Faculty Profile: Samuel Ballas
By: Shelby Fintak
That old graduation speech cliche, the one about doing something you love so you never have to work a day in your life, is a linguistic lie. Anything worth loving is hard work. Lots and lots of work. Movies do not get made, nor gourmet cuisine cooked, nor convex projective geometry explained without feeling frustrated, confused, or stuck along the way. The adage has some truth, though. You should always follow your interests. That doesn't mean we'll all become bohemian loafers in a 19th century novel. Some of us, like Sam Ballas, will willingly think about low dimensional geometry and geometric structures. When your work, which is definitely still work, interests you, the results have meaning. And what else is there but that?
The beauty of math caught Ballas' attention during his undergraduate years at Emory University. Amid all the pre med courses he was taking, math started to stand out. "I started doing really well in the math classes, so I kept taking more. It was something I was good at, that I was interested in," he said, "so, I decided I was going to become a math major."
Ballas describes math as an endless source of puzzles, concealing its inherent order behind a veil of chaotic mystery. "It's very beautiful in a lot of ways." This interesting juxtaposition showed him the structured niceties of the universe. Something that was difficult to do by hand could miraculously be revealed by math. "The universe just arranges it for you."
His primary motivation is to be intrigued. A problem you can't really pour yourself into is doable, but the chances of getting good results greatly increase when you can wholeheartedly cozy up in that mind set, like tea settled into a mug. Sometimes, one mindset leads and bleeds into the next. "I tend to work well by analogy. When I learn something new that seems to have something in common with [my previous studies], I try to push those similarities and see how far they can go, and where they breakdown." If the breakdown happens at a dead end and none of your problems seem to be panning out, don't worry. There's hope. Ballas recollects facing a similar roadblock during his final years of grad school. After attending a Mathematica Research Community on real projective structures, he returned home with a newfound interest in convex projective geometry, a singular focus, and eventually, his graduate thesis.
A grad student on stage. Undergraduate thesis in hand. He puts pieces of his paper on the board with a marker, and reads his own words directly. It feels like a small mercy that only other graduate students can hear him right now. He shudders to think any professor bears witness.
"I tend to work well by analogy. When I learn something new that seems to have something in common with [my previous studies], I try to push those similarities and see how far they can go, and where they breakdown." Samuel Ballas
Everybody's first talks are terrible. "When you see a good speaker, you're sort of fooled into thinking 'this is not a hard thing to do,' but then you start trying to give talks and you realize you're really bad at it."
The goal of the Topology and Geometry Seminar, organized this semester by Dr. Ballas, is two-fold. Overtly, it introduces graduate students to current research with faculty talks and invited guest speakers. But inherently, the main idea is to get graduate students familiar with expositing on mathematics. Which is way harder than it looks. Dr. Ballas encourages the development of this comfortable environment, in which graduate students learn to present confidently, articulately, and hopefully recognize the benefits of neat handwriting.
"I remember a talk where I drastically overestimated how much material I had and finished after like 30 minutes. Usually, talks are 50 minutes to an hour. It's much easier to go over time than it is to go under, so that's a special kind of mistake you can make."
He's certainly improved since then, giving talks in Texas, California, Georgia, France, Germany, and Korea. And what's more, Dr. Ballas teaches by example. He presents his talk on gluing equations for projective structures on three dimensional manifolds at the Topology and Geometry Seminar this April.
Ballas' knack for spotting connections isn't limited to research and geometric concepts. He remembers the effect good teaching can have and attempts to embody those characteristics he admired as a student. He mentions in particular one of his college professor's ability to read a room and pull drifting students away from the lull of daydreams and drool. "He was often unpredictable and would do weird things like occasionally tell us ghost stories. It kind of kept you on your toes," he recalls. "I try to be a little less predictable in the classroom."
Even the research itself benefits his teaching style. Working all day to relate concepts and flex mathematics in new and interesting ways, Ballas often discovers new perspectives on material he learned some time ago. "It often gives me different ways to approach material I'm teaching. I try to incorporate that thought process and explain it to the students. It gives me new ways of trying to relate the material." When today's lesson covers the rigidity properties of a hyperbolic metric on three dimensional manifolds, nothing puts a student at ease better than the teacher having a second and third way of explaining it.