FAU Physicist Receives $675K Grant from the U.S. Air Force to Develop Advanced Mathematics for Complex Information Systems
BOCA RATON, FL (April 18, 2012) – Warner A. Miller, Ph.D., professor and chair of the department of physics in the Charles E. Schmidt College of Science, has received a $675,000 grant from the U.S. Department of Defense for a three-year project titled “Discrete Ricci Flow in Higher Dimensions.” Miller will lead a team of researchers from FAU, Stony Brook University and Harvard University to apply the Hamilton’s Ricci Flow method, a form of geometric mapping and analysis, to characterize and possibly control information-based cyber applications.
The primary purpose of this research is to develop the mathematics of diffusive curvature flow in lattice geometries that are higher than two dimensions. Much work has been done in two dimensions using Ricci Flow already, including facial recognition and medical applications, such as virtual colonoscopy. Miller and his team are conducting this basic research to determine if they can extend Ricci Flow to three and higher dimensions, and to see if it can find exciting applications to three-dimensional objects such as the structure of the brain or heart, for example.
Ricci Flow was first developed in the 1980s by Richard Hamilton, a Columbia University math professor. In addition to its applications to fundamental problems in mathematics such as Perelman’s recent proof of Poincare’s Conjecture, Ricci Flow has many practical applications, including communications, facial recognition, homeland security, medicine, movie animation and resilient routing for computer networks.
“Ricci Flow yields a wealth of information about structure-function relationships, enabling us to transform complex irregular spaces, or systems, into uniform ones so that we can more easily solve problems,” said Miller. “I am proud to be working alongside with my three graduate students here at FAU as well as professor David Gu from Stony Brook and Field Medalist professor S-T Yau at Harvard on this project. Such sharpening of our understanding of geometry and topology is a pathway to future breakthroughs in science.”
The project work will be conducted in three phases, including the development of the first high-dimension discrete Ricci Flow algorithm; testing the algorithm with three-dimensional problems; and finally applying the findings to specific information-based cyber systems.
“Our hope is that the three and higher dimensional Ricci Flow will help give an automated way to achieve a better load balance in a complex communication network, or be used to detect unusual behavior,” said Miller.
Miller is a retired U.S. Air Force colonel who holds an emeritus position at the Air Force Research Laboratory. He worked in Los Alamos National Laboratory as a J. Robert Oppenheimer Distinguished Postdoctoral Fellow, technical staff member and group leader of T-6. Miller received a Ph.D. in physics from the University of Texas at Austin supervised by John Archibald Wheeler.
-FAU-About Florida Atlantic University:
Florida Atlantic University, established in 1961, officially opened its doors in 1964 as the fifth public university in Florida. Today, the University serves more than 29,000 undergraduate and graduate students on seven campuses and sites. FAU’s world-class teaching and research faculty serves students through 10 colleges: the Dorothy F. Schmidt College of Arts and Letters, the College of Business, the College for Design and Social Inquiry, the College of Education, the College of Engineering and Computer Science, the Graduate College, the Harriet L. Wilkes Honors College, the Charles E. Schmidt College of Medicine, the Christine E. Lynn College of Nursing and the Charles E. Schmidt College of Science. FAU is ranked as a High Research Activity institution by the Carnegie Foundation for the Advancement of Teaching. For more information, visit www.fau.edu.