About the Program
The Department of Mathematics offers both a PhD program in Mathematics and Applied Mathematics.
Students are admitted for specific degree programs: the PhD in Mathematics or PhD in Applied Mathematics. Requirements for the Mathematics and Applied Mathematics PhDs differ only in minor respects, and no distinction is made between the two in daytoday matters. Graduate students typically take 56 years to complete the doctorate.
Continuing students wishing to transfer from one program to another should consult the graduate advisor in 910 Evans Hall. Transfers between the two PhD programs are fairly routine, but must be done prior to taking the qualifying examination. It is a formal policy of the department that an applicant to the PhD program who has previous graduate work in mathematics must present very strong evidence of capability for mathematical research.
Students seeking to transfer to the department's PhD programs from other campus programs, including the Group in Logic and the Methodology of Science, must formally apply and should consult the Vice Chair for Graduate Studies.
Admissions
Admission to the University
Minimum Requirements for Admission
The following minimum requirements apply to all graduate programs and will be verified by the Graduate Division:
 A bachelor’s degree or recognized equivalent from an accredited institution;
 A grade point average of B or better (3.0);
 If the applicant has completed a basic degree from a country or political entity (e.g., Quebec) where English is not the official language, adequate proficiency in English to do graduate work, as evidenced by a TOEFL score of at least 90 on the iBT test, 570 on the paperandpencil test, or an IELTS Band score of at least 7 on a 9point scale (note that individual programs may set higher levels for any of these); and
 Sufficient undergraduate training to do graduate work in the given field.
Applicants Who Already Hold a Graduate Degree
The Graduate Council views academic degrees not as vocational training certificates, but as evidence of broad training in research methods, independent study, and articulation of learning. Therefore, applicants who already have academic graduate degrees should be able to pursue new subject matter at an advanced level without the need to enroll in a related or similar graduate program.
Programs may consider students for an additional academic master’s or professional master’s degree only if the additional degree is in a distinctly different field.
Applicants admitted to a doctoral program that requires a master’s degree to be earned at Berkeley as a prerequisite (even though the applicant already has a master’s degree from another institution in the same or a closely allied field of study) will be permitted to undertake the second master’s degree, despite the overlap in field.
The Graduate Division will admit students for a second doctoral degree only if they meet the following guidelines:
 Applicants with doctoral degrees may be admitted for an additional doctoral degree only if that degree program is in a general area of knowledge distinctly different from the field in which they earned their original degree. For example, a physics PhD could be admitted to a doctoral degree program in music or history; however, a student with a doctoral degree in mathematics would not be permitted to add a PhD in statistics.
 Applicants who hold the PhD degree may be admitted to a professional doctorate or professional master’s degree program if there is no duplication of training involved.
Applicants may apply only to one single degree program or one concurrent degree program per admission cycle.
Required Documents for Applications
 Transcripts: Applicants may upload unofficial transcripts with your application for the departmental initial review. Unofficial transcripts must contain specific information including the name of the applicant, name of the school, all courses, grades, units, & degree conferral (if applicable).
 Letters of recommendation: Applicants may request online letters of recommendation through the online application system. Hard copies of recommendation letters must be sent directly to the program, by the recommender, not the Graduate Admissions.

Evidence of English language proficiency: All applicants who have completed a basic degree from a country or political entity in which the official language is not English are required to submit official evidence of English language proficiency. This applies to institutions from Bangladesh, Burma, Nepal, India, Pakistan, Latin America, the Middle East, the People’s Republic of China, Taiwan, Japan, Korea, Southeast Asia, most European countries, and Quebec (Canada). However, applicants who, at the time of application, have already completed at least one year of fulltime academic course work with grades of B or better at a US university may submit an official transcript from the US university to fulfill this requirement. The following courses will not fulfill this requirement:

courses in English as a Second Language,

courses conducted in a language other than English,

courses that will be completed after the application is submitted, and

courses of a nonacademic nature.

Applicants who have previously applied to Berkeley must also submit new test scores that meet the current minimum requirement from one of the standardized tests. Official TOEFL score reports must be sent directly from Educational Test Services (ETS). The institution code for Berkeley is 4833 for Graduate Organizations. Official IELTS score reports must be sent electronically from the testing center to University of California, Berkeley, Graduate Division, Sproul Hall, Rm 318 MC 5900, Berkeley, CA 94720. TOEFL and IELTS score reports are only valid for two years prior to beginning the graduate program at UC Berkeley. Note: score reports can not expire before the month of June.
Where to Apply
Visit the Berkeley Graduate Division application page.
Admission to the Program
Undergraduate students also often take one or more of the following introductory Mathematics graduate courses:
Code  Title  Units 

