Georgia Institute of Technology College of Sciences

What is your research about?

My research area is topology. In topology, we study properties of shapes that persist even when we stretch or bend the shapes. For example, if you have two metal rings that are linked, then they stay linked even if you bend or stretch the metal. A typical question in topology is the following: Someone hands you two rings made of metal; if you are allowed to bend and stretch the metal, can you pull the rings apart or not? 

Most of my research in topology is about surfaces. The surface could be that of a ball or a donut. Surfaces are central in mathematics. They can describe the possible motions of a robot arm or all the possible solutions of a polynomial. My particular research is on the symmetries of surfaces - if we really want to understand an object, we must also understand its symmetries! Some symmetries of surfaces are easy to understand. But when we allow bending and stretching, they more challenging.

Mathematics is important because it describes the world in a beautiful and coherent way. Even the most far-fetched and abstract mathematical ideas can make their way into everyday life. For example, I was very pleased recently to attend a lecture at Georgia Tech by Jesse Johnson, a topologist who is currently working at Google. He described an application of his research on the topology of three-dimensional manifolds to the analysis of large data sets. This was shocking to me and very satisfying.

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

It's always the new thing that's the most exciting. Just recently my computer finished a months-long linear algebra calculation that told my collaborators and me something about an important problem in geometric group theory. We still don't completely understand what the computer is telling us, but for me that is the most exciting part - being on the cusp of discovery.

How did you find your way to mathematics research?

I've had some great teachers from childhood all the way on up. I remember my grandfather explaining trigonometry to me on his back patio. And I remember my dad explaining binary to me at our kitchen table. Both of them were born mathematicians, but they never got the chance.

When I was an undergraduate at Brown University, I took a class called The Fourth Dimension with Tom Banchoff. That's where I first learned about Klein bottles and Mobius strips and other surfaces. I read books by Edwin Abbott Abbott, Martin Gardner, and Ian Stewart. I spent a weekend trying to build a torus (the surface of a donut) with 14 flat triangles. At that point I was hooked.

Dan Margalit, the juggler

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

If you love math, you should do math. Don't be discouraged if people around you seem smarter, faster, or more knowledgeable. There is way more to math than being a genius or a prodigy. If you love what you do, you'll be successful.

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

I don't understand the question.

I'm kidding, but I really have no idea. I enjoy writing and teaching. I especially enjoy finding the right way to explain a particular topic to a particular group of people. I could possibly get that kind of satisfaction from teaching high school or writing popular mathematical or scientific nonfiction.

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

The science!  The sheer volume of exciting scientific research that comes out of Georgia Tech is astounding.

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

They work very hard. And they take responsibility for their successes and failures. I don't know how many times I was expecting a student to complain to me that my test question was too hard, only to have them tell me it was a completely fair question and they should have gotten it.

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

I used to be a very avid juggler, doing stage performances and street performances. I once juggled 7 balls for something like 10 seconds. It was glorious - even though nobody else saw it!

What is your ideal way to relax?

I love hanging out with my family. I love being in the mountains. I love singing and playing music. I try to do something for myself every day.

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

I'm not a big traveler. When I lived in Utah, I developed a love for the great outdoors. Places like Alaska, New Zealand, and Patagonia - dramatic landscapes at the corners of the globe - are appealing to me.

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

I like my life, so I wouldn't make a lot of changes. I have various fantasies for popularizing math and improving math education, so I'd start thinking about ways to act on those.

As part of Mathematics Awareness Month, some of the professors in the School of Mathematics participated in interviews that explored their research focus, highlights of their career, and their personal insights. The interviews became a series of Get to Know the Math Professor articles that were featured on the School of Math website last month. All together, sixteen articles were published, and links to all of the articles are listed below.

• Matt Baker
• Michael Darmon
• Zaher Hani
• Christine Heitsch
• Christian Houdré
• Dan Margalit
• Tom Morley
• Shahaf Nitzan
• Prasad Tetali
• Joe Rabinoff
• Martin Short
• Molei Tao
• Howie Weiss
• Yao Yao
• Xingxing Yu
• Haomin Zhou

Through a series of research papers posted online in recent weeks, mathematicians have solved a problem about the pattern-matching card game, Set, that predates the game itself. The proof, whose simplicity has stunned mathematicians, is leading to advances in other combinatorics problems.

Three mathematicians in particular, Ernie Croot of the Georgia Institute of Technology (pictured to the right), Vsevolod Lev of the University of Haifa, Oranim, in Israel, and Péter Pál Pach of the Budapest University of Technology and Economics in Hungary, posted a paper online, on May 5, showing how to use a polynomial method to solve a closely related problem. In their work, the three researchers used Set attributes with four different options instead of three. For technical reasons, this problem is more tractable than the original Set problem. Not long after this, two mathematicians, Jordan Ellenberg, and Dion Gijswijt, each independently posted papers showing how to modify the argument to polish off the original cap set problem, and a joint paper combining their results. 

