New York University Skip to Content Skip to Search Skip to Navigation Skip to Sub Navigation

Courant Student and Collaborators Crack Decades-Old Equation

September 28, 2012

A researcher at NYU’s Courant Institute of Mathematical Sciences and two collaborators from the University of Toronto have solved a decades-old equation that models several real-world systems, such as the development of cracks in materials, the formation of bacteria, and the growth of liquid crystals.

The Kardar-Parisi-Zhang (KPZ) equation, first published in 1986, describes the temporal evolution of an interface growing in a disordered environment. Solving the equation means computing exact statistics which describe the random fluctuations in the interface growth.

The success came from collaboration between NYU’s Ivan Corwin and the University of Toronto’s Jeremy Quastel and Gideon Amir. At the time of their work on the KPZ equation, Corwin was a doctoral student at Courant and partially supported by a grant from the National Science Foundation’s Partnerships for International Research and Education (PIRE) program. Quastel, a professor at the University of Toronto, received his Ph.D. from Courant in 1990.

Solving the KPZ equation gives researchers another tool to analyze physical disordered systems, with implications in the fields of physics, engineering, materials science, biology, and ecology. The statistics developed in the work will allow for better modeling of such complex systems.

The work also marks the first time mathematicians have obtained an exact solution to a non-linear stochastic partial differential equation—an equation that describes random development in systems dependent on both location and time. In non-linear systems, doubling an input does not necessarily double the output—for example, doubling a patient’s medication may more than double the effect on the body. Non-linear systems are recognized as of great importance, yet relatively little theory has been developed to describe them. The work represents a step in that direction.

Corwin, who obtained his doctorate from Courant in 2011, currently holds the Clay Research Fellowship from the Clay Mathematics Institute as well as the Schramm Memorial Fellowship. He is presently affiliated with Clay, MIT, and Microsoft Research New England.

Type: Article

Press Contact: James Devitt | (212) 998-6808

Courant Student and Collaborators Crack Decades-Old Equation

Search News

NYU In the News

Paying It Backward: NYU Alum Funds Scholarships

The Wall Street Journal profiled Trustee Evan Chesler on why he decided to chair the Momentum fund-raising campaign.

A Nobel Prize Party: Cheese, Bubbles, and a Boson

The New Yorker talked to Professor Kyle Cranmer and graduate student Sven Kreiss about NYU’s role in the discovery of the Higgs boson, which resulted in a Nobel prize for the scientists who predicted its existence.

The World as They Knew It

The New York Times reviewed the exhibit at the Institute for the Study of the Ancient World on how ancient Greeks and Romans mapped the known and unknown areas of their world.

Elite Institutions: Far More Diverse Than They Were 20 Years Ago

NYU made stronger gains over the last 20 years in increasing diversity than any other major research university, according to the Chronicle of Higher Education.

Program Seeks to Nurture ‘Data Science Culture’
at Universities

The New York Times reported on the multi-million collaboration among NYU and two other universities to harness the potential of Big Data, including an interview with Professor Yann LeCun, director of NYU’s Center for Data Science.

NYU Footer