finite dimensions becomes simple.”
Outside of math, Dr. Li told me she’d always had an interest in music. Following graduate school, she began taking piano lessons, but not having a piano of her own to practice at home, she switched instead to voice lessons. “It was convenient because I will always have my voice with me, but I didn’t realize how much of a strain lecturing for hours every day would be.” So, finally, she ended up choosing the violin, which she practiced an hour every day for 8 years until kids came into the picture.
At Georgia Tech Lorraine, students are encouraged to travel as much as they can, so I thought I’d ask Dr. Li a little about her travels. She told me that of all the places she’s been to the Greek islands struck her as the most beautiful, but the place that had the greatest impact, she revealed, was actually Alaska. “I had never seen anything so vast, yet in a way it was romantic and inviting. A place where I would very much like to stay and contribute to the land instead of just pass through.”
Dr. Li’s parting words to me were ones of advice for students here at GTL “don’t miss Metz,” she told me. “As you travel to famous locations all over Europe, don’t forget about the place you are calling home for these 4 months, and the incredible beauty and history that is right in our backyard.”
NOTE FROM THE EDITOR: This story by David Mitchell was first published by the College of Computing on March 9, 2017.
For Jon Eisen, everything has always been about numbers.
The path that led him to speak on behalf of the prominent video game hub Activision, publishers of the popular Call of Duty franchise, at last week’s GVU Brown Bag event has been paved with them.
He majored in Applied Mathematics at the Georgia Institute of Technology, graduating with his degree in 2009 and carrying along a Computer Science minor for good measure. He spent time designing RADAR algorithms for Northrop Grumman Corporation in Baltimore, Md., and then worked as an application developer for a short period at Under Armour.
Even hobbies in his free time are unique because of specific numbers associated with them. Take the number 50, for example: The number of miles he plans to run in his first ultra-marathon, the Quad Rock 50, in May.
While his focus has always been on numbers and equations, though, Eisen said it has been his versatility – merging his background in math and computer science – that has helped him establish a career he’s excited to pursue on a daily basis.
He’s worked at Activision for just over a year, where he combines his fascination with raw numbers with a background in video games.
As a data analyst, he works to answer questions. For example, does the game play fast?
“Well, that’s a broad question,” he explained. “Answering that might involve asking more questions. It’s very research-oriented. You might look at map size or how players play the game or the way different elements are designed.”
It’s a familiar process for Eisen, who has been a sports fan for years. Growing up a fan of the Atlanta Braves and eventually delving deeper into the world of fantasy sports, Eisen learned unique ways to look at the long list of available statistics.
“I started getting into sabermetrics, advanced analytics in baseball,” he said. “I began to understand that there’s a better way to look at stats than just at the typical ones. They help provide answers to questions like whether you should always intentionally walk Barry Bonds. That’s an interesting question. The numbers help answer it. I got really into those question-answer analytics, and at Activision I had the opportunity to go deeper into this stuff.”
He looks at win probability, value metrics, and any number of additional stats that help answer the question: Are you good?
Eisen doesn’t work exclusively in programming, but his understanding of the development side has been a boon to his career, as well.
He earned a minor in computer science at Georgia Tech after realizing he was on track to graduate with his degree in Applied Mathematics too early. In his major, he needed only 120 credit hours, and he carried a fair portion with him from high school.
He had already pursued a working knowledge in computer science beginning in his freshman year of high school, working with Flash and building websites, including one for rush for his fraternity, Alpha Epsilon Pi, in college.
He didn’t pursue a major in the field because, he said, he wanted to learn it all on his own.
“I was a kid,” he said, laughing, by way of explanation.
With his extra time, though, he focused on computer science courses that filled gaps in his knowledge. He was glad that he did.
“Some of those classes helped me get my first job,” he said. “When I was working on the RADAR stuff, I had this unique ability to merge two key disciplines. They had a lot of math people, and they had a lot of CS people. They had to take these algorithms done by the math people and put them into systems. At some point, I found that I was good at that. That helped me take interesting math algorithms and put them into scalable code.”
It’s something he said he has gotten back to doing at Activision.
“Computing is taking over the world,” he said. “If you like your discipline, whatever that is, learning a bit about how to program with it is going to be very beneficial in creating your career.”
Stavros Garoufalidis started his mathematics education in Greece. As a high-school student, he participated in an International Mathematical Olympiad. He received a B.S. in Mathematics from the University of Athens, Greece. He completed M.S. and Ph.D. degrees in mathematics at the University of Chicago. He joined Georgia Tech in 1999. Fluent in four languages—Greek, English, French, and German—he is also an associate editor at the Journal of Knot Theory and Its Ramifications, as well as an avid beekeeper.