MATH 202A  Introduction to Topology and Analysis  4 
MATH 202B  Introduction to Topology and Analysis  4 
MATH 214  Differential Topology  4 
MATH 225A  Metamathematics  4 
MATH 225B  Metamathematics  4 
MATH 228A  Numerical Solution of Differential Equations  4 
MATH 228B  Numerical Solution of Differential Equations  4 
MATH 250A  Groups, Rings, and Fields  4 
MATH 250B  Commutative Algebra  4 
The Math Department admits new graduate students to the fall semester only. The Graduate Division's Online Application will be available in early September at: http://grad.berkeley.edu/admissions/index.shtml. Please read the information on Graduate Division requirements and information required to complete the application.
Copies of official or unofficial transcripts may be uploaded to your application. Please do not mail original transcripts for the review process.
We require three letters of recommendation, which should be submitted online. Please do not mail letters of recommendation for the review process.
For more information, please review the department's graduate admissions webpage at: https://math.berkeley.edu/programs/graduate/admissions. We also recommend reviewing our admissions FAQs page at: https://math.berkeley.edu/programs/graduate/faqs.
Doctoral Degree Requirements
Curriculum
Prerequisites
The Department of Mathematics offers two PhD degrees, one in Mathematics and one in Applied Mathematics. Applicants for admission to either PhD program are expected to have preparation comparable to the undergraduate major at Berkeley in Mathematics or in Applied Mathematics. These majors consist of two full years of lower division work (covering calculus, linear algebra, differential equations, and multivariable calculus), followed by eight onesemester courses including real analysis, complex analysis, abstract algebra, and linear algebra. These eight courses may include some mathematically based courses in other departments, like physics, engineering, computer science, or economics.
Applicants for admission are considered by the department's Graduate Admissions and M.O.C. Committees. The number of students that can be admitted each year is determined by the Graduate Division and by departmental resources. In making admissions decisions, the committee conducts a comprehensive review of applicants considering broader community impacts, academic performance in mathematics courses, level of mathematical preparation, letters of recommendation, and GRE scores.
Degree Requirements
In outline, to qualify for the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.
 During the first year in the PhD program:
 take at least four courses, two or more of which are graduate courses in mathematics;
 and pass the sixhour written preliminary examination covering primarily undergraduate material. (The exam is given just before the beginning of each semester, and the student must pass it within their first three semesters.)
 Pass a threehour, oral qualifying examination emphasizing, but not exclusively restricted to, the area of specialization. The qualifying examination must be attempted within two years of entering the program.
 Complete a seminar offered by the Math department, giving a talk of at least one hour duration. Research presentations held at Mathematical Sciences Research Institute (MSRI), or Lawrence Berkeley National Lab (LBNL) are also acceptable. A Math Department faculty member must be present at the talk and sign the seminar form confirming.
 Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee.
 Meet the University residence requirement of two years or four semesters.
The detailed regulations of the PhD program are as follows:
Course Requirements
Students must take and pass at least four 4unit courses during the first year of the Ph.D. program; at least two courses per semester. At minimum, two of these courses must be graduate courses (200level) offered by the Department of Mathematics. Two upper division (100level) undergraduate courses offered by the Department of Mathematics may also be used toward this requirement. Exceptions may also be considered and must be reviewed by the Head Graduate Advisor for approval.
Preliminary Examination
The preliminary examination consists of six hours of written work given over a twoday period. Most of the examination covers material, mainly in analysis and algebra, and helps to identify gaps in preparation. The preliminary examination is offered twice a year—during the week before classes start in both the fall and spring semesters. A student may repeat the examination twice. A student who does not pass the preliminary examination within 13 months of the date of entry into the PhD program will not be permitted to remain in the program past the third semester. In exceptional cases, a fourth try may be granted upon appeal to committee omega.
Qualifying Examination
To arrange for the qualifying examination, a student must first settle on an area of concentration, and a prospective dissertation supervisor, someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective supervisor, the student forms an examination committee of four members. Committee members must be members of Berkeley's Academic Senate and the Chair must be a faculty member in the Mathematics Department. The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval it is to be circulated to all faculty members of the appropriate sections. The qualifying examination must cover material falling in at least three subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be seen on the Qualifying Examination page on the department website.
The student must attempt the qualifying examination within twentyfive months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the reexamination must be held within thirty months of the student's entrance into the PhD program.
For a student to pass the qualifying examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student, if asked. The student must obtain an official dissertation supervisor within one semester after passing the qualifying examination or leave the PhD program. For more detailed rules and advice concerning the qualifying examination, consult the graduate advisor in 910 Evans Hall.
Master's Degree Requirements
Eligibility
At this time, the MA in Mathematics is a simultaneous degree program only offered to students currently enrolled in a doctoral program at UC Berkeley. The doctoral student must be in good standing in their program and have a faculty adviser in the Mathematics Department who is supportive of the addition of the MA in Mathematics and agrees to supervise the MA work. Current doctoral students must apply during the regular admissions cycle for consideration for fall admission. The degree must be completed prior to or in tandem with the PhD degree. Interested students must inquire with the Mathematics Graduate Student Affairs Officer.
Unit Requirements
Plan I requires at least 20 semester units of upper division and graduate courses and a thesis. At least 8 of these units must be in graduate courses (200 series). These 8 units are normally taken in the Department of Mathematics at Berkeley. In special cases, upon recommendation of the Graduate Adviser and approval of the Dean of the Graduate Division, some of the 8 graduate units may be taken in other departments.
Plan II requires at least 24 semester units of upper division and graduate courses, followed by a comprehensive final examination, the MA examination. At least 12 of these units must be in graduate courses (200 series). These 12 units are normally taken in the Department of Mathematics at Berkeley. In special cases, upon recommendation of the graduate advisor and approval of the dean of the Graduate Division, some of the 12 graduate units may be taken in other departments. All courses fulfilling the above unit requirements must have significant mathematical content. In general, MA students are encouraged to take some courses outside the Department of Mathematics. In many jobs, at least some acquaintance with statistics and computer science is essential; and, for some students, courses in such fields as engineering, biological or physical sciences, or economics are highly desirable.
A breadth requirement consisting of at least one course in each of three fields must be met by all students. Fields include algebra, analysis, geometry, foundations, history of mathematics, numerical analysis, probability and statistics, computer science, and various other fields of applied mathematics. The last category specifically covers courses in a variety of departments, and the graduate adviser may allow more than one such course to count toward the breadth requirement. A depth requirement consisting of a coherent program of three courses all in one of the above fields, at least two of these courses being at the graduate level, must be met. Students interested in a field of applied mathematics are encouraged to take some of these courses outside the department.
Curriculum
Code  Title  Units 

