Graduate programs

Inquiries concerning the graduate program in mathematics should be sent to Bernadette Alston-Facey.  Some useful links:

Chairman: Yair Minsky

Director of Graduate Studies: Alexander Goncharov

 Professors Donald Brown (Economics), Andrew Casson, Ronald Coifman, Michael Frame (Adjunct), Igor Frenkel, Howard Garland, Alexander Goncharov, Roger Howe, Peter Jones, Ravindran Kannan (Computer Science), Mikhail Kapranov, Alexander Lubotzky (Adjunct), Gregory Margulis, Yair Minsky, Vincent Moncrief (Physics), David Pollard (Statistics), Vladimir Rokhlin (Computer Science), Van Vu, Gregg Zuckerman

 Assistant Professors:  Amanda Folsom, Alex Kontorovich, Sam Payne

 Gibbs Assistant Professors: Yael Algom Kfir, Ian Biringer, Nicoleta Corina Calinescu, Swarnendu Datta, Yen Quang Do, Asaf Hadari, Marketa Havlickova, Anna Lachowska, Garving Kevin Luli, Zhenqi Wang, Zhiren Wang Fields of Study

 Fields include real analysis, complex analysis, functional analysis, classical and modern harmonic analysis; linear and nonlinear partial differential equations; dynamical systems and ergodic theory; geometric analysis; kleinian groups, low dimensional topology and geometry; differential geometry; finite and infinite groups; geometric group theory; finite and infinite dimensional Lie algebras, Lie groups, and discrete subgroups; representation theory; automorphic forms, L-functions; algebraic number theory and algebraic geometry; mathematical physics, relativity; numerical analysis; combinatorics and discrete mathematics.

Special Requirements for the Ph.D. Degree

 All students are required to: (1) complete eight term courses at the graduate level, at least two with Honors grades; (2) demonstrate a reading knowledge of two of the following languages: French, German, or Russian; (3) pass qualifying examinations on their general mathematical knowledge; (4) submit a dissertation prospectus; (5) participate in the instruction of undergraduates; (6) be in residence for at least three years; and (7) complete a dissertation that clearly advances understanding of the subject it considers. The normal time for completion of the Ph.D. program is four years. Requirement (1) normally includes basic courses in algebra, analysis, and topology; these should be taken during the first year. The first language examination must be completed by the beginning of the third year of study, the second no later than the end of that year. A sequence of three qualifying examinations (algebra and number theory, real and complex analysis, topology) is offered each term, at intervals of about one month. All qualifying examinations must be taken by the end of the third term. The thesis is expected to be independent work, done under the guidance of an adviser. This adviser should be contacted not long after the student passes the qualifying examinations. A student is admitted to candidacy after completing requirements (1)–(6) and obtaining an adviser.

 In addition to all other requirements, students must successfully complete MATH 991a, Ethical Conduct of Research, prior to the end of their first year of study. This requirement must be met prior to registering for a second year of study.

Honors Requirement: Students must meet the Graduate School’s Honors requirement by the end of the fourth term of full-time study.

Master’s Degrees:  M.Phil. In addition to the Graduate School’s Degree Requirements (see under Policies and Regulations), a student must undertake a reading program of at least two terms’ duration in a specific significant area of mathematics under the supervision of a faculty adviser and demonstrate a command of the material studied during the reading period at a level sufficient for teaching and research.

 M.S. A student must complete six term courses with at least one Honors grade, pass one language examination, perform adequately on the general qualifying examination, and be in residence at least one year.

 Note that the M.Phil. and M.S. degrees are conferred only en route to the Ph.D.; there is no separate master’s program in Mathematics.

 Program materials are available upon request to the Director of Graduate Studies, Mathematics Department, Yale University, PO Box 208283, New Haven CT 06520-8283.

Courses:  MATH 500au, Modern Algebra I Mikhail Kapranov, MW 2:30–3:45

 MATH 501bu, Modern Algebra II Gregg Zuckerman, TTH 2:30–3:45

 MATH 515bu, Intermediate Complex Analysis Yen Quang Do, MW 2:30–3:45

 MATH 520au, Measure Theory and Integration Gregory Margulis, TTH 1–2:15

 MATH 525bu, Introduction to Functional Analysis Garving Kevin Luli, MWF 11:35–12:25

 MATH 544a, Introduction to Algebraic Topology I Ian Biringer,  TTH 2:30–3:45

 MATH 545b, Introduction to Algebraic Topology II Staff

 MATH 573au, Algebraic Number Theory Alexander Goncharov,  TTh 2:30–3:45

 MATH 825b, Computational Algebraic Geometry Tobias Dyckerhoff,  TTh 1–2:15

 MATH 991a/CPSC 991a, Ethical Conduct of Research Igor Frenkel, HTBA