Princeton University

Professors Robert Calderbank and Ingrid Daubechies, and assistant professor Amit Singer, were awarded $980,000 from the National Science Foundation to construct algorithms, or methods, that address large-scale computational problems not yet solved by traditional approaches. These problems have arisen in recent years in parallel with exciting developments in mathematics and computer science, opening up new frontiers for computational mathematics. The research includes work in the areas of network analysis, large-scale signal analysis and data mining, which have potential applications in biomedical research and many other applied areas of science and engineering.

Professor Emily Carter was awarded $600,000 from the National Science Foundation to support a project on the development of methods that predict the behavior of molecules and materials. These tools have the potential to shed light on the combustion behavior of proposed alternative fuel sources. Additionally, the techniques can be used to predict how lightweight metal alloys intended for use in fuel-efficient vehicles would withstand the external stresses encountered during travel. Taken together, these insights could inform the design and development of highly efficient cars, among other advances.

Professors Charles Fefferman and Elias Stein were awarded $959,000 from the National Science Foundation to continue their work on Fourier analysis and partial differential equations, which are significant to the development of mathematical and physical theories. Fefferman's work will sharpen his earlier results on fitting a smooth function to data, which has applications in many areas, including computer-aided design and machine learning. Stein, a recipient of the National Medal of Science, will further develop the theory of singular integrals -- equations that are key to the field of harmonic analysis. Beyond fundamental mathematical significance, the research has wide-ranging importance for many scientific endeavors, including biological modeling and signal processing.

Instructor Michael Hochman was granted $159,000 from the National Science Foundation to expand his recent work on widely used models that describe the changes that occur over time in physical and artificial systems. Hochman intends to determine the theoretical limitations of these models and identify new subclasses that may be more amenable for use in a variety of fields, including biology, thermodynamics, information theory and computer science.

Professor Paul Seymour has received $220,000 from the National Science Foundation to continue his work on graph theory and explore a conjecture about the structure of graphs made nearly 30 years ago by Indian theorist S. B. Rao. Seymour intends to prove the conjecture and answer side questions that arise, further expanding his already major contributions to graph theory.

Professor Christopher Skinner was honored with $120,000 from the National Science Foundation toward research on fundamental problems in algebraic number theory, especially those pertaining to the topics of Galois representations and L-functions. The work will build upon significant advances that have been made in number theory over the past several years, including the long-sought proof of Fermat's Last Theorem. A branch of pure mathematics, number theory has practical applications in a variety of fields, including biology, acoustics and computing.

Instructor Micah Warren has received $146,000 from the National Science Foundation to continue his investigation of mathematical tools called Hessian and special Lagrangian equations, using them to describe special objects featuring minimal surfaces with unique properties. A greater knowledge of these objects, called "special Lagrangian submanifolds," may further the understanding of string theory and also address questions about optimal transportation. The work has implications for many areas of science, including medical imaging, fluid mechanics and meteorology.