## Overview

The Department of Mathematics is generally recognized as one of the broadest, liveliest, and most distinguished departments of mathematics in the world. With approximately 55 regular faculty members representing most of the major fields of current research, along with 25 to 30 postdoctoral scholars, 180 graduate students, 475 undergraduate majors, one of the finest mathematics libraries in the nation, and a favorable climate in one of America's most exciting and cosmopolitan centers for mathematics research and teaching, UC Berkeley has become a favorite location for the study of mathematics by students and faculty from all over the world.

UC Berkeley is increasingly interested in developing the talents of outstanding mathematics students and has a number of challenging honors-level courses. The department encourages all major students to participate in the annual William Lowell Putnam Mathematical Competition. Additionally, the department sponsors undergraduate teams in the annual Mathematical Contest in Modeling, in which teams of three write mathematical solutions to real-life problems. An active Mathematics Undergraduate Student Association (MUSA), of which all departmental majors are automatically members, contributes to making Berkeley a stimulating and rewarding place to study mathematics. In addition, the Noetherian Ring, an organization seeking to promote and support women in mathematics at Berkeley, is open to undergraduate students.

Berkeley's mathematics education program is greatly enriched by its large number of graduate students, postdoctoral faculty and fellows, and visiting teachers in residence each year. They come from all over the world to teach courses, participate in seminars, collaborate in research, give talks at the weekly Mathematics Colloquium, and be available as consultants. An affiliated interdisciplinary group, with its own doctoral program, is the Group in Logic and the Methodology of Science. There are two NSF funded Research Training Groups: one in Representation Theory, Geometry and Combinatorics and one in Geometry, Topology and Operator Algebras. These groups run seminars, workshops, and other activities and support graduate student and postdoctoral fellows in their areas of interest. The department has several graduate student groups: the Mathematics Graduate Student Association (MGSA), comprising all graduate students; the Noetherian Ring, a group of women in mathematics; and a student lecture series, Many Cheerful Facts.

### Facilities

The Mathematics Library on the first floor of Evans Hall, part of the system of University of California Libraries, provides researchers and students with access to world-class collections.

The Mathematical Sciences Research Institute (MSRI) was founded by the National Science Foundation in 1981. In a beautifully designed building on the hills above the Berkeley campus and overlooking San Francisco Bay, about 1,700 mathematicians from around the world come each year to participate in research programs in a wide variety of mathematical topics. The combined and cooperative efforts of the department, the center, and the MSRI provide a program of mathematics courses, workshops, seminars, and colloquia of remarkable variety and exciting intensity.

### Undergraduate Programs

Applied Mathematics: BA

Mathematics: BA (also available with a Teaching Concentration), Minor

### Graduate Programs

Applied Mathematics: PhD

Mathematics: MA, PhD

## Faculty and Instructors

**+ **Indicates this faculty member is the recipient of the Distinguished Teaching Award.

#### Faculty

**Mina Aganagic, Professor. **Particle physics.

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**Ian Agol, Professor. **Low-dimensional topology.

**David Aldous, Professor. **Mathematical probability, applied probability, analysis of algorithms, phylogenetic trees, complex networks, random networks, entropy, spatial networks.

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**Denis Auroux, Professor. **Mirror symmetry, symplectic topology.

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**Richard H. Bamler, Assistant Professor. **

**Richard E. Borcherds, Professor. **Mathematics, lie algebras, vertex algebras, automorphic forms.

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**+ F. Michael Christ, Professor. **Mathematics, harmonic analysis, partial differential equations, complex analysis in several variables, spectral analysis of Schrodinger operators.

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**James W. Demmel, Professor. **Computer science, scientific computing, numerical analysis, linear algebra.

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

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**David Eisenbud, Professor. **Mathematics, algebraic geometry, commutative algebra, computation.

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**Lawrence C. Evans, Professor. **Optimization theory, nonlinear partial differential equations, calculus of variations.

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**Steven N. Evans, Professor. **Genetics, random matrices, superprocesses and other measure-valued processes, probability on algebraic structures -particularly local fields, applications of stochastic processes to biodemography, mathematical finance, phylogenetics and historical linguistics.

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**Edward Frenkel, Professor. **Mathematics, representation theory, integrable systems, mathematical physics.

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**Alexander B. Givental, Professor. **Mathematics, mathematical physics, symplectic geometry, singularities, mirror symmetry.

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**Ming Gu, Professor. **Mathematics, scientific computing, numerical linear algebra, adaptive filtering, system and control theory, differential and integral equations.

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**Mark D. Haiman, Professor. **Mathematics, algebraic geometry, algebra, combinatorics, diagonal coinvariants, Hilbert schemes.

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**Alan Hammond, Associate Professor. **Statistical mechanics.

**Jenny Harrison, Professor. **Mathematics, geometric analysis.

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**Olga V. Holtz, Professor. **Numerical analysis, matrix and operator theory, approximation theory, wavelets and splines, orthogonal polynomials and special functions, analysis of algorithms and computational complexity.

