Assaf Naor, an associate professor at New York University’s Courant Institute of Mathematical Sciences, has been named a recipient of a 2008 Packard Fellowship for Science and Engineering. Naor was one of 20 scientific researchers to receive a fellowship. Each fellow receives an unrestricted research grant of $875,000 over five years.
Naor, who was previously a researcher at Microsoft Research and who has been at Courant since 2006, has done extensive work in geometry. Under the Packard Fellowship, he will continue his work on metric spaces, which are abstract mathematical “universes” in which one can quantitatively measure the distance between any two points. The familiar three- dimensional world in which we live is a good example, though the notion of a metric space encompasses much more complicated and higher dimensional geometries.
“Metric spaces are ubiquitous in mathematics and science,” Naor explains. “The most commonly understood are the classical Euclidean spaces, in which the distance between points is simply the length of the line segment joining them. But metric spaces also occur in Internet searches, where the distance between any two web sites is the minimum number of clicks required to pass from one site to another, as well as biology, where one needs to measure the similarity between proteins, and in image processing, where one needs to measure the similarity between images.”
“One of the main consequences of my research is that the very general axioms that define a metric space impose a hidden structure,” he adds. “This structural information can be harnessed for a variety of applications, ranging from pure mathematics to computer science.” The 2008 Packard Fellows, which are supported by the David and Lucile Packard Foundation’s Fellowships for Science and Engineering program, include faculty members at universities across the United States. These fellows are addressing some of the most important research questions today in science and engineering on topics such as Alzheimer’s disease, stem cell function, evolutionary theory, and the relationship between disease and environment.