CMU mathematics Ph.D. student dives into new area of research

This summer, Central Michigan University Mathematics Ph.D. student M. Nader Al-Homsi had the opportunity to dive into a new area of mathematics while working alongside Dr. Debraj Chakrabarti.

Through an NSF-supported research program at CMU, Al-Homsi spent Summer 2026 studying the Laplace–Beltrami operator on Riemannian manifolds of higher codimension, a project that connects differential geometry and mathematical analysis.

For Al-Homsi, the project was a chance to expand beyond his primary research interests in numerical analysis, partial differential equations and scientific computing.

“Dr. Chakrabarti has been an exceptional mentor,” Al-Homsi said. “He introduced me to advanced concepts, encouraged independent thinking, and guided me in developing the project toward a manuscript that is currently in preparation.”

The experience also gave Al-Homsi a chance to work on research as an active contributor rather than simply learning about mathematics in the classroom.

“Working with a mathematician of his expertise has been an invaluable part of my academic development,” he said.

The NSF support allowed Al-Homsi to dedicate focused time to the project while building his skills in research, problem-solving and academic writing.

He said the experience is one example of the opportunities available to graduate students in CMU’s Department of Mathematics, where students can work closely with faculty on research projects.

Al-Homsi’s project is continuing, with a manuscript currently in preparation.