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**Michael Hutchings, Professor. **Mathematics, low dimensional, symplectic topology, geometry.

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**Michael J. Klass, Professor. **Statistics, mathematics, probability theory, combinatorics independent random variables, iterated logarithm, tail probabilities, functions of sums.

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**Lin Lin, Assistant Professor. **Numerical analysis, computational quantum chemistry, computational materials science.

**John W. Lott, Professor. **Differential geometry.

**Antonio Montalban, Associate Professor. **Mathematical logic.

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**David Nadler, Professor. **Geometric representation.

**Martin Olsson, Professor. **Algebraic geometry, arithmetic geometry.

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**Per-Olof Persson, Associate Professor. **Applied mathematics, numerical methods, computational fluid and solid mechanics.

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**James W. Pitman, Professor. **Fragmentation, statistics, mathematics, Brownian motion, distribution theory, path transformations, stochastic processes, local time, excursions, random trees, random partitions, processes of coalescence.

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**Nicolai Reshetikhin, Professor. **Mathematics, representation theory, mathematical physics, low-dimensional topology.

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**Fraydoun Rezakhanlou, Professor. **Mathematics, probability theory, partial differential equations.

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**Kenneth A. Ribet, Professor. **Mathematics, algebraic geometry, algebraic number theory.

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**Marc Rieffel, Professor. **Mathematics, operator algebras, non-commutative geometry, non-commutative harmonic analysis, quantum geometry.

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**Thomas Scanlon, Professor. **Mathematics, model theory, applications to number theory.

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**Vera Serganova, Professor. **Mathematics, Super-representation theory.

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**James A. Sethian, Professor. **Mathematics, applied mathematics, partial differential equations, computational physics, level set Methods, computational fluid mechanics and materials sciences. fast marching methods.

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**Chris Shannon, Professor. **Economics, mathematical economics, economic theory.

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**Vivek V. Shende, Assistant Professor. **Geometry.

**Sug Woo Shin, Associate Professor. **Number theory, automorphic forms.

**Pierre Simon, Assistant Professor. **Mathematical Logic, Model theory.

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**Theodore A. Slaman, Professor. **Mathematics, recursion theory.

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**Nikhil Srivastava, Assistant Professor. **Theoretical computer science, random matrices, geometry of polynomials.

**Zvezdelina Stankova, Teaching Professor. **Algebraic geometry, representation theory, combinatorics, Olympiad problem solving, Berkeley Math Circle.

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**John Strain, Professor. **Mathematics, numerical analysis, applied mathematics, fast algorithms, materials science.

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**Bernd Sturmfels, Professor. **Mathematics, combinatorics, computational algebraic geometry.

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**Song Sun, Associate Professor. **Differential Geometry.

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**Daniel Ioan Tataru, Professor. **Mathematics, partial differential equations, nonlinear waves.

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**Constantin Teleman, Professor. **Lie algebras, algebraic geometry, Lie groups, topology, topological quantum field theory.

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**Luca Trevisan, Professor. **Computational complexity, spectral graph theory.

**Dan Voiculescu, Professor. **Random matrices, pperator algebras, free probability theory.

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**Paul A. Vojta, Professor. **Mathematics, algebraic geometry, diophantine geometry, Nevanlinna theory, Arakelov theory.

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**Katrin Wehrheim, Associate Professor. **Low-dimensional and symplectic topology.

**Jon Wilkening, Professor. **Applied mathematics, numerical analysis, computational solid and fluid mechanics.

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**Lauren K. Williams, Professor. **Algebraic combinatorics.

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**Mariusz Wodzicki, Professor. **Analysis, mathematics, Non-commutative and algebraic geometry, K-theory.

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**Xinyi Yuan, Assistant Professor. **Number theory.

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**Maciej Zworski, Professor. **Mathematics, partial differential equations, mathematical physics, mathematical aspects of quantum mechanics, scattering theory, microlocal analysis.

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#### Lecturers

**Emiliano Gomez, Lecturer. **

**Alexander Paulin, Lecturer. **

**Kelli Talaska, Lecturer. **

#### Visiting Faculty

**Carolyn Abbott, Visiting Assistant Professor. **

**Semeon Artamonov, Visiting Assistant Professor. **

**Daniel Bragg, RTG Postdoc. **

**James Conway, Visiting Assistant Professor. **

**David Corwin, RTG Postdoc. **

**Wilfrid Gangbo, Chancellor's Professor. **

**Charles Hadfield, Visiting Assistant Professor. **

**Marina Iliopoulou, Visiting Assistant Professor. **

**Casey Jao, NSF Postdoc. **

**Tim Laux, Visiting Assistant Professor. **

**Koji Shimizu, Visiting Assistant Professor. **

**Slobodan Simic, Visiting Professor. **

**Dmitry Tonkonog, Visiting Assistant Professor. **

**Dimitry Vaintrob, Visiting Assistant Professor. **

**Xuwen Zhu, Visiting Assistant Professor. **

#### Emeritus Faculty

**John W. Addison, Professor Emeritus. **Mathematics, theory of definability, descriptive set theory, model theory, recursive function theory.

