A University of Hawaiʻi at Mānoa Department of Mathematics faculty member has received a $211,262 grant from the National Science Foundation to study a specialized area of mathematics with wide-ranging applications.
Running through 2027, the project focuses on conformal and quasiconformal mappings. Conformal mappings are transformations of the plane that locally preserve angles, a property that makes them valuable in mathematics and sciences. One example is the Mercator projection used in cartography, which provides a reliable representation of the round surface of the Earth on a flat, two-dimensional map. Quasiconformal mappings are a more flexible version that allow controlled distortion of angles. This adaptability has made them important in complex analysis, probability, computer vision and other fields.
“This research may sound abstract, but it’s about finding patterns that help us better understand the world,” said Principal Investigator and Associate Professor Malik Younsi, who also recently started as chair of the Department of Mathematics. “It’s exciting to share this work globally while also training the next generation of mathematicians here in Hawaiʻi.”
Beyond advancing theory, the project supports graduate student training and mentoring. Two UH Mānoa PhD students under Younsi’s direction are contributing to the research, including one who recently participated in a workshop hosted by the Fields Institute in Toronto, a leading international center for mathematical research.
Global impact
In June 2025, Younsi presented findings from the project at the international conference “Curves, Trees and Surfaces” in Berlin. The plenary talk placed UH Mānoa on a global stage alongside other invited speakers, including two recipients of the Fields medal, consistently regarded as the top award in the field of mathematics worldwide.
The research builds on earlier work published in Inventiones Mathematicae, one of the world’s leading mathematics journals. The 54-page paper, written in 2020, laid the foundation for the current project by studying the rigidity of certain geometric structures called circle domains.
By combining new research, student training and international collaboration, the grant strengthens UH Mānoa’s role in advancing mathematics while providing opportunities for Hawaiʻi students to engage with a global network of scholars.
The Department of Mathematics is housed in UH Mānoa’s College of Natural Sciences.
