DIRECTOR OF THE COURANT INSTITUTE OF MATHEMATICAL SCIENCES; HEAD, DEPARTMENTS OF MATHEMATICS AND COMPUTER SCIENCE:
Leslie Greengard

DEPUTY DIRECTOR OF THE INSTITUTE:
W. Stephen Childress

CHAIR OF THE DEPARTMENT:
Professor Yuri Tschinkel

DIRECTOR OF GRADUATE STUDIES:
Professor Fedor A. Bogomolov

The Department of Mathematics of the Courant Institute of Mathematical Sciences offers several degree programs. The Ph.D. programs offer research opportunities and instruction at the highest level in a range of core, multidisciplinary, and computational mathematics. In addition to the Ph.D. program in mathematics, the department offers a Ph.D. program in atmosphere ocean science. The master’s programs provide professional training in financial modeling and computation and mathematical and computational techniques of scientific computing, as well as in traditional core areas of mathematics.

The philosophy of the Courant Institute, developed over several decades, has been to maintain a balanced interaction between pure and applied mathematics. The Institute has long been a leader in mathematical analysis, applied mathematics, and computational science. In core mathematics, strengths include partial differential equations, stochastic processes, differential geometry and topology, and dynamical systems. In multidisciplinary mathematics, the Institute's program encompasses research activities not found in most mathematics departments: wave propagation, computational fluid dynamics (including aerodynamics, magnetofluid dynamics, and biofluid dynamics), atmosphere ocean science, mathematical biology, financial modeling, and materials science. Much of the research is externally funded and involves postdoctoral scientists. There is an active program of research seminars, and participation by students is strongly encouraged.

New York University is a member of the Inter-University Doctoral Consortium, whose members include Columbia University; CUNY Graduate Center; Fordham University; The New School; Princeton University; Rutgers University; Stony Brook University; and Teachers College, Columbia University. With permission, doctoral students who are in good standing and beyond the first year of study may cross-register for courses in these institutions and thus have access to a very broad range of mathematics and related fields. (See the Admission section of this bulletin for details.)

The Department of Mathematics is housed in Warren Weaver Hall, which contains a mathematical sciences library of 70,000 volumes, over 250 journal backfiles in paper, and an extensive array of electronic resources, such as Web of Science (ISI) and MathSciNet. Over 13,000 electronic journal titles across all fields are available at the University. Every Ph.D. student has a workstation on his or her desk. In addition, workstations and PCs are available in public locations. The Applied Mathematics Laboratory is an experimental facility in fluid mechanics and other applied areas. The Center for Atmosphere Ocean Studies is the locus for multidisciplinary studies and research in critical environmental problems, such as global warming, ozone depletion, monsoon and El Niño cycles, and pollution of air and water; it organizes a weekly colloquium and brings together interested faculty and students from different departments.

Faculty

Marco M. Avellaneda, Professor. Ph.D. 1985 (mathematics), Minnesota; Lic. en Cien. 1981 (mathematics), Buenos Aires.
Applied mathematics; mathematical modeling in finance; probability.

Jinho Baik, Associate Professor. Ph.D. 1999 (mathematics), New York; B.S. 1995 (mathematics), Korea Advanced Institute of Science and Technology (KAIST).
Asymptotics of integrable systems; random matrices; random permutations; orthogonal polynomials.

Gerard Ben Arous, Professor. Ph.D. 1981 (mathematics), Paris VII; DEA 1979 (probability), Paris VI; DEA 1979 (statistics), Orsay; Maîtrise 1978 (mathematics), Paris VII.
Probability theory and applications; statistical mechanics.

Simeon M. Berman, Professor. Ph.D. 1961 (mathematical statistics), M.A. 1958 (mathematical statistics), Columbia; B.A. 1956 (economics), City College (CUNY).
Stochastic processes; probability theory; applications.

Fedor A. Bogomolov, Professor. D.Sc. 1984 (mathematics), Ph.D. 1974 (mathematics), Steklov Institute of Mathematics; M.A. 1970 (mathematics), Moscow.
Algebraic geometry and related problems in algebra, topology, and number theory.