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**Robert Anderson, Professor Emeritus. **Finance, probability theory, mathematical economics, nonstandard analysis.

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**Grigory I. Barenblatt, Professor Emeritus. **Applied mathematics, Solid mechanics, Fluid mechanics, similarity methods asymptotics, mechanics of deformable solids.

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**George Bergman, Professor Emeritus. **Mathematics, associative rings, universal algebra, category theory, counterexamples.

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**Elwyn R. Berlekamp, Professor Emeritus. **Computer science, electrical engineering, mathematics, combinatorial game theory, algebraic coding theory.

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**Robert Bryant, Professor Emeritus. **Symplectic geometry, differential geometry, Lie groups, geometric partial differential equations.

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**Alexandre J. Chorin, Professor Emeritus. **Applied mathematics, numerical methods, hydrodynamics, sampling and Monte Carlo methods.

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**Paul Concus, Professor Emeritus. **Fluid mechanics, numerical analysis, applied mathematics, capillarity.

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**Heinz O. Cordes, Professor Emeritus. **Mathematics, classical analysis.

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**F. Alberto Grunbaum, Professor Emeritus. **Medical imaging, x-ray crystallography, imaging of structures of biological interest, classical and quantum random walks, matrix valued orthogonal polynomials, quasi birth-and-death processes.

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**+ Ole H. Hald, Professor Emeritus. **Mathematics, numerical analysis.

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**Leo A. Harrington, Professor Emeritus. **Mathematics, model theory, recursion theory, set theory.

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**Robert C. Hartshorne, Professor Emeritus. **Mathematics, algebraic geometry.

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**Morris W. Hirsch, Professor Emeritus. **Game theory, dynamical systems, topology, biological models.

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**Wu-Yi Hsiang, Professor Emeritus. **Mathematics, transformation groups, differential geometry.

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**Vaughan F. R. Jones, Professor Emeritus. **Mathematics, Von Neumann algebras.

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**William M. Kahan, Professor Emeritus. **Error analysis, Numerical computations, Computers, Convexity, Large matrices, Trajectory problems.

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**Robion C. Kirby, Professor Emeritus. **Mathematics, topology of manifolds.

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**Tsit-Yuen Lam, Professor Emeritus. **

**R. Sherman Lehman, Professor Emeritus. **

**H. W. Lenstra, Professor Emeritus. **

**Ralph N. McKenzie, Professor Emeritus. **Mathematics, logic, universal algebra, general algebra, lattice theory.

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**Keith Miller, Professor Emeritus. **Mathematics, partial differential equations, numerical methods for PDE's.

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**Calvin C. Moore, Professor Emeritus. **Operator algebras, ergodic theory, representations and actions of topological groups, foliations and foliated spaces, K- theory.

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**John Neu, Professor Emeritus. **

**Andrew Ogg, Professor Emeritus. **

**Arthur E. Ogus, Professor Emeritus. **Mathematics, algebraic geometry, algebraic differential equations, log poles.

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**Beresford N. Parlett, Professor Emeritus. **Numerical analysis, scientific computation.

**Charles C. Pugh, Professor Emeritus. **Mathematics, global theory of differential equations.

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**John L. Rhodes, Professor Emeritus. **Mathematics, algebra, semigroups, automata.

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**Rainer K. Sachs, Professor Emeritus. **Mathematical biology.

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**Isadore M. Singer, Professor Emeritus. **Mathematics, physics, partial differential equations, geometry.

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**Stephen Smale, Professor Emeritus. **Algorithms, mathematics, numerical analysis, global analysis.

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**Robert M. Solovay, Professor Emeritus. **

**John Steel, Professor Emeritus. **Mathematics, descriptive set theory, set theory, fine structure.

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**Peter Teichner, Professor Emeritus. **Topology, quantum field theory.

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**John B. Wagoner, Professor Emeritus. **Mathematics, dynamical systems, differential topology, algebraic K-theory.

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**Alan Weinstein, Professor Emeritus. **Mathematics, mathematical physics, symplectic geometry.

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**Joseph A. Wolf, Professor Emeritus. **Harmonic analysis, differential geometry, Lie groups.

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**W. Hugh Woodin, Professor Emeritus. **Mathematics, set theory, large cardinals.

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**Hung-Hsi Wu, Professor Emeritus. **Real and complex geometry, school mathematics education.

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## Contact Information

#### Vice-Chair for Undergraduate Affairs

Olga Holtz

821 Evans Hall

Phone: 510-642-2122

#### Vice-Chair for Graduate Affairs

Jon Wilkening

1051 Evans Hall

Phone: 510-643-7990