# 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 | Lecturer | Partial Differential Equations; Stochastic Processes |

Shi-Zhuo Looi | Visiting Scholar | Nonlinear dispersive PDEs |

## Postdocs

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

Georgios Moschidis | Miller Research Fellow | General relativity, hyperbolic PDEs, differential geometry |

Peng Zhou | Morrey Visiting Assistant Professor | Mathematical physics, mirror symmetry, semiclassical analysis |

## 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 |

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 | Applied mathematics, Numerical analysis, Fast algorithms, Materials science |

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 |
---|---|

Emily Bain | |

Yonah Borns-Weil | |

Garrett Brown | |

Dan Daniel Erdmann-Pham | Yun Song, Steve Evans |

Carlos Esparza | |

Rockford Foster | |

Ian Francis | |

Michael Franco | Per-Olof Persson |

Yujie Fu | |

Aubrey Gross | |

Milind Hegde | |

Xiaoyu Huang | |

Zhen Huang | |

Jeffrey Kuan | |

Mingyang Li | |

Jeffmin Lin | Lin Lin |

Yuchen Mao | |

Satyaki Mukherjee | |

Angxiu Ni | |

Izak Oltman | |

Benjamin Pineau | Daniel Tataru |

James Rowan | Daniel Tataru |

Ely Sandine | |

Andrew Scharf | |

Michael Smith | |

Jiazhen Tan | |

Zhongkai Tao | |

Mitchell Taylor | |

Peter Vinella | L. Craig Evans |

Jian Wang | |

Haoren Xiong | |

Tianrui Xu | |

Jiahao Yao | |

Dongxiao Yu | |

Jason Zhao | |

Zirui Zhou |

## Recent Ph.D.s

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

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 |

Elan Bechor | Two Models of Coagulation With Instantaneous Gelation | Fraydoun Rezakhanlou | 2017 |

Alexis Drouot | Stability of Resonances under Singular Perturbations | Maciej Zworski | 2017 |

Cristian Dan Gavrus | Global well-posedness and parametrices for critical Maxwell-Dirac and massive Maxwell-Klein-Gordon equations with small Sobolev data | Daniel Tataru | 2017 |

Eugenia Kim | Numerical methods for the Landau-Lifshitz equation in micromagnetics : the mimetic finite difference method and the mass-lumped finite element method | Jon Wilkening | 2017 |