Applied Mathematics Research - UC Berkeley Department of Mathematics

Faculty and students interested in the applications of mathematics are an integral part of the Department of Mathematics; there is no formal separation between pure and applied mathematics, and the Department takes pride in the many ways in which they enrich each other. We also benefit tremendously from close collaborations with faculty and students in other departments at UC Berkeley as well as scientists at Lawrence Berkeley National Laboratory and visitors to the Mathematical Sciences Research Institute.

The Department regularly offers courses in ordinary and partial differential equations and their numerical solution, discrete applied mathematics, the methods of mathematical physics, mathematical biology, the mathematical aspects of fluid and solid mechanics, approximation theory, scientific computing, numerical linear algebra, and mathematical aspects of computer science. Courses in probability theory, stochastic processes, data analysis and bioinformatics are regularly offered by the Department of Statistics, while courses in combinatorial and convex optimization are regularly offered by the Department of Industrial Engineering and Operations Research. Our students are encouraged to take courses of mathematical interest in these and many other departments.

Topics explored intensively by our faculty and students in recent years include scientific computation and the mathematical aspects of quantum theory, computational genomics, image processing and medical imaging, inverse problems, combinatorial optimization, control, robotics, shape optimization, turbulence, hurricanes, microchip failure, MEMS, biodemography, population genetics, phylogenetics, mathematical biology, and computational approaches to historical linguistics.

Faculty

Tenured and tenure-track:

David Aldous, Theoretical and applied probability.
Robert M. Anderson, Mathematical economics, Nonstandard analysis, Probability theory.
Grigory I. Barenblatt, Applied mathematics, Solid mechanics, Fluid mechanics, Similarity methods asymptotics.
Elwyn R. Berlekamp, Combinatorial game theory, Algebraic coding theory, Electrical engineering, Computer science.
Alexandre J. Chorin, Applied mathematics, Numerical methods, Hydrodynamics.
Paul Concus (Emeritus), Fluid mechanics, Numerical analysis, Applied mathematics.
James W. Demmel, Numerical analysis, Applied control theory.
Steven N. Evans, Probability and stochastic processes.
David A. Freedman, Probability theory, Game theory, Statistics.
David Gale (Emeritus), Mathematical Economics.
F. Alberto Grünbaum, Analysis, Probability, Integrable systems, Medical imaging.
Ming Gu, Numerical linear algebra, Scientific computing.
Ole H. Hald, Numerical analysis.
Olga Holtz, Matrix analysis, approximation theory, analysis of algorithms.
William M. Kahan, Error analysis, Numerical computations, Computers, Convexity, Large matrices, Trajectory problems.
Richard Karp, Computer science and bioengineering.
Michael J. Klass, Probability theory, Combinatorics.
Jerrold E. Marsden (Emeritus), Mechanics, Applied dynamics, Control theory.
C. Keith Miller (Emeritus), Partial differential equations, Numerical methods for PDE's.
John C. Neu, Applied mathematics.
Lior Pachter, Mathematical and computational biology.
Beresford N. Parlett (Emeritus), Numerical analysis, Scientific computation.
James Pitman, Probability and stochastic processes.
Murray H. Protter (Emeritus), Partial differential equations, Applied mathematics.
Rainer K. Sachs (Emeritus), Mathematical biology.
James A. Sethian, Applied mathematics, Computational physics, Partial differential equations.
Chris Shannon, Mathematical Economics.
Stephen Smale (Emeritus), Algorithms, Numerical analysis, Global analysis.
John Strain, Applied mathematics, Numerical analysis, Fast algorithms, Materials science.
Jon Wilkening, Applied mathematics, Materials science, Fluid Mechanics, Scientific computing.

Visitors and postdoctoral fellows (2006-2007):

Raanan Fattal, Computer graphics, image processing and computational fluid mechanics of complex fluids.
Dror Givon, Optimal prediction, Computational mathematics and Multiscale analysis for Stochastic processes.
Stanislava Kuckova, Computational mathematics, Numerical methods for differential equations, Mathematical modeling in radiobiology.
Panos Stinis, Fluid mechanics, renormalization, inference, filtering.
Xuemin Tu, Numerical analysis (domain decomposition methods, multilevel methods).

