Faculty Notes
New Faculty
NOHA ABDELGHANY
“I just fell in love with it,” she said. “It was the best class that I had ever taken at that time. I would do my computer science homework really quickly and get back to the math.”
Even though math sparked something inside of her, she didn’t really consider pursuing a degree in mathematics.
“I was a little resistant because I didn’t want to be a teacher. And that was the only thing that came to mind. If I’m going to major in math, my only career option is to be a teacher,” said Abdelghany, an assistant teaching professor of mathematical sciences.
But Abdelghany realized that math was her passion, so she switched majors, earning her bachelor’s of science in mathematics from Cairo University and her Ph.D. at Western Michigan University. Her research interests are in algebraic coding theory, the math that’s behind-the-scenes of many areas of communications, including television, email and text messaging. In her research, Abdelghany works to design error-correcting codes that can reliably transmit information across noisy channels.
Abdelghany loves doing research — but here’s the ironic part — she ended up loving teaching more than anything.
Seeing students actually getting it, seeing that light bulb go on, is rewarding for Abdelghany. And she also sees the value in being herself — a female mathematician — and how important it is for students to see relatable role models. As a visiting assistant professor at Colby College, Abdelghany interacted with a lot of minority math students.
“They would come to me and say: I loved it when I saw you in the classroom. It was really nice to see someone who is not the standard older white male. Seeing you, I feel like I can achieve something,” she said.
For someone who did not want to be a teacher, Abdelghany has found her calling. And she doesn’t hesitate to pass along her wisdom to her students.
“The problem-solving skills and critical-thinking skills you learn from majoring in math put you on the path to do anything you set your mind to,” she said.
■ Amy Pavlak Laird
THERESA ANDERSON
“It was just so liberating, seeing the creative aspect of math and seeing that yes, the way I think has a place here,” said Anderson, an assistant professor of mathematical sciences.
Sixteen years after that inspiring math class, Anderson still gravitates toward math problems that are not so rigid, ones that she can approach from a variety of perspectives. Her area of expertise is in harmonic analysis and number theory, two fields that may seem like a non-traditional pairing, but make perfect sense to Anderson.
“I tend to connect areas of mathematics and not constrain myself. I pull techniques from a variety of fields and go out of my comfort zone to explore new things,” said Anderson, who earned a master’s degree and Ph.D. in mathematics from Brown University and completed an NSF Mathematical Sciences Postdoctoral Research Fellowship at the University of Wisconsin-Madison.
Along the way she’s discovered that her unconventional way of approaching mathematical problems is inspiring to students, including the fact that she herself — a woman doing math — is still somewhat unconventional. In Anderson’s experience, just being that face on the web page is huge.
“People see that, and it’s very powerful. Oh look, it’s a woman. Students will just come and talk to me, and those talks oftentimes lead to mentoring relationships,” Anderson said.
Anderson plans to continue fostering those types of relationships in her role at Carnegie Mellon, especially when it comes to supporting minority students interested in math. Anderson’s family is not white, and her experiences as a white member of a minority community have shifted her perspective.
“I think for people who don’t have that perspective, they just have no idea. That’s one of the things I want to try to help with — getting the next generation more involved and more aware of how small things can actually have big impacts on minority communities,” she said. “That’s what I have in mind throughout my teaching, whether it be a math course or a social justice course: to open a student’s mind to not just fill it with information but also to open it to different perspectives.”
■ Amy Pavlak Laird
KONSTANTIN TIKHOMIROV
“I realized that there are truly gifted software engineers who set up companies and create beautiful products. I felt that my personality is not of that type. Whereas in math, I’ve always had feelings that I can do much more,” said Tikhomirov, an associate professor of mathematical sciences.
Tikhomirov started taking graduate courses in math while working part-time at a software company. He earned a candidate of sciences degree in Pure Mathematics at Samara State University and his Ph.D. from the University of Alberta, Canada. Between his undergraduate degree in applied math and his software engineering job, Tikhomirov lost touch with his long-standing interest in pure math questions. During his doctoral work, he found himself back in familiar territory.
“I was attracted to beautiful proofs, aesthetically pleasing statements with no real sort of applications,” he said. But then he began working on questions in probability, and things started to shift.
“I would say now, when I work on a question, I have in mind this applied perspective,” he said. “It doesn’t mean I see the engineering applications of my work, but I hope that a method that I develop along the way can be useful in some applied context.”
Much of Tikhomirov’s research has focused on asymptotic geometric analysis, random matrices, probability theory and convex geometry. He recently started to work on topics in probabilistic combinatorics — a hybrid of probability and combinatorics, where the main object of study is probability distributions on discrete structures. Tikhomirov is especially interested in questions related to random graphs, including graph matching. Tikhomirov’s career has taken him to many different places — Russia, Canada, Princeton, Berkeley, Atlanta — and he is excited to call Pittsburgh home.
“Carnegie Mellon’s math department is famous for several directions, especially combinatorics and probabilistic combinatorics,” Tikhomirov said. “In that respect, the department is perfect for my research interests.”
■ Amy Pavlak Laird
Retiring Faculty
BOB PEGO
Throughout his 40-year career, Bob Pego has come to expect the unexpected. The discovery of a surprising formula led to years of exciting research, and collaborations spurred creative new research directions.
“It’s always nice to see these directions flourish unexpectedly,” said Pego, an emeritus professor of mathematical sciences. “Being a mathematician with the freedom to chase after those things is a really good situation to be in.”
Shortly after arriving at Carnegie Mellon University in 2004, Pego’s research took off in a completely different way after he and a colleague found a novel formula for the pressure in the Navier-Stokes equations for incompressible fluid flow. That discovery led to a series of papers over the next few years. His work on nonlinear waves also changed course thanks to the insight of a visiting Japanese mathematician. Together with Tetsu Mizumachi from Hiroshima and Shuming Sun from Virginia Tech, Pego made progress on stability of solitary waves, including solitary water waves. Pego’s research interests are broad but generally concern dynamical behavior in nonlinear partial differential equations that model a wide range of phenomena. Some of those events include incompressible fluid flow, water waves, coagulation dynamics — and the size distribution of schooling ocean fish.
Pego and his collaborators Jian-Guo Liu and Pierre Degond were fascinated by studies done by a Japanese fisheries scientist. They knew they had something to offer.
“We knew that the kind of models we were studying, in principle, were capable of describing this size distribution,” Pego said. “But in the end, the research involved some lovely new math for generating functions of sequences of moments, which is related to work of Hausdorff.”
Over the years, Pego has found joy in interacting with colleagues and students. While at CMU, he advised six Ph.D. students and several undergraduates pursuing honors theses.
“There was always some problem you can pose and have young people work on it in exciting ways,” he said. “With each one, it was a wonderful adventure in discovery.”
As he heads into retirement, Pego plans to tackle his backlog of research issues, with the goal of getting together more often and for longer stretches with his collaborators.
“I find it best to work in teams, with people I can bounce ideas off of,” he said. “The number of times where it seems like you are leapfrogging with the other person — there’s one good idea, and another good idea that just stacks on top of it — it turns into something really unexpected. It’s been an amazing ride.”
■ Amy Pavlak Laird