Oliver Bühler, Associate Professor, Mathematics (Atmosphere Ocean Science); Director, Center for Atmosphere Ocean Science. Ph.D. 1996 (applied mathematics), Cambridge; Diplom 1992 (applied physics), Technical (Berlin); M.S.E. 1990 (aerospace engineering), Michigan.
Geophysical fluid dynamics; waves and vortices in the atmosphere and ocean; statistical mechanics; stochastic wave theory.

David Cai, Associate Professor. Ph.D. 1994 (physics), M.S. 1989 (physics), Northwestern; B.S. 1984 (physics), Peking.
Nonlinear stochastic behavior in physical and biological systems.

Sylvain E. Cappell, Professor. Ph.D. 1969 (mathematics), Princeton; B.A. (summa cum laude) 1966 (mathematics), Columbia.
Algebraic and geometric topology; symplectic and algebraic geometry.

Jeff Cheeger, Professor; Silver Professor. Ph.D. 1967 (mathematics), M.S. 1966 (mathematics), Princeton; B.A. 1964 (mathematics), Harvard.
Differential geometry and its connections to analysis and topology.

Yu Chen, Associate Professor. Ph.D. 1991 (mathematics), M.S. 1988 (mathematics), Yale; B.S. 1982 (mathematics), Tsinghua.
Inverse scattering theory and algorithms; ill-posed problems; scientific computing; FM theory and applications for imaging and sensing.

Francesca Chiaromonte, Associate Professor, Mathematics, Biology. Ph.D. 1996 (statistics), Minnesota; Laurea 1990 (statistical and economic sciences), Rome La Sapienza.
Multivariate analysis and regression; Markov modeling; analysis and modeling of large-scale genomic data.

W. Stephen Childress, Professor; Deputy Director, Courant Institute of Mathematical Sciences. Ph.D. 1961 (aeronautics and mathematics), California Institute of Technology; M.S.E. 1958 (aeronautical engineering), B.S.E. 1956 (aeronautical engineering), Princeton.
Fluid dynamics; magnetohydrodynamics; biological fluid mechanics.

Tobias H. Colding, Professor. Ph.D. 1992 (mathematics), Pennsylvania.
Differential geometry; geometric analysis; partial differential equations; three-dimensional topology.

Percy A. Deift, Professor. Ph.D. 1976 (mathematical physics), Princeton; M.S. 1971 (physics), Rhodes; M.S. 1970 (chemical engineering), B.S. 1967 (chemical engineering), Natal (Durban).
Spectral theory; inverse spectral theory; integrable systems; random matrix theory.

Paul R. Garabedian, Professor. Ph.D. 1948 (mathematics), M.A. 1947 (mathematics), Harvard; B.A. 1946 (mathematics), Brown.
Complex analysis; computational fluid dynamics; plasma physics.

Jonathan B. Goodman, Professor. Ph.D. 1982 (mathematics), Stanford; B.S. 1977 (mathematics), Massachusetts Institute of Technology.
Wave propagation; computational physics; computational finance.

Leslie Greengard, Professor; Director, Courant Institute of Mathematical Sciences. M.D./Ph.D. 1987 (computer science), Yale; B.A. 1979 (mathematics), Wesleyan.
Applied and computational mathematics; partial differential equations; computational chemistry; imaging; computational biology.

Frederick P. Greenleaf, Professor. Ph.D. 1964 (mathematics), M.A. 1961 (mathematics), Yale; B.S. 1959 (engineering physics), Pennsylvania State.
Noncommutative harmonic analysis; Lie groups and group representations; invariant partial differential operators.

Mikhail Gromov, Jay Gould Professor of Mathematics. D.Sc. 1973 (mathematics), Ph.D. 1969 (mathematics), Leningrad.
Riemannian manifolds; symplectic manifolds; infinite groups; mathematical models of biomolecular systems.

