Research in Applied 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 offered by the Department of Statistics, while courses in combinatorial and convex optimization are 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, and computational approaches to historical linguistics. Within the department we also have a Laboratory for Mathematical and Computational Biology.


Course Descriptions
Courses offered by the Statistics Department
Courses offered by the Computer Science Department
Courses offered by the Industrial Engineering and Operations Research Department

Undergraduate upper division 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.

Graduate courses

Math 202A,B. Introduction to Topology and Analysis.
Math 203. Asymptotic Analysis in Applied Mathematics.
Math 204. Ordinary 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 C223A,B. Stochastic Processes.
Math 224A,B. Mathematical Methods for the Physical Sciences.
Math 228A,B. Numerical Solution of Differential Equations.
Math 239. Discrete Mathematics for the Life Sciences.
Math 258. Classical Harmonic Analysis.
Math 273. Topics in Numerical Analysis.
Math 275. Topics in Applied Mathematics.


Applied Mathematics Seminar (Chorin, Strain, Wilkening)
Matrix Computations and Scientific Computing Seminar (Demmel, Gu, Parlett)
Computational Biology Seminar (Pachter, Sturmfels)
Probability Seminar (Chatterjee, Bhadimi)
Interdisciplinary Stochastic Processes Colloquium (Aldous)

Senate Faculty

Name Title Research Interests
Robert M. Anderson Professor Emeritus Mathematical economics, Nonstandard analysis, Probability theory
Sunčica Čanić Professor Applied mathematics, partial differential equations, computational methods, biomedical research
Jennifer Chayes Professor Probability theory, graph theory, graphons, mathematical statistical physics, and machine learning.
Alexandre J. Chorin University Professor Emeritus Applied mathematics, numerical methods, computational physics, computational statistics.
Paul Concus Professor Emeritus Fluid mechanics, Numerical analysis, Applied mathematics
James W. Demmel Professor Numerical analysis, Applied control theory
F. Alberto Grünbaum Professor Emeritus Analysis, Probability, Integrable systems, Medical imaging
Ming Gu Professor Numerical linear algebra, Scientific computing
Venkatesan Guruswami Professor Theory of Computing, Error-correcting codes, Combinatorics and Discrete Mathematics, Algebra and Computation, Approximate optimization
Ole H. Hald Professor Emeritus Numerical analysis
Olga Holtz Professor Numerical analysis, matrix theory, algebra and combinatorics, computational complexity
William M. Kahan Professor Emeritus Error analysis, Numerical computations, Computers, Convexity, Large matrices, Trajectory problems
Richard Karp Professor Emeritus Computer science and bioengineering
Lin Lin (林霖) Professor Numerical analysis; Quantum chemistry; Quantum algorithms
Michael J. Lindsey Assistant Professor Numerical analysis, optimization, Monte Carlo methods
C. Keith Miller Professor Emeritus Partial differential equations, Numerical methods for PDE's
John C. Neu Professor Emeritus Applied mathematics
Beresford N. Parlett Professor Emeritus Numerical analysis, Scientific computation
Per-Olof Persson Professor Applied Mathematics, Numerical Methods, Computational Fluid and Solid Mechanics
Rainer K. Sachs Professor Emeritus Mathematical biology
James A. Sethian Professor Applied mathematics, Computational physics, Partial differential equations
Chris Shannon Professor Mathematical economics
Stephen Smale Professor Emeritus Algorithms, Numerical analysis, Global analysis
Nikhil Srivastava Associate Professor Theoretical computer science, random matrices, geometry of polynomials
John Strain Professor Emeritus Applied mathematics, Numerical analysis, Fast algorithms, Materials science
Bernd Sturmfels Professor Emeritus Algebraic Geometry, Combinatorics, Optimization and Statistics
Franziska Weber Assistant Professor Applied mathematics, numerical analysis, nonlinear partial differential equations
Jon Wilkening Professor Applied mathematics, Numerical methods, Partial Differential Equations

Visiting Faculty

Name Title Research Interests
Nilin Abrahamsen Simons Fellow Quantum many-body problems, computational quantum chemistry
Ryan A. Hass Unit 18 Lecturer Numerical analysis, medical imaging
Krutika Tawri Morrey Visiting Assistant Professor Partial differential equations, fluid dynamics
Alexander Teytelboym Chancellor's Professor Mathematical economics.


