James Sethian
Encyclopedia
James Albert Sethian is a professor of mathematics
at the University of California, Berkeley
, and the head of the Mathematics Grouphttp://math.lbl.gov/ at the United States Department of Energy's
Lawrence Berkeley National Laboratory
.
He received his Ph.D
from Berkeley in 1982 under the direction of Alexandre Chorin
. Afterward he was an National Science Foundation
postdoctoral fellow at the Courant Institute, under Peter Lax
. He returned to Berkeley in 1985 where he is now a full professor. Sethian was elected member of the National Academy of Engineering
(NAE) in 2008. Sethian has acted as Interim Director Research at Thinking Machines Corporation, as well as held visiting positions at the National Center for Atmospheric Research and the National Institute of Standards and Technology.
in 1988, which was developed jointly with Stanley Osher
.
These are numerical algorithms for tracking moving interfaces in complex situations, and have proved instrumental in a wide collection of applications, including semiconductor processing, fluid mechanics
, medical imaging
, computer graphics
, and material sciences.
Jointly with D. Adalsteinsson, Sethian then introduced the idea of adaptivity to level set methods, in which computational labor is focused on the evolving front: their Adaptive Narrow Band level set method and its variants are what makes level set methods efficient and practical, and are
the most common form of these techniques in practice today.
Together with Alexander Vladimirsky, Sethian developed a class of Dijkstra-like ordered upwind methods for solving static Hamilton–Jacobi equation
s. In the case of an Eikonal equation, the first method to do so was developed by Jon N. Tsitsiklis using a control-theoretic approach: followed shortly by Sethian's work on high order finite difference Dijkstra-like Fast Marching
Methods. Ravikanth Malladi and Sethian pioneered the application of these techniques to image segmentation, Ron Kimmel
and Sethian introduced them to robotic navigation and extended them to curved domains,
and Mihai Popovici and Sethian were the first to
use them as fast wave solvers in geophysical seismic imaging.
Together with Sergey Fomel, Sethian invented Escape Arrival Methods for computing multiple arrivals in wave propagation and geophysical imaging.
Algorithms based on the work of Sethian and his colleagues are now part of everyday production code in throughout science and engineering. They inform engineers how to design more precise ink jet plotters, allow physicians to analyze brain and cardiac images, aid oil companies in locating
petroleum reserves, tell process engineers how to build reliable computer chips.
He maintains the "level set methods and fast marching methods" webpagehttp://math.berkeley.edu/~sethian/, which is a popular resource for these methods, and provides a variety of applets, movies, and explanations for both the popular and technical audiences.
in 2008 for the development of efficient methods of tracking moving interfaces. He received the Norbert Wiener Prize in Applied Mathematics
in 2004, jointly awarded by the Society for Industrial and Applied Mathematicians (SIAM) and the American Mathematical Society (AMS). This prize was awarded "for an outstanding contribution to applied mathematics in the highest and broadest sense." Sethian was honoured "for his seminal work on the computer representation of the motion of curves, surfaces, interfaces, and wave fronts, and for his brilliant applications of mathematical and computational ideas to problems in science and
engineering." Previous recipients include Richard Bellman
, Peter Lax
, Alexandre Chorin
, Jerrold Marsden
, Tosio Kato, Gerald Whitham
, Arthur Winfree
, and Harold Widom
.
In addition to numerous other awards and honours, Sethian is a renowned speaker and teacher: he received the SIAM I.E. Block Community Lecture Prize.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, and the head of the Mathematics Grouphttp://math.lbl.gov/ at the United States Department of Energy's
United States Department of Energy
The United States Department of Energy is a Cabinet-level department of the United States government concerned with the United States' policies regarding energy and safety in handling nuclear material...
Lawrence Berkeley National Laboratory
Lawrence Berkeley National Laboratory
The Lawrence Berkeley National Laboratory , is a U.S. Department of Energy national laboratory conducting unclassified scientific research. It is located on the grounds of the University of California, Berkeley, in the Berkeley Hills above the central campus...
.
He received his Ph.D
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
from Berkeley in 1982 under the direction of Alexandre Chorin
Alexandre Chorin
Alexandre J. Chorin is a professor of mathematics at the University of California, Berkeley who works in applied mathematics. He is known for his contributions to the field of Computational fluid dynamics....
. Afterward he was an National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
postdoctoral fellow at the Courant Institute, under Peter Lax
Peter Lax
Peter David Lax is a mathematician working in the areas of pure and applied mathematics. He has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields...
. He returned to Berkeley in 1985 where he is now a full professor. Sethian was elected member of the National Academy of Engineering
National Academy of Engineering
The National Academy of Engineering is a government-created non-profit institution in the United States, that was founded in 1964 under the same congressional act that led to the founding of the National Academy of Sciences...
(NAE) in 2008. Sethian has acted as Interim Director Research at Thinking Machines Corporation, as well as held visiting positions at the National Center for Atmospheric Research and the National Institute of Standards and Technology.
Work
Sethian has worked on numerical algorithms for tracking moving interfaces for over three decades, starting with his seminal 1982 work on curve and surface propagation in combustion, and his 1985 work on entropy conditions, curvature, stability of numerical algorithms. This work led to development of level set methodLevel set method
The level set method is a numerical technique for tracking interfaces and shapes. The advantage of the level set method is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects...
in 1988, which was developed jointly with Stanley Osher
Stanley Osher
Stanley Osher is an American mathematician, known for his many contributions in shock capturing, level set methods, and PDE-based methods in computer vision and image processing...
.
These are numerical algorithms for tracking moving interfaces in complex situations, and have proved instrumental in a wide collection of applications, including semiconductor processing, fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
, medical imaging
Medical imaging
Medical imaging is the technique and process used to create images of the human body for clinical purposes or medical science...
