# 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 |

Heinz O. Cordes | Professor Emeritus | Classical analysis |

Semyon Dyatlov | Assistant Professor | Microlocal analysis, scattering theory, quantum chaos, PDE |

L. Craig Evans | Professor | Partial differential equations |

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

Vaughan F. R. Jones | Professor Emeritus | Von Neumann algebras |

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 |

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 |

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

## Visiting Faculty

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

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

Wilfrid Gangbo | Chancellor's Professor | Calculus of Variations; Nonlinear Analysis; Partial Differential Equations; Kinetic Theory; Functional Analysis; Fluid Mechanics |

Brian Krummel | Visiting Assistant Researcher | Geometric analysis, calculus of variations, partial differential equations |

Anna Skripka | Visiting Scholar | Operator theory, noncommutative analysis |

Elie Studnia | Visiting Scholar | Semiclassical analysis |

## Postdocs

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

Ian Charlesworth | NSF Post-doctoral Scholar | Free probability and operator algebras |

Cristian Dan Gavrus | Postdoc | Dispersive partial differential equations |

Charles Hadfield | Morrey Visiting Assistant Professor | Microlocal analysis, mathematical physics, dynamical zeta functions |

Peter Hintz | Miller Research Fellow | Mathematical physics, partial differential equations, microlocal analysis. |

Marina Iliopoulou | Morrey Visiting Assistant Professor | Harmonic analysis, geometric measure theory, incidence geometry |

Casey Jao | Postdoc | Dispersive partial differential equations |

Tim Laux | Morrey Visiting Assistant Professor | Calculus of variations, nonlinear partial differential equations, geometric analysis, applied analysis |

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

Brent Nelson | NSF Postdoctoral Fellow | Free probability, non-tracial von Neumann algebras |

Thibault de Poyferré | Miller Research Fellow | Dispersive partial differential equations; water waves |

Martin Vogel | Postdoc | Semiclassical/microlocal analysis, spectral theory, random operators, large random objects |

Xuwen Zhu | Morrey Visiting Assistant Professor | Geometric analysis, microlocal analysis, partial differential equations, 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 |

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 | Assistant 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 |
---|---|

Benson Au | Steven N. Evans |

Elan Bechor | |

Justin T. Brereton | Daniel Tataru |

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

Rockford Foster | |

Michael Franco | |

Bryan Gillespie | Olga Holtz |

Milind Hegde | |

Mikayla Kelley | |

Chao Kusollerschariya | Marc A. Rieffel |

Jonathan Leake | |

Michael Lindsey | Lin Lin |

Dominique Maldague | |

Satyaki Mukherjee | |

Kyeongsik Nam | Fraydoun Rezakhanlou |

Anh Martina Neuman | |

Angxiu Ni | |

Kevin O'Neill | Michael Christ |

Chanwoo Oh | Fraydoun Rezakhanlou |

James Rowan | |

Michael Smith | |

Peter Vinella | L. Craig Evans |

Jian Wang | |

Jiahao Yao | |

Dongxiao Yu |

## Recent Ph.D.s

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

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 |

Meire Fortunato | Curved and anisotropic unstructured mesh generation and adaptivity using the Winslow equations | 2016 | |

Oran Gannot | Quasinormal modes of anti-de Sitter black holes | Maciej Zworski | 2016 |

Minjae Lee | Spectral Analysis on Point Interactions | Maciej Zworski | 2016 |

Weihua Liu | Noncommutative Distributional Symmetries and Their Related de Finetti Type Theorems | Dan-Virgil Voiculescu | 2016 |

Christopher Wells Miller | Methods for Optimal Stochastic Control and Optimal Stopping Problems Featuring Time-Inconsistency | L. Craig Evans | 2016 |

Peyam R. Tabrizian | Asymptotic PDE Models for Chemical Reactions and Diffusions | L. Craig Evans | 2016 |

Christopher A. Wong | Bilinear Quadratures and Their Application | John A. Strain | 2016 |

Khalilah Beal | L. Craig Evans | 2015 | |

Woo-Hyun Cook | Transformations of PDEs: Optimal Transport and Conservation Laws | 2015 | |

Jeffrey E. Galkowski | Distribution of Resonances in Scattering by Thin Barriers | Maciej Zworski | 2015 |

Boaz E. Haberman | 2015 | ||

Benjamin Harrop-Griffiths | Quasilinear dynamics of KdV-type equations | Daniel Tataru | 2015 |

Long Jin | Maciej Zworski | 2015 | |

Andre Kornell | Marc A. Rieffel | 2015 | |

Adam B. Merberg | Noncommutative generalized Brownian motions with multiple processes | Dan-Virgil Voiculescu | 2015 |

Marcos Charalambides | Extremal Problems in Analysis | F. Michael Christ | 2014 |

Taryn Flock | On extremizers for certain inequalities of the k-plane transform and related topics | F. Michael Christ | 2014 |

Eric Wayman | Steven N. Evans | 2014 | |

Semyon Dyatlov | Resonances in General Relativity | Maciej Zworski | 2013 |

Boris Ettinger | Well-posedness of the Three-form Field Equation and the Minimal Surface Equation in Minkowski Space | Daniel Tataru | 2013 |

Michael Hartglass | Free Probability, Planar Algebras, and the Multicolored Guionnet-Jones-Shlyakhtenko Construction | Vaughan F. R. Jones | 2013 |

Alexandru Hening | Two Models of Default from Finance and a Model of Invasion from Ecology | Steven N. Evans | 2013 |

Matthew Tucker-Simmons | Marc A. Rieffel, Nicolai Reshetikhin | 2013 |