Courses Required  
Breadth Requirement:  
Select one courses in three fields from the following:  
algebra; analysis, geometry, foundations, history of mathematics, numerical analysis, probability and statistics, computer science, applied mathematics  
Depth Requirement:  
Select a coherent program of three courses all in one field from the following:  
algebra; analysis, geometry, foundations, history of mathematics, numerical analysis, probability and statistics, computer science, applied mathematics 
 Advancement to Candidacy
 Capstone/Thesis (Plan I)
 Capstone/Comprehensive Exam (Plan II)
 Capstone/Master's Project (Plan II)
Faculty and Instructors
* Indicates this faculty member is the recipient of the Distinguished Teaching Award.
Faculty
Mina Aganagic, Professor. Particle physics.
Research Profile
Ian Agol, Professor. Lowdimensional topology.
David Aldous, Professor. Mathematical probability, applied probability, analysis of algorithms, phylogenetic trees, complex networks, random networks, entropy, spatial networks.
Research Profile
Denis Auroux, Professor. Mirror symmetry, symplectic topology.
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Richard H. Bamler, Assistant Professor. Geometric analysis, differential geometry, topology.
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Richard E. Borcherds, Professor. Mathematics, lie algebras, vertex algebras, automorphic forms.
Research Profile
* 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.
Research Profile
Semyon Dyatlov, Assistant Professor. Microlocal analysis, scattering theory, quantum chaos, PDE.
Research Profile
David Eisenbud, Professor. Mathematics, algebraic geometry, commutative algebra, computation.
Research Profile
Lawrence C. Evans, Professor. Optimization theory, nonlinear partial differential equations, calculus of variations.
Research Profile
Steven N. Evans, Professor. Genetics, random matrices, superprocesses and other measurevalued processes, probability on algebraic structures particularly local fields, applications of stochastic processes to biodemography, mathematical finance, phylogenetics and historical linguistics.
Research Profile
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.
Research Profile
Ming Gu, Professor. Mathematics, scientific computing, numerical linear algebra, adaptive filtering, system and control theory, differential and integral equations.
Research Profile
Mark D. Haiman, Professor. Mathematics, algebraic geometry, algebra, combinatorics, diagonal coinvariants, Hilbert schemes.
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Alan Hammond, Associate Professor. Statistical mechanics.
Research Profile
Jenny Harrison, Professor. Mathematics, geometric analysis.
Research Profile
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.
Research Profile
Michael Hutchings, Professor. Mathematics, low dimensional, symplectic topology, geometry.
Research Profile
Michael J. Klass, Professor. Statistics, mathematics, probability theory, combinatorics independent random variables, iterated logarithm, tail probabilities, functions of sums.
Research Profile
Lin Lin, Assistant Professor. Numerical analysis, computational quantum chemistry, computational materials science.
John W. Lott, Professor. Differential geometry.
Antonio Montalban, Associate Professor. Mathematical logic.
Research Profile
David Nadler, Professor. Geometric representation.
Martin Olsson, Professor. Algebraic geometry, arithmetic geometry.
Research Profile
PerOlof Persson, Associate Professor. Applied mathematics, numerical methods, computational fluid and solid mechanics.
Research Profile
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, lowdimensional 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, noncommutative geometry, noncommutative 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, Superrepresentation 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.
Research Profile
Vivek V. Shende, Assistant Professor. Geometry.
Sug Woo Shin, Associate Professor. Number theory, automorphic forms.
Pierre Simon, Assistant Professor. Mathematical Logic, Model theory.
Research Profile
