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

Postdocs

Name Title Research Interests
Peter Hintz Miller Research Fellow Mathematical physics, partial differential equations, microlocal analysis.
Mihaela Ifrim Postdoc Nonlinear partial differential equations, fluid dynamics, harmonic analysis
Marina Iliopoulou Morrey Visiting Assistant Professor Harmonic analysis, geometric measure theory, incidence geometry
Casey Jao Postdoc Nonlinear dispersive partial differential equations
Brent Nelson NSF Postdoctoral Fellow Free probability, non-tracial von Neumann algebras

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 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 Associate Professor Applied mathematics, Numerical methods, Partial Differential Equations

Recent Ph.D.s

Name Dissertation Title Dissertation Supervisor Year
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 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
Baoping Liu Low Regularity Solutions of Korteweg-deVries and Chern-Simons-Schrödinger Equations Daniel Tataru 2012
Rene Quilodran On Extremizers for Adjoint Fourier Restriction Inequalities and a Result in Incidence Geometry F. Michael Christ 2012
Ivan Ventura Applications of Semiclassical Analysis to Partial Differential Equations Maciej Zworski 2012