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 |
|---|---|---|
| Paul R. Chernoff | Professor Emeritus | Functional analysis, Operator theory |
| F. Michael Christ | Professor | Harmonic analysis, Partial differential equations, Complex analysis in several variables |
| Heinz O. Cordes | Professor Emeritus | Classical analysis |
| Stephen P.L. Diliberto | Professor Emeritus | Ordinary differential equations, Celestial mechanics |
| L. Craig Evans | Professor | Partial differential equations |
| Jacob Feldman | Professor Emeritus | Ergodic theory, Stochastic processes |
| Jenny Harrison | Professor | Geometric analysis |
| 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 |
| Marina Ratner | Professor Emeritus | Ergodic theory |
| Fraydoun Rezakhanlou | Professor | Probability theory, Partial differential equations |
| Marc A. Rieffel | Professor | Non-commutative harmonic analysis, Operator algebras, Quantum geometry |
| Donald E. Sarason | Professor | Complex function theory, Operator theory |
| 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 |
|---|---|---|
| Jean Bourgain | Visiting Scholar | Analysis |
| François Hamel | Visiting Scholar | Partial differential Equations, nonlinear analysis, applied mathematics |
| Ilya Zakharevich | Visiting Lecturer | Integrable systems |
Postdocs
| Name | Title | Research Interests |
|---|---|---|
| Benjamin Dodson | NSF Postdoctoral Fellow | Partial differential equations, harmonic analysis |
| Olivier Kneuss | Postdoctoral Fellow | Partial Differential Equations, Calculus of Variations |
| Paul Smith | NSF Postdoctoral Fellow | Partial Differential Equations, Harmonic Analysis |
Faculty with Related Research Interests
| Name | Title | Research Interests |
|---|---|---|
| Steven N. Evans | Professor | Probability and stochastic processes |
| F. Alberto Grünbaum | Professor | 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 |
| Yuval Peres | Adjunct Professor | Probability theory and Hausdorff dimension |
| James Pitman | Professor | Probability, stochastic processes, combinatorics, machine learning |
| Nicolai Reshetikhin | Professor | Mathematical physics, Low-dimensional topology, Representation theory |
| James A. Sethian | Professor | Applied mathematics, Computational physics, Partial differential equations |
| 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, Materials science, and Scientific computing |
Graduate Students
| Name | Dissertation Supervisor |
|---|---|
| Benson Au | |
| Khalilah Beal | L. Craig Evans |
| Elan Bechor | |
| Marcos Charalambides | F. Michael Christ |
| Semyon Dyatlov | Maciej Zworski |
| Boris Ettinger | Daniel Tataru |
| Jeffrey E. Galkowski | Maciej Zworski |
| Cristian-Dan Gavrus | |
| Boaz E. Haberman | |
| Benjamin Harrop-Griffiths | Daniel Tataru |
| Michael Hartglass | Vaughan F. R. Jones |
| Alexandru Hening | Steven N. Evans |
| Long Jin | Maciej Zworski |
| Andre Kornell | Marc A. Rieffel |
| Minjae Lee | |
| Weihua Liu | Dan-Virgil Voiculescu |
| Adam B. Merberg | Dan-Virgil Voiculescu |
| Cody M. Mitchell | Marc A. Rieffel |
| Terry Rodriguez | |
| Peyam R. Tabrizian | L. Craig Evans |
| Matthew Tucker-Simmons | Marc A. Rieffel, Nicolai Reshetikhin |
| Eric Wayman | Steven N. Evans |
| Christopher A. Wong |
Recent Ph.D.s
| Name | Dissertation Title | Dissertation Supervisor | Year |
|---|---|---|---|
| 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 SemiclassicalAnalysis to Partial Differntial Equations | Maciej Zworski | 2012 |
| Stephen Curran | Quantum Symmetries in Free Probability | Dan-Virgil Voiculescu | 2010 |
| Ryan Hynd | Partial Differential Equations with Gradient Constraints Arising in the Optimal Control of Singular Stochastic Processes | Craig Evans | 2010 |
| Patrick LaVictoire | Pointwise Ergodic Therrems for Nonconventional L1 Averages | Michael Christ | 2010 |
| Ivan Matic | Homogenization and Large Deviations | Fraydoun Rezakhanlou | 2010 |
| Mira Alexander Peterka | Finitely-Generated Projective Modules over theta-deformed Spheres | Marc Rieffel | 2010 |
| Charles Smart | On the Infinity Laplacian and Hrushouski's Fusion | Craig Evans, Leo Harrington | 2010 |
| Scott Armstrong | Principal half-eigenvalves of fully nonlinear homogeneous elliptic operators | L. Craig Evans | 2009 |
| Zachary Judson | Connectivity in the Higson Carona of the Positive Real Axis | Donald Sarason | 2009 |
| Yun Long | Mixing time of the Swendsen-Wang Dynamics in Complete graph and trees | Yuval Peres | 2009 |
| Emily Peters | A planar algebra construction of te Haagerup subfacto | Vaughan Jones | 2009 |
| Jeremy Sain | Berezin Quantization for Ergodic Actions of Campact Quantum Groups and Quantum Granov-Hassdoff Distance | Marc Rieffel | 2009 |
| Stephanie Jane Somersille | Biased Tug-of-War, The Biased Infinity Laplacian and Comparison with Exponential Cones | Yuval Peres | 2009 |
| Lindsay Elizabeth Stovall | Lp inequalities for certain generalized Radon transforms | Michael Christ | 2009 |
| Mihai Tohaneanu | Local energy estimates and Strichartz estimates on Schwarzchild and Kerr black hole backgrounds | Daniel Tataru | 2009 |
| Maxim Trokhimchouk | Regularity for certain parabolic diffusion systems | L. Craig Evans | 2009 |
| Guoliang Wu | Impulse control of multidimensional diffusion and jump diffusion processes | L. Craig Evans | 2009 |
| Richard David Burstein | Hadamard Subfactors of Bisch-Hagerup Type | Vaughan Jones | 2008 |
| Aubrey Clayton | Mutation-Selection Balance for Polynomial Selection Costs and Matrix-Valued Orthogonal Polynomials | Steven Evans | 2008 |
| Asaf Nachmias | Critical Percolation on Finite Graphys | Yuval Peres | 2008 |