Theodore A. Slaman, Professor. Mathematics, recursion theory.
Research Profile
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.
Research Profile
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.
Research Profile
Luca Trevisan, Professor. Computational complexity, spectral graph theory.
Research Profile
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.
Research Profile
Katrin Wehrheim, Associate Professor. Lowdimensional and symplectic topology.
Jon Wilkening, Professor. Applied mathematics, numerical analysis, computational solid and fluid mechanics.
Research Profile
Lauren K. Williams, Professor. Algebraic combinatorics.
Research Profile
Mariusz Wodzicki, Professor. Analysis, mathematics, Noncommutative and algebraic geometry, Ktheory.
Research Profile
Xinyi Yuan, Assistant Professor. Number theory.
Research Profile
Maciej Zworski, Professor. Mathematics, partial differential equations, mathematical physics, mathematical aspects of quantum mechanics, scattering theory, microlocal analysis.
Research Profile
Lecturers
Emiliano Gomez, Lecturer.
* Alexander Paulin, Lecturer. Number theory, arithmetic geometry, algebraic geometry, padic analytic geometry, Dmodule theory, padic Hodge theory, motive theory and higher category theory.
Research Profile
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.
Research Profile
Robert Anderson, Professor Emeritus. Finance, probability theory, mathematical economics, nonstandard analysis.
Research Profile
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.
Research Profile
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.
Research Profile
Alexandre J. Chorin, Professor Emeritus. Applied mathematics, numerical methods, hydrodynamics, sampling and Monte Carlo methods .
Research Profile
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, xray crystallography, imaging of structures of biological interest, classical and quantum random walks, matrix valued orthogonal polynomials, quasi birthanddeath 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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WuYi 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.
Research Profile
TsitYuen 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.
Research Profile
Keith Miller, Professor Emeritus. Mathematics, partial differential equations, numerical methods for PDE's.
Research Profile
Calvin C. Moore, Professor Emeritus. Operator algebras, ergodic theory, representations and actions of topological groups, foliations and foliated spaces, K theory.
Research Profile
John Neu, Professor Emeritus.
Andrew Ogg, Professor Emeritus.
Arthur E. Ogus, Professor Emeritus. Mathematics, algebraic geometry, algebraic differential equations, log poles.
Research Profile
Beresford N. Parlett, Professor Emeritus. Numerical analysis, scientific computation.
Charles C. Pugh, Professor Emeritus. Mathematics, global theory of differential equations.
Research Profile
John L. Rhodes, Professor Emeritus. Mathematics, algebra, semigroups, automata.
Research Profile
Rainer K. Sachs, Professor Emeritus. Mathematical biology.
Research Profile
Isadore M. Singer, Professor Emeritus. Mathematics, physics, partial differential equations, geometry.
Research Profile
Stephen Smale, Professor Emeritus. Algorithms, mathematics, numerical analysis, global analysis.
Research Profile
Robert M. Solovay, Professor Emeritus.
John Steel, Professor Emeritus. Mathematics, descriptive set theory, set theory, fine structure.
Research Profile
Peter Teichner, Professor Emeritus. Topology, quantum field theory.
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John B. Wagoner, Professor Emeritus. Mathematics, dynamical systems, differential topology, algebraic Ktheory.
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Alan Weinstein, Professor Emeritus. Mathematics, mathematical physics, symplectic geometry.
Research Profile
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.
Research Profile
HungHsi Wu, Professor Emeritus. Real and complex geometry, school mathematics education.
Research Profile
Contact Information
Graduate Student Affairs Officer
Jon Phillips
910 Evans Hall
Phone: 5106420665