Mathematics and computer science professor Ronald Coifman won the 2018 Rolf Schock Prize in Mathematics, one of the highest honors in his field, on March 15.

Along with an award of 400,000 Swedish krona, or about $49,000, Coifman won one of the four annual Rolf Schock Prizes, which also honor leaders in three other categories — logic and philosophy, visual arts and musical arts. Coifman was recognized for his contributions to pure and applied harmonic analysis, according to the Royal Swedish Academy of Sciences, the organization that selected Coifman for the award.

“It’s an honor to be in the company of the other awardees, which include mathematicians and musical soloists,” said Coifman, a member of the National Academy of Sciences who won the National Medal of Science in 1999. “Moreover, this award serves as a recognition that what we have been doing in using mathematics in the context of complicated information structures is productive.”

Coifman, who has been teaching at Yale since 1980, has made monumental contributions in many different fields, particularly in harmonic analysis, according to Michael Benedicks, a professor at Uppsala University in Sweden and a member of the Royal Swedish Academy of Sciences. Benedicks added that Coifman’s original contributions, as well as his skills in leadership and collaboration, led to his selection for the prize.

Harmonic analysis is the study and understanding of complicated graphs, Coifman explained. The field enables researchers and professionals to extract the important features of graphs while ignoring unneeded noise, he said. Harmonic analysis has significant medical applications, including analysis of blood pressure graphs and electroencephalograms, which are used to detect electrical activity in the brain.

“I develop geometric and analytic tools to discover structure in data,” Coifman said. “These tools can be used for cybersecurity and medical data to organize information.”

He added that work in harmonic analysis and machine learning is particularly important now given the rise of big data.

Coifman has led the field of harmonic analysis by using geometric diffusions — graphs which represent data in Euclidean space — as tools to find structures in large data sets.

“[Coifman’s] work in diffusion maps has had a big impact on data analysis and machine learning,” said University of California, Davis professor James Bremer GRD ’07, who worked under Coifman to earn his doctoral degree. “It is now being used for algorithms for threat detection, image recognition and a host of other machine learning and data analysis tasks.”

Along with his long-time collaborator French mathematician Yves Meyer, Coifman is also known for his role in the development of the theory of wavelets, which are mathematical functions in the form of short waves. Wavelets can be used to represent certain types of functions efficiently and have profoundly affected signal processing — especially in compressing and filtering images and music.

Several of Coifman’s students and collaborators noted that he has performed extensive work in both the pure and applied aspects of mathematics.

“The applications of these methods [in machine learning that Coifman developed] are boundless, and Raphy has been involved in both the mathematical theory and deploying these tools for use on scientific problems, especially medical applications,” said Princeton postdoctoral associate William Leeb GRD ’15, who worked under Coifman as a graduate student at Yale.

Bremer said one of the most important things that Coifman taught him was that there is no real distinction between “pure” and “applied” math. Coifman’s approach to solving difficult applied problems is to deeply study their underlying mathematical structure, he added.

“The emphasis on solving problems that are needed for important applications is a principle of Raphy followed by many of his students in the last twenty years,” said Gilad Lerman GRD ’00, a professor at the University of Minnesota Twin Cities who received his doctoral degree under the direction of Coifman and Yale math professor Peter Jones.

Coifman’s breadth of knowledge has also inspired him to continue pursuing new research directions, Lerman added. He said that as a professor, he now tries to follow Coifman’s lead in helping his students develop projects that can lead to original directions of study.

“[Coifman] was always accessible to his students,” Leeb said. “He is a treasure-trove of ideas, information and experience. It was a privilege working with him.”

On Oct. 15, Coifman will travel to Sweden to attend the award ceremony at the Royal Swedish Academy of Fine Arts. In addition to the presentation of awards to the four laureates, the ceremony will also include a small conference featuring the laureates’ work, Benedicks said.

Rolf Schock, who left a large fortune after his death in 1986, stated in his will that the Royal Swedish Academy, Royal Academy of Fine Arts and Royal Swedish Academy of Music should name four laureates in logic and philosophy, mathematics, visual arts and musical arts — fields that notably do not have a Nobel Prize associated with them.

Amy Xiong | amy.xiong@yale.edu