Mathematical Research from UC Riverside Selected as a Highlight by the National Science Foundation

Professor Michel Lapidus is accustomed to being misunderstood

Image of the fractal drum by John DePillis, professor emeritus, UCR

RIVERSIDE, Calif. ( – UC Riverside Professor and mathematician Michel Lapidus sometimes has trouble simplifying his work far enough so that it is  understood by the average person. But that doesn’t mean his work isn’t important. 

In fact, his work will be cited as a highlight of the research funded by the National Science Foundation (NSF) Division of Mathematical and Physical Sciences when the funding agency submits its 2015 budget proposal to Congress and the Office of the President.

“It is an unusually high honor to be included in this document as NSF selects highlights based on the significance of the work,” said Professor of Chemistry Cynthia Larive, a divisional dean in the College of Natural and Agricultural Sciences. “You so seldom see mathematicians get the public kudos that they deserve, even researchers who are well-respected in their field like Professor Lapidus.” she said.

The research project selected as a highlight by the NSF titled “Can One Hear the Shape of a Fractal Drum?” was funded by a 2011 grant for $164,999.  Professor Lapidus offers an analogy to help explain the project.

Michel Lapidus

Michel Lapidus

“Imagine someone playing a drum, and a few yards from her, another person trying to guess the shape of the drum just by listening to its music. This is a notoriously difficult and important problem in contemporary mathematics, with many applications to physics, chemistry, biology and engineering. Now, there is a twist to the story. Indeed, the drum is allowed to have an intricate, wrinkled shape, at all scales—either in its interior or on its boundary; in short, it is a fractal drum.”

Lapidus has established unexpected connections with the celebrated Riemann hypothesis, the most important open problem in mathematics. “In essence,” Lapidus said, “the Riemann hypothesis encodes key properties of the prime numbers, which are the building blocks (or the DNA) of arithmetic, and thereby, of all of mathematics.”

Understanding fractal structures, such as trees, blood vessels, rivers and clouds, is one way scientists study how and why they arise in nature and how they evolve. Part of Lapidus’s work provides some of the clues towards resolving this long-standing open problem.

The mathematical theories underlying the work are complicated. But for those immersed in that world, Lapidus is a highly sought after mentor. He earned UC Riverside’s graduate mentoring award in 2012. He also works with postdoctoral fellows and junior faculty members in various aspects of the work.

“Ultimately, it is simply a tribute to the beauty of mathematics, and to its surprising and mysterious power on reality, even when it is formulated in a seemingly abstruse language and according to rules and concepts which are unfortunately not understandable to most people,” Lapidus said.

This is the second time that the work of Professor Lapidus has been selected as a highlight of research funded by the National Science Foundation; his work was first recognized in 1990.

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