Purdue Today

Mathematician totally engaged in exploring partial differential equations

Nothing in nature is perfect. Svitlana Mayboroda's mathematical work with analysis and partial differential equations hinges on this fact.

In particular, Mayboroda, assistant professor of mathematics, focuses on the ways in which irregular geometry and internal inhomogeneity influence the behavior of physical systems.

Irregularities found in the world are not present in most classical examples of partial differential equations (PDEs), and the smooth approximations that are do not reflect what happens in real life.

"Of course it's easier to work with something that is nice and smooth," Mayboroda says, "but perfectly uniform systems do not exist because every real object inadvertently possesses impurities. Physicists and engineers have agreed for some time that these irregularities are a driving force of occurring phenomena modeled by PDEs. That is why I am so interested in studying this."

With her aptitude and enjoyment of the subject, mathematics was a natural choice for Mayboroda when she entered university in Kharkiv, Ukraine, at the age of 16. During work on her undergraduate thesis, she encountered PDEs and analysis, and the research spark was ignited.

Her fascination with the subject has not gone unnoticed by others in the discipline. She was recognized with a National Science Foundation Faculty Early Career Development Award and the Alfred P. Sloan Research Fellowship.

As with many involved in scientific research, Mayboroda says she eats, sleeps, breathes and dreams her work, her mind drifting on and off the subject, constantly pondering the next step in proving a theorem.

While most of her research is in pure (abstract) mathematics, Mayboroda is currently working with physicists on theoretical and experimental applications. One application relates to vibrations of clamped plates, which can be found on bulkheads of ships, coverings of airplanes, in plaster walls and tiled ceilings.

"We are studying how these plates react under loads and heat," she says. "We want to enhance the structures, reduce cracking and predict how the plates would vibrate if a particular load was applied."

For many people, the tangible applications of their dedicated work help solidify their research, but for Mayboroda the excitement of discovering an organic result and advancing the field is verification enough.

"My research in general is driven by mathematics itself. Because of this, I don't measure my findings in terms of applications; I appreciate them for what they are," she says. "There is such an exhilaration and happiness surrounding a really true discovery and proving something which no one has ever thought of or worked on before."

As a professor, Mayboroda wants to share the experience of discovery with her students. "I view teaching as a privilege and an opportunity to share the beauty and subtlety of mathematics," she says. "My role goes beyond teaching a particular equation or imposing solutions on my students. It's about empowering them by uncovering solutions and approaches together and helping them realize their potential."