What is your research about?
My main area of research is quantum topology, which is a combination of studying all three-dimensional shapes, building physical theories about them, and thinking of each shape as a possible universe. 3-D shapes can be described by drilling tubes through a solid (for example, cheese) and then filling them in after possibly twisting. The holes are known as knots in three-dimensional space, that is circles that are allowed to move as long as they do not meet themselves.
What has been the most exciting time so far in your research life?
I have enjoyed collaborating with more than 54 researchers over the years on several projects, discovering new connections and predicting outcomes of difficult computations.
One of those predictions involves the number 697, which we found in some numerical computations with Don Zagier, the American mathematician who is now the director of the Max Planck Institute for Mathematics. The number appeared in totally unrelated mathematical physics computations in a different context. The presence of that number gave us confidence that our results are not coincidental, and in fact, they formed the foundation of deep conjectures and theorems in number theory, quantum topology, and mathematical physics.
How did you find your way to mathematics research?
When I was a high school senior in Greece, I participated in the high school math competitions and took part in the 24th International Mathematical Olympiad, in 1983 in Paris. I got a bronze medal and a distinction for a solution to a number theory problem that was originally rejected, but eventually accepted as very original by the committee.
I was equally interested in physics and mathematics at that time, but I chose to study mathematics as an undergraduate. Mathematics was clear and conceptual for me. This path brought me to do a Ph.D. in the University of Chicago—my first ever time in the U.S.—where I realized what first-rate research is all about. I continued to be exposed to world-class research at MSRI, MIT and Harvard.
What advice would you give to a college freshman who wants to be a mathematician?
There are a lot of misconceptions about mathematics taught at U.S. high schools. I would advise a freshman to learn the concepts of math, not be afraid of real mathematical thought, and to practice proofs and computations.
If you could not be a mathematician, in what line of work would you be now?
In the past eight years, I have been involved with beekeeping, as a way to stay in tune with nature, seasons and geography, as well as an entrance to an alien world of insects working together as a superorganism. Beekeeping could become a profession if math was not available.
What three destinations are still in your travel to-do list?
I love traveling and have been to 30 countries so far, but I have always been thinking of visiting Africa, India, and Antarctica. Since my teenage years, and while learning history of the Middle East, I've been fascinated about the idea of traveling through Turkey, Iraq, Iran, Afganistan, Pakistan, and eventually reach India. Such a trip would be rich in experience, history, and culture. Unfortunately, the times that we live in make this idea impractical.
If you could have dinner with any person in history, whom would you invite?
I wish I could have dinner with Archimedes and Gauss—the two best mathematicians of all times.
Lutz Warnke is an assistant professor in the School of Mathematics. Before he joined Georgia Tech in January 2017, he received the 2016 Dénes König Prize from the Society of Industrial and Applied Mathematics. The Hungarian mathematician Dénes König (1884-1944) was a pioneer of discrete mathematics.
What is your research about?
The main mathematical objects I study are called graphs, which are also known as networks in everyday language. In simple terms, a graph is a collection of points with links (or line-segments) connecting them. Besides being of theoretical interest, graphs have a number of different applications. For example, in network science, they are used to gain insights into concrete networks such as food chains and communication networks. Certain models of graphs are also used to simulate or predict properties of real-world networks, such as Facebook (where points correspond to members, and links represent friendships).
Random graphs are my core area of research. These graphs are constructed by adding the links or points in a random way (for example, by flipping coins to decide which ones to add). While some people consider random graphs to be toy models for real-world networks, I like to think of them as idealized reference models that can, for example, guide the study of concrete networks (to help identify which parameters and phenomena are interesting/worth studying, and which are not).
I have extensively studied the connectivity properties of random graphs. Perhaps surprisingly, random graphs can undergo “phase transitions,” similar to how water changes its state. Indeed, as we add more and more links to the graph, the size and structure of the connected sets of points undergo quite a dramatic change. They can go from small sets made of relatively few points to a situation where there is a big set containing 1% of all points (and a bunch of smaller sets). To put this into context, if the underlying random graph represented a model for the paths along which diseases spread amongst a population, then the aforementioned sizes of the connected sets could, for example, be vital in predicting the possibility of a pandemic.
Nowadays researchers from a variety of different backgrounds study random graphs, ranging from applied mathematics to physics and to biology. Motivated by applications, such interdisciplinary effort often leads to new viewpoints and questions, which I find particularly exciting from the perspective of pure mathematics.
What is the work for which you received the Dénes König Prize?
