# 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.

## Courses

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.

## Seminars

**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. |

## Postdocs

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 |

## Graduate Students

Name | Dissertation Supervisor |
---|---|

Yulia Alexandr | Bernd Sturmfels, Serkan Hosten |

Joao Basso | |

Ainsley Clark | |

Luke Corcos | |

Brian Cruz | Steven Evans, Federico Ardila |

Rongyi (Amy) Dai | |

Franny Dean | |

Isabel Detherage | |

Yulong Dong | |

Jacob Elafandi | |

Yuchen Fang | |

Yujie Fu | |

Gil Goldshlager | |

Michael Heinz | |

Erik Herrera | |

Max Hirsch | |

Zhen Huang | |

Hugh Kadhem | |

Michael Kielstra | |

Raehyun Kim | |

Zack McNulty | |

Arnold Mong | |

Lewis Pan | |

Tom Schang | Prof. Franziska Weber |

Andrew Scharf | |

Rikhav Shah | |

Jiasu Wang | |

Tianrui Xu | |

Jiahao Yao | |

Haixiang Zhang |

## 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 |