DiBenedetto, mathematician who advanced knowledge on differential equations, has died

photograph of Emmanuele DiBenedetto in front of ocean
Emmanuele DiBenedetto (submitted photo)

Emmanuele DiBenedetto, a retired mathematics professor who made significant contributions to the understanding of partial differential equations, died on May 11 after a 15-month struggle with cancer.

DiBenedetto, Centennial Professor of Mathematics, Emeritus, was 74.

He was born in Lentini, Sicily, on April 4, 1947, to Nunzio DiBenedetto and Elvira Papalino. DiBenedetto was able to attend the Liceo Cutelli di Catania, an excellent public school system, and graduated in 1966. He then wanted to explore new places and spent some time working in France and Germany.

DiBenedetto’s successes at Liceo led him toward a career in academia, and he enrolled at the University of Florence. His research career blossomed under the guidance of Professor Carlo Pucci, who encouraged DiBenedetto to apply to the doctoral program at the University of Texas at Austin. While in Florence, DiBenedetto met an American student, Heidi Hamm, who would become his lifelong companion and wife. After graduation, they both enrolled at UT–Austin, where she was accepted into the graduate program in biological sciences.

As a doctoral student, DiBenedetto developed a set of new tools to shed light on open problems in the theory of elliptic and parabolic equations. He earned a doctor of philosophy in 1979 and received a postdoctoral fellowship at the University of Wisconsin–Madison prior to faculty appointments at Indiana and Northwestern universities.

“Emmanuele DiBenedetto was a powerhouse in the area of real analysis and partial differential equations,” said Gieri Simonett, Vanderbilt professor of mathematics. “His many and deep research contributions will have a long-lasting legacy.”

DiBenedetto was recruited to Vanderbilt in 2000 as Centennial Professor of Mathematics. He received an additional appointment as professor of molecular physiology and biophysics in 2001. His teaching and research at Vanderbilt focused on the study of partial differential equations, particularly elliptic and parabolic ones. One of his most significant contributions to the theory of parabolic partial differential equations is called “intrinsic scaling,” a new way to look at the regularity properties of parabolic equations, which he developed with several collaborators. In addition, he had research interests in the area of mathematical biology.

DiBenedetto was a mentor to several graduate students and numerous postdoctoral fellows who have gone on to work across various branches of pure and applied mathematics. One of them was Colin Klaus, BA’11, MS’17, and PhD’17, a postdoctoral research fellow at Ohio State University.

“Emmanuele was a brilliant intellectual and passionate mentor whose research interests were far-ranging—from some of the most technical and deep areas of mathematics to their applications in neighboring scientific fields, such as biology,” Klaus said. “He created unique collaborative opportunities for me in my scientific career, such as a project developing a novel multiscale geometric model of visual transduction in photoreceptor cells, and I will always be grateful to him. Emmanuele was fond of saying that mathematics and research are activities you do with your friends. He is dearly missed.”

Another one of his students with great memories is Naian Liao, MS’11, and PhD’14, a postdoctoral fellow at the University of Salzburg. “I would summarize three attitudes that I learned from him: Problems should have good motivations; never be afraid of calculations; and papers should be written tersely and remain focused,” Liao said. “I also remember once I got a partial result and could not wait to write and publish it (like many other young researchers). He convinced me to keep it for myself for the moment and try to make the result more complete and the paper heavier. These attitudes somehow made things temporarily difficult, but the high standards they set clearly show their value later on and will absolutely continue.”

DiBenedetto was a prolific writer, authoring more than 120 papers and six books, several of which had second and third editions. A new book, Harnack Inequalities and Nonlinear Operators, is forthcoming. It is a compilation of works by mathematicians who attended a 2017 symposium in DiBenedetto’s honor.

DiBenedetto was awarded a U.S. patent, an unusual distinction for a mathematician.

He also served as editor in chief of the Journal on Mathematical Analysis of the Society for Industrial and Applied Mathematics. In addition, he was on more than 20 editorial boards and gave numerous invited talks.

His service to Vanderbilt included terms on the Graduate Faculty Council and the College of Arts and Science Faculty Council.

DiBenedetto is survived by his wife of 46 years, Heidi Hamm, professor of pharmacology and the Aileen M. Lange and Annie Mary Lyle Chair in Cardiovascular Research. Other survivors include his sister, Enza DiBenedetto; brother, Aldo DiBenedetto; and mother, Elvira Papalino.