I was awarded the Dénes König Prize for my contributions to the study of phase transitions in random graphs that change over time. Achlioptas processes are interesting variants of classical random graph models that are easy to define, but hard to analyze. In a nutshell, the standard mathematical techniques in the area did not apply to these models due to a number of technical difficulties. In joint work with Oliver Riordan I was able to overcome some of these difficulties and prove a number of properties which were hitherto out of reach. Our new techniques have recently also found further applications, enabling us to prove some very precise results for a large class of random graph models.
What attracted you to mathematics?
As an undergraduate student I was initially interested in theoretical computer science and was fascinated by the idea that random choices can make algorithms faster (and simpler). At first this might sound quite counterintuitive, but one of the basic ideas is surprisingly simple.
Indeed, suppose that we have a bag of real and fake coins, of which at least half are real. If we then pick one coin at random from the bag (which roughly corresponds to “blindly” grabbing from the bag), then we fail to find a real coin with probability at most 1/2. Similarly, after two attempts we fail to find a real coin with probability at most 1/2 × 1/2 = 1/4, and so on.
In other words, by repeating this random experiment a few times we are very likely to find a real coin (in a very simple way). These and related examples motivated my subsequent course choices. In classes on probabilistic combinatorics and random graphs, I learned about further remarkable phenomena in random discrete structures and a number of beautiful proof techniques. In my opinion the mix of both is quite attractive, and since my graduate studies I have been doing research in this exciting area of mathematics.
What has been the highlight of your professional career so far?
One highlight has been my work on the so-called “explosive percolation” phenomenon. Loosely speaking, a large number of simulations and heuristics suggested that an important parameter “jumps” (grows very abruptly) in a number of intriguing random graph processes, which was considered a big surprise by many mathematicians and physicists.
However, in joint work with Oliver Riordan I was able to mathematically prove that the simulations were all misleading; that is, the parameter always grows in a “smooth” way. This result was published in Science, and it attracted a great deal of interdisciplinary attention (more than 150 citations). For me it was particularly encouraging to see that a number of people outside of pure mathematics were interested in our findings and arguments.
What do you bring to Georgia Tech as a mathematics professor and researcher?
My research complements the existing strengths in graph theory and the Algorithms, Combinatorics and Optimization program (ACO). Naturally, I thus hope to contribute some new topics to the curriculum. For example, I envision an advanced course in the area of probabilistic combinatorics, which might benefit the research of graduate students in the area of discrete mathematics, theoretical computer science, and the ACO program, say. Such a course could discuss some modern tools and techniques in the area, and I hope to transfer some of my own enthusiasm to the students. Of course, it would be great if some of them develop an interest in pursuing research in the area.
The Southeast Geometry Seminar (SGS), is a semiannual series of one-day events focusing on geometric analysis. The 26th annual SGS was held this past February in Skiles. The School of Mathematics' John McCuan and Mohammad Ghomi organized the event, along with Joseph Fu (UGA), Vladimir Oliker (Emory), and Junfang Li (UAB).
The first presentation of this program was given by Yuanzhen Shao (Perdue University) on "Degenerate and Singular Elliptic Operators on Manifold with Singularities". Shao was followed by Sungho Park , who studied at Hankuk University of Foreign Studies and Georgia Tech. Park presented "Circle-foliated minimal and CMC surfaces in S3".
Following Presentations included:
Radial Limits of Bounded Nonparametric Prescribed Mean Curvature Surfaces by Mozhgan (Nora) Entekhabi (Wichita State University)
Freeform lenses, Jacobian equations, and supporting quadric method (SQM) by Vladimir Oliker (Emory University)
Stability and bifurcation for surfaces with constant mean curvature by Miyuki Koiso (Kyushu University)
Unexpected non-uniqueness of equilibria for the 2D floating Ball by Ray Treinen (Texas State University)
Abstract of these presentations can be found here.
The largest mathematics meeting in the world, the Joint Mathematics Meetings, returned to Atlanta in early January. Over 6,000 mathematicians attended this week long event. Georgia Tech was well represented at the meeting, with over 30 paper contributions, 6 AMS special sessions hosted by several faculty members, panelists, and many more organizers of sessions and events.
Two School of Mathematics professors had plenary roles. Michael Damron gave a series of lectures in an American Mathematics Society (AMS) Short Course on Random Growth Models. Damron was also an organizer of an AMS special session. Matt Baker was an invited speaker this year. He presented in the Current Events Bulletin on Hodge Theory in Combinatorics.
The Georgia Tech School of Mathematics is proud to have been well represented at the 2017 JMM.