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.


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


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


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

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