# Research in Mathematical Analysis

In a rough division of mathematics, mathematical analysis deals with inequalities and limits. In some of its branches, such as asymptotic analysis, these aspects of the subject matter are readily apparent. in others, such as operator algebras, they are concealed in the topology of an algebras or its structure as an infinite-dimensional vector space. Our department offers a wealth of different perspectives on mathematical analysis.

## Courses

### Undergraduate upper divison courses

**Math C103.** Introduction to Mathematical Economics.

**Math 104, H104.** Introduction to analysis.

**Math 105.** Second course in analysis.

**Math 118.** Fourier analysis, wavelets, and signal processing.

**Math 121A,B.** Mathematical Tools for the Physical Sciences.

**Math 123.** Ordinary Differential Equations.

**Math 126.** Introduction to Partial Differential Equations.

**Math 140.** Metric Differential Geometry.

**Math 141.** Elementary Differential Topology.

**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 206.** Banach Algebras and Spectral Theory.

**Math 208.** C*- algebras.

**Math 209.** Von Neumann algebras.

**Math 212.** Several Complex Variables.

**Math 214.** Differentiable Manifolds.

**Math C218A,B.** Probability Theory.

**Math 222A,B.** Partial Differential Equations.

**Math 224A,B.** Mathematical Methods for the Physical Sciences.

**Math 240.** Riemannian Geometry.

**Math 241.** Complex Manifolds.

**Math 242.** Symplectic Geometry.

**Math 258.** Classical Harmonic Analysis.

**Math 261A,B.** Lie Groups.

**Math 278.** Topics in Analysis.

**Math 279.** Topics in Partial Differential Equations

## Seminars

### Fall 2008

**Analysis Seminar** (Bade, Cordes, Helson, Sarason)

**PDE/Analysis Seminar** (Tataru, Zworski)

**Probabilistic Operator Algebra** (Voiculescu)

**Quantum Geometry Seminar** (Rieffel, Tucker-Simmons)

**Student PDE Seminar** (Evans)

**Subfactor Seminar** (Jones)

**Interdisciplinary Stochastic Processes Colloquium** (Aldous)

**Probability Seminar** (Aldous, Haulk)

**The Berkeley Bonn Paris Analysis Seminar** (Delort, Koch, Zworski)

### Spring 2009

**Analysis Seminar** (Bade, Cordes, Helson, Sarason)

**PDE/Analysis Seminar** (Tataru, Zworski)

**Probabilistic Operator Algebra** (Voiculescu)

**Quantum Geometry Seminar** (Rieffel, Tucker-Simmons)

**Student PDE Seminar** (Evans)

**Subfactor Seminar** (Jones)

**Interdisciplinary Stochastic Processes Colloquium** (Aldous)

**Probability Seminar** (Aldous)

**The Berkeley Bonn Paris Analysis Seminar** (Delort, Koch, Zworski)

## Senate Faculty

Name | Title | Research Interests |
---|---|---|

Michael Christ | Professor | Harmonic analysis, Partial differential equations, Complex analysis in several variables |

L. Craig Evans | Professor Emeritus | Partial differential equations |

Jenny Harrison | Professor | Functional analysis, Geometric measure theory, Calculus of variations, Mathematical physics |

C. Keith Miller | Professor Emeritus | Partial differential equations, Numerical methods for PDE's |

Calvin C. Moore | Professor Emeritus | Representations and actions of topological groups, Operator algebras |

Sung-Jin Oh | Assistant Professor | Nonlinear partial differential equations |

Fraydoun Rezakhanlou | Professor | Probability theory, Partial differential equations |

Marc A. Rieffel | Professor | Non-commutative harmonic analysis, Operator algebras, Quantum geometry |

Daniel Tataru | Professor | Partial differential equations |

Dan-Virgil Voiculescu | Professor | Operator algebras, Hilbert space operators modulo normed ideals, Free probability and its applications to random matrices and von Neumann algebras |

Mariusz Wodzicki | Professor | Non-commutative and algebraic geometry, Analysis, K-theory |

Ruixiang Zhang | Assistant Professor | Harmonic analysis, analytic number theory, additive combinatorics |

Maciej Zworski | Professor | Partial differential equations, Mathematical physics |

## Visiting Faculty

Name | Title | Research Interests |
---|---|---|

Khalilah Beal | Unit 18 Lecturer | Partial Differential Equations; Stochastic Processes |

Arash Farahmand | Unit 18 Lecturer | Nonlinear Programming, Frobenius Numbers |

Eva A. Gallardo Gutiérrez | Visiting Scholar | Operator Theory, Complex Analysis, Harmonic Analysis |

Frédéric Klopp | Visiting Scholar | Mathematical physics, random operators, Schrödinger operators, semiclassical analysis |

John E. McCarthy | Visiting Scholar | Complex analysis, Operator theory |

## Postdocs

Name | Title | Research Interests |
---|---|---|

Federico Pasqualotto | Morrey Visiting Assistant Professor | Partial differential equations: nonlinear waves, fluid dynamics, general relativity. |