Faculty listed in other sections who are also interested in applied math:

Mina Aganagic, String theory.
David H. Blackwell (Emeritus), Set theory, Recursive functions, Measure theory, Stochastic processes, Game theory, Information theory, Linear programming.
Paul R. Chernoff (Emeritus), Functional analysis, Operator theory.
L. Craig Evans, Partial differential equations.
Jenny Harrison, Geometric analysis.
Morris W. Hirsch (Emeritus), Dynamical systems, Neural networks.
Hendrik W. Lenstra, Jr. (Emeritus), Algebraic number theory, Algorithms.
Yuval Peres, Probability theory and Hausdorff dimension.
John L. Rhodes (Emeritus), Algebra, Semigroups, Automata.
Marc A. Rieffel, Non-commutative harmonic analysis, Operator algebras, Quantum geometry.
Nicolai Reshetikhin, Mathematical physics, Low-dimensional topology, Representation theory.
Fraydoun Rezakhanlou, Probability theory, Partial differential equations.
Bernd Sturmfels, Combinatorics, Computational algebraic geometry.
Alan D. Weinstein, Symplectic geometry, Mathematical physics.
Mariusz Wodzicki, Non-commutative and algebraic geometry, Analysis, K-theory.
Maciej Zworski, Partial differential equations, Mathematical physics.

Courses

Undergraduate upper divison courses

Math C103. Introduction to Mathematical Economics.
Math 104, H104. Introduction to analysis.
Math 105. Second course in analysis.
Math 110, H110. Linear algebra.
Math 113, H113. Introduction to abstract algebra.
Math 118. Fourier analysis, wavelets, and signal processing.
Math121A,B. Mathematical Tools for the Physical Sciences.
Math 123. Ordinary Differential Equations.
Math 126. Introduction to Partial Differential Equations.
Math 127. Mathematical and Computational Methods in Molecular Biology.
Math 128A,B. Numerical Analysis.
Math 170. Mathematical Methods for Optimization.
Math 172. Combinatorics.
Math 185, H185. Introduction to Complex Analysis.
Math 189. Mathematical Methods in Classical and Quantum Mechanics.
Courses offered by the Statistics Department
Courses offered by the Computer Science Department
Courses offered by the Industrial Engineering and Operations Research Department

Graduate courses

Math 202A,B. Introduction to Topology and Analysis.
Math 204A,B. Ordinary and Partial Differential Equations.
Math 205. Theory of Functions of a Complex Variable.
Math C218A,B. Probability Theory.
Math 220. Methods of Applied Mathematics.
Math 221. Advanced Matrix Computations.
Math 222A,B. Partial Differential Equations.
Math 224A,B. Mathematical Methods for the Physical Sciences.
Math 228A,B. Numerical Solution of Differential Equations.
Math 258. Classical Harmonic Analysis.
Math 273. Topics in Numerical Analysis.
Math 275. Topics in Applied Mathematics:
  Spring 2007: Flow, Deformation and Fracture (Barenblatt).
  Spring 2006: Flow, Deformation and Fracture(Barenblatt).
  Spring 2006: Statistical Mechanics, Combinatorics and Representation Theory (Reshetikhin).
  Fall 2005: Finite Element and Boundary Integral Methods for Solid and Fluid Mechanics (Wilkening).
Math C290C. Topics in Fluid Mechanics.

Seminars

Applied Mathematics Seminar (Chorin, Strain, Wilkening)

Matrix Computations and Scientific Computing Seminar (Demmel, Parlett)

Computational Biology Seminar (Pachter, Sturmfels)

Probability Seminar (Chatterjee, Bhadimi, Nachmias)

Interdisciplinary Stochastic Processes Colloquium (Aldous)

Current Thesis Students: Name (Advisor)

Nicolas Bray (Pachter)
Stephen Canon (Miller)
Tianbing Chen (Strain)
Aubrey Clayton (S. Evans)
Peter Huggins (Pachter)
Ivan Matic (Rezakhanlou)
Radu Mihaescu (Pachter)
Darren Rhea (Rezakhanlou)
Ian Sammis (Strain)
Anne Shiu (Sturmfels/Pachter)
Jia Yu (Wilkening)