The work of Ernie Croot and his collaborators is continuing to make huge waves, with many interesting consequences now unfolding. Their work has already been applied to matrix multiplication, tri-colored sum-free sets, and the Erdös-Szemerédi sunflower conjecture, which concerns sets that overlap in a sunflower pattern. Their work was also featured in an article in Quanta Magazine, which gives a more detailed history of this recent breakthrough.

The Topology Students Workshop to be held during June 6-10, 2016 will feature research talks by leading mathematicians in geometry and topology, and will have hands-on training and panel discussions on professional development topics such as:

• Creating and delivering research presentations
• The grant writing process
• The publishing process
• Navigating the hiring process
• Writing teaching statements and research statements
• Working with Sage, Beamer, and Inkscape
• Creating a professional web page
• Careers in and out of academia
• Teaching effectively and efficiently
• Applying for jobs

Participants will also have the opportunity to give their own 20 minute lectures and have them critiqued in a constructive environment. The workshop is geared towards graduate students in the areas of geometry and topology.

Professors Matt Baker and Josephine Yu are organizers of the SIAM 2016 Minisymposium on Tropical Mathematics to be held at Georgia State University during June 6-10, 2016. Professor Joseph Rabinoff is one of the speakers.

Dr. Matt Baker is a featured speaker at the Benjamin Peirce Centennial Conference which will be held at Harvard University in June 2016.  This prestigious gathering of mathematicians includes Fields Medalists and other leading researchers.  It celebrates 100 years of the Benjamin Peirce Fellowship at Harvard.

Dr. Matt Baker is a featured speaker at the Benjamin Peirce Centennial Conference which will be held at Harvard University in June 2016.  This prestigious gathering of mathematicians includes Fields Medalists and other leading researchers.  It celebrates 100 years of the Benjamin Peirce Fellowship at Harvard.

Conference Poster

Five faculty members in the College of Sciences are among the recent recipients of the early-career grants from the National Science Foundation (NSF). The highly competitive awards are from the NSF Faculty Early Career Development (CAREER) program; they provide five years of funding to junior faculty.

Of the five College of Sciences CAREER award recipients, four are assistant professors in the School of Mathematics. Their names and research interests are:

• Michael K. Damron - dynamical systems, probability, and statistics

• Esther Ezra - discrete geometry, combinatorics, probability, discrepancy theory, and approximation algorithms

• Jennifer C. Hom - low-dimensional topology, Heegaard Floer homology, knot theory, concordance, and Dehn surgery

• Kirsten G. Wickelgren - algebra, geometry, and topology

Amit R. Reddi, an assistant professor in the School of Chemistry and Biochemistry, is the fifth College of Sciences CAREER awardee. Reddi studies metalloproteins. His lab is interested in determining the cellular, molecular, and chemical mechanisms by which these proteins are activated in cells and their roles in cell metabolism and physiology. 

"I'm thrilled - but not at all surprised - by the recognition of accomplishment and promise by our early-career colleagues that these NSF CAREER awards signal. Their successes reflect the vigor they bring to their respective schools and to mathematics and the sciences at Georgia Tech," says College of Sciences Dean Paul M. Goldbart.

The CAREER awards are NSF's most prestigious grant to support junior faculty who exemplify the role of teacher-scholars. Through five years of sustained support, the award enables promising and talented researchers to build a foundation for a lifetime of leadership in integrating education and research.

During July 11-15, 2016 Georgia Tech will host Summer School on Real Algebraic Geometry and Optimization organized by Greg Blekherman and Rainer Sinn (Georgia Tech) and Mauricio Velasco (Universidad de los Andes). The summer school is aimed at graduate students and recent PhD's with the goal of introducing them to latest developments in the theory of nonnegative polynomials and sums of squares and applications. The topics for the school are:

• Geometry of Sums of Squares and Nonnegative Polynomials, recent connections with Classical Algebraic Geometry
• Applications of Sums of Squares Methods in Optimization and Engineering

Location: Skiles 006.

Dan Margalit, has been selected to receive the inaugural 2016 Leddy Family Faculty Fellowship.

The Leddy Family Faculty Fellowship is awarded to a tenure track faculty member in the College of Sciences. The award is made to further the goals of the College by supporting development of the research and training program and quality of instruction of a mid-career faculty member (loosely defined as a tenured Associate Professor, or one who is just before promotion to this rank, or just after promotion from this rank). This award is made possible through a generous gift to the College of Sciences from Jeff '78 (Physics) and Pam Leddy.