by Jeff Cutler
Ting Zhou is an associate professor in the College of Science’s Department of Mathematics. Following a path that took her from her native China and Nanjing University, Zhou pursued and achieved her PhD at the University of Washington and subsequently arrived in Boston at Northeastern University.
If all math problems were as clear cut as her journey, Zhou would be out of a job. But the main tenet of mathematics and science is discovery and that path isn’t always clear. Luckily, Zhou derives satisfaction from both the math solutions and the collaborative process.
“Besides the satisfaction after solving a problem and discovering a new thing, which is 90 percent of the joy and excitement,” she said. “I like the interaction and communication among mathematicians, who are so genuine and passionate about what they do. This is mutual between me and my collaborators, and I’m striving to make my students feel the same.”
Zhou’s passion has fueled her various fields of study: using partial differential equations (PDE) for real-life modeling while getting her masters at the University of Victoria; and leveraging the math behind inverse problems to focus on solutions for medical imaging and geophysical prospection.
In the case of inverse problems, she says the connection between math and physics is obvious. In fact, even the type of mathematical analysis used in solving such problems is a lot of times motivated by plain physics.
“I am fascinated by such math that you can visualize,” said Zhou.
It’s this type of math that often offers solutions that are immediately applicable in the real world. Focused on imaging technology, she and her colleagues used math to determine new ways to use current imaging techniques and to improve on them.
For instance, she used inverse problem solving to measure electromagnetic fields near the surface of the object of interest to reconstruct the electromagnetic property inside the object. Since property values vary dramatically depending on tissue types (cancerous vs. healthy tissue), she and her collaborator Pedro Caro were able to answer “the uniqueness question of such inverse problems for Maxwell’s equations.”
Blurring the lines between traditional science and science fiction, Zhou is also working on transformation optics based cloaking. That’s right, cloaking. She explains that waves of light can be bent if you know how to modify electromagnetic fields.
“The idea is that the mathematics predicts certain design of an electromagnetic shell would bend electromagnetic waves (including lights),” said Zhou. “Away from the center region the shell encloses and return it back later to its original path. So whatever is inside the center is not visible. A motivation of such research is the advancement in material science, namely the availability of metamaterials, which allows customization of electromagnetic materials.”
Lastly, going back to advances that can help medical professionals, she’s working on coupled physics medical imaging modality. By combining two types of wave propagations, for example sound waves and optical waves, there is a hope that they can produce images with better contrast and higher resolution. Existing modalities include photo-acoustic tomography, which has produced very sharp images of blood vessels under skin.
If changing lives and delving into cool technology weren’t enough, Zhou actually walks the walk. She professes that you need to love what you do – no matter what you’re doing. She says that people need to know what they want to do so they can focus on discovery and not be distracted.
To that end, Northeastern and the College of Science have provided Zhou with an ideal environment. She says the collaborative atmosphere and the administration help make her job as a professor and researcher more productive and successful.
“The college oversees the faculty members in all the departments and they have a very good idea of their research strength and impact,” said Zhou. “This makes them the best party to realize interdisciplinary collaborations. This happens not only inside the college, but among colleges too. As an applied mathematician, this is an important passage to see our research having impact on areas that is closer to real life.”
The future for Zhou – as for all of us – is unwritten. She says that her dreams are in-line with her past successes, but also driven by her desire to discover.
“I have big dreams as everyone else, solving the most important problems and make great discoveries that change the world fundamentally,” she said. “But most of the time, I am realistic and focus on any thing that has the potential to improve the life of the world using my skills.”
As a professor, her goal is to teach and ignite a fire for discovery in her students. As a researcher, she wants to see her findings applied in imaging technologies broadly and successfully.
“Jackpot if I can see a real invisible cloak is built one day,” said Zhou. “We are in a golden age of science. People believe in, almost blindly, that scientific discoveries always help the development of human kind. I believe that too. As the only subject in this realm, scientists/scientific community (including those in the universities, research departments of major technology companies and so on) have never been so powerful in the history and hence they don’t help drive discovery, rather their work is to discover.”