Mathematical Analysis Research - UC Berkeley Department of Mathematics

In a rough division of mathematics, mathematical analysis deals with inequalities and limits. In some of its branches, such as asymptotic analysis that is immediately apparent, in others, such as operator algebras it is hidden in the definitions of topologies of the algebras and in their infinite dimensional structures. Our department offers a great wealth of perspectives on mathematical analysis.

Faculty

Professors:

F. Michael Christ, Harmonic Analysis, Partial Differential Equations.
L. Craig Evans, Partial differential equations.
Steve Evans, Probability
Jenny Harrison, Geometric analysis.
Vaughan Jones, Von Neumann Algebras, Topology, Mathematical Physics.
Yuval Peres, Probability theory and Hausdorff dimension.
Jim Pitman, Probability.
Marina Ratner, Ergodic Theory, Analysis on Symmetric Spaces.
Fraydoun Rezakhanlou, Probability theory, Partial differential equations.
Marc A. Rieffel, Non-commutative harmonic analysis, Operator algebras, Quantum geometry.
Don Sarason, Complex Analysis, Functional Analysis.
Daniel Tataru, Partial differential equations.
Dan-Virgil Voiculescu, Operator Algebras, Free Probability.
Mariusz Wodzicki, Non-commutative and algebraic geometry, Analysis, K-theory.
Maciej Zworski, Partial differential equations, Mathematical physics.

Emeritus Professors:

William B. Arveson, Functional analysis, Operator algebras.
William G. Bade, Functional analysis, Banach algebras.
David Blackwell, Set theory, Recursive functions, Measure theory, Stochastic processes, Game theory, Information theory, Linear programming.
Paul R. Chernoff, Functional analysis, Operator theory.
Heinz O. Cordes, Classical analysis.
Stephen P. L. Diliberto, Ordinary differential equations, Celestial mechanics.
Jacob Feldman, Ergodic theory, Stochastic processes.
Henry Helson, Harmonic analysis, Function theory.
C. Keith Miller, Partial differential equations, Numerical methods.
Calvin C. Moore, Representations and actions of topological groups, Operator algebras.

Current Visitors and Postdoctoral Fellows:

Calder Daenzer, Noncommutative geometry and mathematical physics.
Franz Luef, Time-frequency analysis, Mathematical physics, Non-commutative geometry.
Rob Martin, Operator theory, reproducing kernel Hilbert spaces, self-adjoint extensions of symmetric operators, sampling.
Michael VanValkenburgh, Partial differential equations.
Atilla Yilmaz, Probability theory and statistical mechanics.

Faculty listed in other sections who are also interested in mathematical analysis:

F. Alberto Grünbaum, Analysis, Probability, Integrable systems, Medical imaging.
Ole H. Hald, Numerical analysis.
John C. Neu, Applied mathematics.
Nicolai Reshetikhin, Mathematical physics, Low-dimensional topology, Representation theory.
James A. Sethian, Applied mathematics, Computational physics, Partial differential equations.
John Strain, Applied mathematics, Numerical analysis, Fast algorithms, Materials science.
Alan D. Weinstein, Symplectic geometry, Mathematical physics.
Jon Wilkening, Applied mathematics, Materials science, Fluid Mechanics, Scientific computing.

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 187. Senior Level 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 207. Unbounded Operators.
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 261A,B. Lie Groups.
Math 258. Classical Harmonic Analysis.
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)

Recent Ph.D.s: Name (Adviser) Thesis title

2009

Scott Nathan Armstrong (L.C. Evans) Principal Half-eigenvalues of Fully Nonlinear Homogeneous Elliptic Operators
Zachary James Judson (Sarason) Connectivity in the Higson Corona of the Positive Real Axis
Yun Long (Peres) Mixing Time of the Swendsen-Wang Dynamics in Complete Graph and Trees
Emily Elizabeth Peters (Jones) A Planar Algebra Construction of the Haagerup Subfactor
Jeremy Neil Sain (Rieffel) Berezin Quantization from Ergodic Actions of Compact Quantum Groups and Quantum-Gromov-Hausdorff Distance
Stephanie Jane Somersille (Peres) Biased Tug-of-War, The Biased Infinity Laplacian and Comparison with Exponential Cones
Lindsay Elizabeth Stovall (Christ) L^p Inequalities for Certain Generalized Radon Transforms
Mihai Horia Tohaneanu (Tataru) Local Energy Estimates on Schwarzschild and Kerr Black Hole Background
Maxim Trokhimtchouk (L.C. Evans) Regularity for Certain Parabolic Diffusion Systems
Guoliang Wu (L.C. Evans) Impulse Control of Multidimensional Diffusion and Jump Diffusion Processes

2008

Richard D. Burstein (Jones) Hadamard Subfactors of Bisch-Haagerup Type
Aubrey I. Clayton (S. Evans) Mutation-Selection Balance for Polynomial Selection Costs and Matrix-Valued Orthogonal Polynomials
Asaf Y. Nachmias (Peres) Critical Percolation on Finite Graphs

2007

Hans Christianson (Zworski) Quantum Monodromy and Non-concentration Near a Closed Semi-hyperbolic Orbit
Dennis J. Courtney (Arveson) Asymptotic lifts of UPC semigroups
Jonathan Dorfman (Evans) Fast Diffusion PDE Models for Sandpiles and Lake-River Dynamics
Jeremy Marzuola (Tataru) A Stable Class of Perturbations for Minimal Mass Solitons of Saturated NLSE in 3d
Scott Morrison (Jones) A Diagrammatic Category for the Representation Theory of Uq(sln)

Dissertation Supervisors/Advisees

Spring 2009

Michael Christ/Patrick LaVictoire, Diogo Oliveira e Silva, Rene Quilodran
L. Craig Evans/Aaron Chen, Ryan Hynd, Hung Tran
Jenny Harrison/Patrick Barrow, Khalilah Beal
Vaughan Jones/Jose Alameida, Katie Liesinger, David Penneys
Fraydoun Rezakhanlou/Ivan Matic
Marc Rieffel/Andre Kornell, Sasha Peterka, Matthew Tucker-Simmons
Daniel Tataru/Boris Ettinger, Baoping Liu
Dan Voiculescu/Stephen Curran
Maciej Zworski/Kiril Datchev, Subhroshekhar Gosh, Ivan Ventura