Recent Ph.D.s: Name (Advisor) Thesis title

2007

Jomy Alappattu (Pitman) An Analysis of Randomized Algorithms on Trees
Maria Cameron (Sethian) Seismic Velocity Estimation from Time Migration
Elizabeth Chester (Sethian) Fast Methods for Computing All-to-All Geodesic Paths for the Eikonal Equation
Jae-Seok Huh (Sethian) Implicit Interface Finite Element Method for Elliptic Interface Problems
Kay Kirkpatrick (Rezakhanlou) Rigorous Derivation of the Landau Equation in the Weak Coupling Limit
Ying Shan (Sethian) Solving Partial Differential Equations on Irregular Domains with Moving Interfaces, with Applications to Superconformal Electrodeposition in Semiconductor Manufacturing
Jonathan Weare (Chorin) Smoothing and Filtering Of Stochastic Ordinary and Partial Differential Equations by Efficient Path Sampling

2006

Nicholas Karl Eriksson (Sturmfels) Algebraic Combinatorics for Computational Biology
Joseph (Yossi) Farjoun (Neu) Nucleation, Growth, and Coarsening: A Global View on Aggregation
Alfonso Gracia-Saz (Weinstein) The Symbol of a Function of a Pseudodifferential Operator
Jiawang Nie (Demmel, Sturmfels) Global Optimization of Polynomial Functioins and Applications
Jianlin Xia (Gu) Fast Direct Solvers for Structured Linear Systems of Equations
Yuan Yao (Smale) A Dynamic Theory of Learning

2005

Dan Levy (Pachter,Sachs) Applications of Graph Theory to Chromosome Aberrations and Phylogenetics
Luisa Miranian (Grünbaum) Matrix Valued Orthogonal Polynomials
Pavel Okunev (Chorin) Renormalization Methods With Applications to Spin Systems and Finance
Yelena Shvets (Barenblatt) Problems of Flooding in Porous and Fissured Porous Rock
Aaron Nathan Siegel (Berlekamp) Loopy Games and Computation
Jiang Zhu (Gu) Structured Eigenvalue Problems and Polynomial Eigenvalue Problems

2004

No applied math students received their Ph.D.'s in 2004.

2003

Peter Graf (Chorin) Optimization of Model Reduction for Linear Ordinary Differential Equations
Eugene Ingerman (Chorin) Modelling the Loss of Information in Optimal Prediction
Joshua Levenberg (Strain) Accurate Adaptive Contour Finding Using C1 Data
Kevin Lin (Chorin) Random Perturbations of SRB Measures and Numerical Studies of Chaotic Dynamics
Omar Mirza (MacFarlane) Naturalism and Darwin's Doubt
Aaditya Rangan (Strain) Fast Adaptive Solvers for Viscous Conservation Laws

2002

Joon Bang (Evans) Sandpile Problems on a Steep Landscape
Brandoch Calef (Grünbaum) Optimal sampling of the discrete Fourier transform
Christopher Cameron (Chorin) A comparative analysis of methods for sampling stationary stochastic processes
William Fraser (Berlekamp) Computer-Assisted Thermographic Analysis of Go Endgames
David des Jardins (Berlekamp) Precise coding with noiseless feedback
Plamen Koev (Demmel) Accurate and efficient computations with structured matrices
Jon Wilkening (Sethian) Mathematical analysis and numerical simulation of electromigration

2001

Kashi Abhyankar (Hirsch) Smale Strategies for Prisoner's Dilemma Type Games
Bendek Hansen (Chihara) Causal Inference via Covariance Adjustment: Investigation on Model Uncertainty in Observational Studies
Julia Kempe (Berlekamp) Universal noiseless quantum computation: mathematical theory and applications
Alexander Vladimirsky (Sethian) Fast Methods for Static Hamilton-Jacobi Partial Differential Equations

2000

Deborah Goldman (Papadimitriou) Algorithmic aspects of protein folding and protein structure similarity
Darin Goldstein (Klass) Algorithms on Networks of Finite-State Automata
Chong Xu (Marsden) Asymptotic Stability for Equilibria of Nonlinear Semiflows with Applications to Rotating Viscoelastic Rods