, computer graphics
Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
, and material sciences.
Jointly with D. Adalsteinsson, Sethian then introduced the idea of adaptivity to level set methods, in which computational labor is focused on the evolving front: their Adaptive Narrow Band level set method and its variants are what makes level set methods efficient and practical, and are
the most common form of these techniques in practice today.
Together with Alexander Vladimirsky, Sethian developed a class of Dijkstra-like ordered upwind methods for solving static Hamilton–Jacobi equation
Hamilton–Jacobi equation
In mathematics, the Hamilton–Jacobi equation is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations. In physics, the Hamilton–Jacobi equation is a reformulation of classical mechanics and, thus, equivalent to other formulations such as...
s. In the case of an Eikonal equation, the first method to do so was developed by Jon N. Tsitsiklis using a control-theoretic approach: followed shortly by Sethian's work on high order finite difference Dijkstra-like Fast Marching
Methods. Ravikanth Malladi and Sethian pioneered the application of these techniques to image segmentation, Ron Kimmel
Ron Kimmel
Ron Kimmel is a professor of Computer Science atthe Technion Israel Institute of Technology.He holds a D.Sc. degree in electrical engineering from the Technion,and spent a post-doctoral position at UC Berkeley and Berkeley Labs, and a visiting...
and Sethian introduced them to robotic navigation and extended them to curved domains,
and Mihai Popovici and Sethian were the first to
use them as fast wave solvers in geophysical seismic imaging.
Together with Sergey Fomel, Sethian invented Escape Arrival Methods for computing multiple arrivals in wave propagation and geophysical imaging.
Algorithms based on the work of Sethian and his colleagues are now part of everyday production code in throughout science and engineering. They inform engineers how to design more precise ink jet plotters, allow physicians to analyze brain and cardiac images, aid oil companies in locating
petroleum reserves, tell process engineers how to build reliable computer chips.
He maintains the "level set methods and fast marching methods" webpagehttp://math.berkeley.edu/~sethian/, which is a popular resource for these methods, and provides a variety of applets, movies, and explanations for both the popular and technical audiences.
Awards
Sethian wins the ICIAM Pioneer Prize in 2011 for pioneering work, introducing applied mathematical methods and scientific computing techniques to an industrial problem area and new scientific fields of applications. Sethian was elected member of the National Academy of EngineeringNational Academy of Engineering
The National Academy of Engineering is a government-created non-profit institution in the United States, that was founded in 1964 under the same congressional act that led to the founding of the National Academy of Sciences...
in 2008 for the development of efficient methods of tracking moving interfaces. He received the Norbert Wiener Prize in Applied Mathematics
Norbert Wiener Prize in Applied Mathematics
The Norbert Wiener Prize in Applied Mathematics is a $5000 prize awarded every three years to for an outstanding contribution to "applied mathematics in the highest and broadest sense." It was endowed in 1967 in honor of Norbert Wiener by MIT's mathematics department and is provided jointly by the...
in 2004, jointly awarded by the Society for Industrial and Applied Mathematicians (SIAM) and the American Mathematical Society (AMS). This prize was awarded "for an outstanding contribution to applied mathematics in the highest and broadest sense." Sethian was honoured "for his seminal work on the computer representation of the motion of curves, surfaces, interfaces, and wave fronts, and for his brilliant applications of mathematical and computational ideas to problems in science and
engineering." Previous recipients include Richard Bellman
Richard Bellman
Richard Ernest Bellman was an American applied mathematician, celebrated for his invention of dynamic programming in 1953, and important contributions in other fields of mathematics.-Biography:...
, Peter Lax
Peter Lax
Peter David Lax is a mathematician working in the areas of pure and applied mathematics. He has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields...
, Alexandre Chorin
Alexandre Chorin
Alexandre J. Chorin is a professor of mathematics at the University of California, Berkeley who works in applied mathematics. He is known for his contributions to the field of Computational fluid dynamics....
, Jerrold Marsden
Jerrold E. Marsden
Jerrold Eldon Marsden , was an applied mathematician. He was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology. Marsden is listed as an ISI highly cited researcher.-Career:Marsden earned his B.Sc...
, Tosio Kato, Gerald Whitham
Gerald B. Whitham
Gerald Beresford Whitham is an American applied mathematician and the Charles Lee Powell Professor of Applied Mathematics of Applied & Computational Mathematics at the California Institute of Technology. He received his Ph.D. from the University of Manchester in 1953 under the direction of Sir...
, Arthur Winfree
Arthur Winfree
Arthur Taylor Winfree was a theoretical biologist at the University of Arizona. He was born in St. Petersburg, Florida, United States....
, and Harold Widom
Harold Widom
Harold Widom is an American mathematician well known for his contributions to operator theory and random matrices. He was appointed to the Department of Mathematics at the University of California, Santa Cruz in 1968 and became professor emeritus in 1994. ...
.
In addition to numerous other awards and honours, Sethian is a renowned speaker and teacher: he received the SIAM I.E. Block Community Lecture Prize.
Books
- Vortex Methods and Vortex Motion
- Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Sciences
- Level Set Methods and Fast Marching Methods
External links
- Berkeley Lab Mathematicians Awarded Prestigious Math Prizes
- Advancing the science of advancing interfaces at United States Department of EnergyUnited States Department of EnergyThe United States Department of Energy is a Cabinet-level department of the United States government concerned with the United States' policies regarding energy and safety in handling nuclear material...
- Sethian's home page at Berkeley
- Sethian receives the Norbert Wiener Prize
- ITK in real-world medical imaging applications.