Name Title Research Interests
Zhiyan Ding Morrey Visiting Assistant Professor Numerical analysis, Machine learning, Quantum computing
Anuj Kumar Morrey Visiting Assistant Professor Fluid dynamics, turbulent flow.
Federico Pasqualotto Morrey Visiting Assistant Professor Partial differential equations: nonlinear waves, fluid dynamics, general relativity.
Kevin Stubbs Postdoc-Employee Numerical analysis; Quantum chemistry; Quantum information theory

Faculty with Related Research Interests

Name Title Research Interests
Mina Aganagic Professor String theory, mathematical physics
David Aldous Professor Emeritus Theoretical and applied probability
L. Craig Evans Professor Emeritus Partial differential equations
Steven N. Evans Professor Probability and stochastic processes
Michael J. Klass Professor Emeritus Probability theory, Combinatorics
Hendrik W. Lenstra, Jr. Professor Emeritus Algebraic number theory, Algorithms
James Pitman Professor Probability, stochastic processes, combinatorics, machine learning
Nicolai Reshetikhin Professor Emeritus Mathematical physics, Low-dimensional topology, Representation theory
Fraydoun Rezakhanlou Professor Probability theory, Partial differential equations
John L. Rhodes Professor Emeritus Algebra, Semigroups, Automata
Marc A. Rieffel Professor Non-commutative harmonic analysis, Operator algebras, Quantum geometry
Alan D. Weinstein Professor Emeritus, Professor of the Graduate School Symplectic geometry, Mathematical physics
Mariusz Wodzicki Professor Non-commutative and algebraic geometry, Analysis, K-theory
Maciej Zworski Professor Partial differential equations, Mathematical physics

Recent Ph.D.s

Name Dissertation Title Dissertation Supervisor Year
Emily Bain Correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit Nicolai Reshetihkin 2023
Haotian Gu Mean-Field Cooperative Multi-agent Reinforcement Learning: Modelling, Theory, and Algorithms Fraydoun Rezakhanlou, Xin Guo 2023
Jeffrey Kuan Deterministic and stochastic fluid-structure interaction Suncica Canic 2023
Michael Franco Efficient solvers for the implicit time integration of matrix-free high-order methods Per-Olof Persson 2022
Jeffmin Lin Neural Network Antisymmetries for Quantum Many-Body Simulation   Lin Lin 2022
Yu Tong Quantum Eigenstate Filtering and Its Applications Lin Lin 2022
Michael Yeh An Efficient, Tolerance-Based Algorithm for the Truncated SVD Ming Gu 2022
Yiling You Mathematical Models and Control Algorithms for Traffic Automation   Alexandre Bayen, Jon Wilkening 2022
Dong An Simulating Many-body Quantum Dynamics on Classical and Quantum Computers Lin Lin 2021
Dan Daniel Erdmann-Pham Probabilistic Models and Statistical Tools for Gene Expression Analysis   Yun Song, Steve Evans 2021
Rockford Foster Algorithms for Computing Highly Oscillatory Indefinite Integrals and Applications in Plasma Physics   Jon Wilkening 2021
Zixi Hu James Sethian 2021
Noble Macfarlane High Order Partitioned Fully Implicit Runge-Kutta Solvers for Fluid-Structure Interaction   Per-Olof Persson 2021
Angxiu Ni Numerical Differentiation of Stationary Measures of Chaos John Strain 2021
Isabelle Shankar Sums of Squares and Symmetric Polynomials Serkan Hosten, Jon Wilkening 2021
Jiefu Zhang Structure-Informed Neural Network Architecture in Regression Applications   Lin Lin 2021
Xinyu Zhao Spatially Quasi-Periodic Gravity-Capillary Waves   Jon Wilkening 2021
Yanhe Huang A Boundary Integral Method for Modeling Axisymmetric Flow Around a Rising Bubble in a Vertical Tube and Accurate Numerical Evaluation of Orthogonal Polynomials 2020
Alexander Appleton Singularities in U (2)-invariant 4d Ricci flow Richard Bamler, Jon Wilkening 2019
Eric Hallman Error Estimates for Least-Squares Problems Ming Gu 2019
Michael Lindsey The Quantum Many-Body Problem: Methods and Analysis Lin Lin 2019
Haoran Tang Towards Informed Exploration for Deep Reinforcement Learning 2019
Ze Xu Density Functional Perturbation Theory and Adaptively Compressed Polarizability Operator 2019
Qiuyi Richard Zhang Fast Algorithms for Interior Point Methods 2019
Maryam Farahmand-Asil The Arithmetic of Graph Polynomials   Matthias Beck, Mark Haiman 2018
Danny Hermes High-order Solution Transfer between Curved Meshes and Ill-conditioned Bézier Curve Intersection   Per-Olof Persson 2018
RuoChen Liang Fast and Stable Low-Rank Symmetric Eigen-Update   Ming Gu 2018
Will Pazner Efficient implicit solvers for the discontinuous Galerkin method (PhD, Brown University) Per-Olof Persson, Chi-Wang Shu 2018
Saad Qadeer Simulating Nonlinear Faraday Waves on a Cylinder   Jon Wilkening 2018
Ryan George Thorngren Combinatorial Topology and Applications to Quantum Field Theory   Vivek Shende 2018
Jianwei Xiao Spectrum-Revealing Randomized Matrix Factorization: Theory and Algorithms Ming Gu 2018