Achi Brandt
The Elaine and Bram Goldsmith Professor of Applied Mathematics
My main goal is solving nature's equations.
In most branches of physics, chemistry and engineering, the fundamental laws
of the investigated system are well established, stating the relations that
always hold between its microscopic parts. Yet, to derive from these laws the
macroscopic behavior of the system at given surrounding conditions is usually
a formidable computational task, even with modern supercomputers. The inherent
inefficiency of existing computational methods is the major bottleneck in many
fields of study. It bars scientists from the theoretical derivation of, for
example, the mass of the proton and other properties of elementary particles.
It defeats attempts to compute the structure and interactions of chemical compounds,
needed to understand and design materials, proteins, drugs, etc. This inefficiency
also hampers calculations in fluid dynamics, medical imaging, radar analysis,
astrophysics, weather prediction, oil prospecting, lubrication theory, acoustics,
image processing, and so on. New mathematical methods to eliminate the inefficiency
and to drastically reduce the complexity of all these computational tasks are
being developed, based on a novel hierarchical approach to the organization
of space and time. Related methods are also emerging for solving large graph
problems, image segmentation and recognition, clustering and classification,
with surveillance, biomedical and other applications.
Recent Publications
- Multiscale Scientific Computation: Review 2001. In: Barth, T. J., Chan, T. F. and Haimes, R. (eds.): Multiscale and Multiresolution Methods: Theory and Applications, Springer Verlag, Heidelberg, 2001.
- [with E. Sharon, M. Galun, D. Sharon, and R. Basri] Hierarchy and adaptivity in segmenting visual scenes. Nature 442 (7104) (2006) 719-846.
- Principles of systematic upscaling, in Bridging the Scales in Science and Engineering, J. Fish (Ed.), Oxford University Press, 2008.