Mengxuan Yang | Morrey Visiting Assistant Professor | Partial Differential Equations, Spectral Theory, Mathematical Physics. |

## Faculty with Related Research Interests

Name | Title | Research Interests |
---|---|---|

Steven N. Evans | Professor | Probability and stochastic processes |

F. Alberto Grünbaum | Professor Emeritus | Analysis, Probability, Integrable systems, Medical imaging |

Ole H. Hald | Professor Emeritus | Numerical analysis |

Olga Holtz | Professor | Numerical analysis, matrix theory, algebra and combinatorics, computational complexity |

Michael J. Lindsey | Assistant Professor | Numerical analysis, optimization, Monte Carlo methods |

John C. Neu | Professor Emeritus | Applied mathematics |

James Pitman | Professor | Probability, stochastic processes, combinatorics, machine learning |

James A. Sethian | Professor | Applied mathematics, Computational physics, Partial differential equations |

Nikhil Srivastava | Associate Professor | Theoretical computer science, random matrices, geometry of polynomials |

John Strain | Professor Emeritus | Applied mathematics, Numerical analysis, Fast algorithms, Materials science |

Franziska Weber | Assistant Professor | Applied mathematics, numerical analysis, nonlinear partial differential equations |

Alan D. Weinstein | Professor Emeritus, Professor of the Graduate School | Symplectic geometry, Mathematical physics |

Jon Wilkening | Professor | Applied mathematics, Numerical methods, Partial Differential Equations |

## Graduate Students

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

Katalin Berlow | |

Yonah Borns-Weil | |

Garrett Brown | |

Isabel Detherage | |

Carlos Esparza | |

Ian Francis | |

Yujie Fu | |

Aubrey Gross | |

Xiaoyu Huang | |

Zhen Huang | |

Mingyang Li | |

Yuchen Mao | |

Izak Oltman | |

Benjamin Pineau | Daniel Tataru |

Ely Sandine | |

Tom Schang | |

Andrew Scharf | |

Olivine Silier | |

Jiazhen Tan | |

Ning Tang | |

Zhongkai Tao | |

Tianrui Xu | |

Jiahao Yao | |

Jason Zhao | Sung-Jin Oh |

Zirui Zhou |

## Recent Ph.D.s

Name | Dissertation Title | Dissertation Supervisor | Year |
---|---|---|---|

Jeffrey Kuan | Deterministic and stochastic fluid-structure interaction | Suncica Canic | 2023 |

James Rowan | Construction of Long-time Solutions for Inviscid Fluid Flows | Daniel Tataru | 2023 |

Mitchell Taylor | A Collection of Results on Nonlinear Dispersive Equations, Banach Lattices and Phase Retrieval | Daniel Tataru | 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 |

Haoren Xiong | Scattering resonances and the complex absorbing potential method | Maciej Zworski | 2022 |

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 |

Milind Hegde | Probabilistic and geometric methods in last passage percolation | Alan Hammond, Shirshendu Ganguly | 2021 |

Satyaki Mukherjee | Pseudospectra of matrices and Point spectra of infinite graphs | James Pitman, Nikhil Srivastava | 2021 |

Angxiu Ni | Numerical Differentiation of Stationary Measures of Chaos | John Strain | 2021 |

Michael Smith | Curvature Bounds in Riemannian Geometry | Richard Bamler | 2021 |

Peter Vinella | Coefficient Optimal Control Problems for Elliptic PDE | L. Craig Evans | 2021 |

Jian Wang | Microlocal analysis for 0th order pseudodifferential operators | Maciej Zworski | 2021 |

Dongxiao Yu | Modified scattering for a scalar quasilinear wave equation satisfying the weak null condition | Daniel Tataru | 2021 |

Kyeongsik Nam | Singular stochastic differential equations with elliptic and hypoelliptic diffusions | Fraydoun Rezakhanlou | 2020 |

Chao Kusollerschariya | Dirac Triples for Unital AF Algebras | Marc A. Rieffel | 2019 |

Jonathan Leake | Analytic and Combinatorial Features of Stable Polynomials | Olga Holtz | 2019 |

Michael Lindsey | The Quantum Many-Body Problem: Methods and Analysis | Lin Lin | 2019 |

Dominique Maldague | A constrained optimization problem for the Fourier transform | Michael Christ | 2019 |

Kevin O'Neill | Multilinear and Sharpened Inequalities | Michael Christ | 2019 |

Chanwoo Oh | Metastability of Zero Range Processes | Fraydoun Rezakhanlou | 2019 |

Benson Au | Rigid structures in traffic probability: with a view toward random matrices | Steven N. Evans | 2018 |

Justin T. Brereton | A method of constructing invariant measures at fixed mass | Daniel Tataru | 2018 |

Bryan Gillespie | The Generalized External Order, and Applications to Zonotopal Algebra | Olga Holtz | 2018 |

Anh Martina Neuman | Functions of nearly maximal Gowers-Host-Kra norms on Euclidean spaces | F. Michael Christ | 2018 |