C. Sinan Güntürk, Associate Professor. Ph.D. 2000 (applied and computational mathematics), Princeton; B.S. 1996 (mathematics and electrical engineering), Bog?aziçi.
Harmonic analysis; information theory; signal processing.

Eliezer Hameiri, Professor. Ph.D. 1976 (mathematics), New York; M.S. 1972 (physics and applied mathematics), B.S. 1970 (physics and applied mathematics), Tel Aviv.
Applied mathematics; magnetohydrodynamics; plasma physics.

Fengbo Hang, Associate Professor. Ph.D. 2001 (mathematics), New York; M.S. 1996 (mathematics), Beijing; B.S. 1993 (mathematics), Tsinghua.
Geometric analysis and nonlinear partial differential equations.

Helmut Hofer, Professor; Silver Professor. Ph.D. 1981 (mathematics), Dip. 1979, Zurich.
Symplectic geometry; dynamical systems; partial differential equations.

David M. Holland, Associate Professor, Mathematics (Atmosphere Ocean Science). Ph.D. 1993 (atmospheric and oceanic sciences), McGill; B.A. 1992 (mathematics and computer science), M.S. 1986 (physical oceanography), B.S. 1984 (physics), Memorial.
Climate theory; sea-level change; ice and ocean modeling; geophysical fluids laboratory experiments.

Richard Kleeman, Professor, Mathematics (Atmosphere Ocean Science). Ph.D. 1986 (mathematical physics), Adelaide; B.S. 1980 (theoretical physics), Australian National.
Predictability of dynamical systems relevant to the atmosphere and ocean; climate dynamics.

Robert V. Kohn, Professor. Ph.D. 1979 (mathematics), Princeton; M.Sc. 1975 (mathematics), Warwick; B.A. 1974 (mathematics), Harvard.
Nonlinear partial differential equations; materials science; mathematical finance.

Petter Kolm, Clinical Associate Professor. M.A. 2007 (finance), Ph.D. 2000 (applied mathematics), M.S. 1999 (applied mathematics), Yale; M.S. 1994, Swiss Federal Institute of Technology.
Mathematical finance.

Fang-Hua Lin, Professor; Silver Professor. Ph.D. 1985 (mathematics), Minnesota; B.S. 1981 (mathematics), Zhejiang.
Partial differential equations; geometric measure theory.

Andrew J. Majda, Samuel F. B. Morse Professor of Arts and Science; Professor, Mathematics. Ph.D. 1973 (mathematics), M.S. 1971 (mathematics), Stanford; B.S. 1970 (mathematics), Purdue.
Modern applied mathematics; atmo-sphere ocean science; partial differential equations.

Nader Masmoudi, Associate Professor. Ph.D. 1999 (mathematics), Dipl. Adv. Stud. 1996 (applied mathematics), Paris-Dauphine.
Nonlinear partial differential equations.

Henry P. McKean, Professor; Silver Professor. Ph.D. 1955 (mathematics), Princeton; B.A. 1952 (mathematics), Dartmouth.
Probability; partial differential equations; complex function theory.

David W. McLaughlin, Professor, Mathematics, Neural Science; Provost, New York University. Ph.D. 1971 (theoretical physics), M.S. 1969 (physics), Indiana; B.S. 1966 (mathematics and physics), Creighton.
Applied mathematics; nonlinear wave equations; neural science.

Assaf Naor, Associate Professor. Ph.D. 2002, M.S. 1998, B.S. 1996 (mathematics), Hebrew.
Analysis; probability; convex geometry; applications to combinatorics, mathematical physics, and theoretical computer science.

Charles M. Newman, Professor. Ph.D. 1971 (physics), M.A. 1968 (physics), Princeton; B.S. 1966 (mathematics and physics), Massachusetts Institute of Technology.
Probability theory; statistical physics; stochastic models.

Olivier Pauluis, Assistant Professor, Mathematics (Atmosphere Ocean Science). Ph.D. 2000 (atmospheric and oceanic sciences), Princeton; Licence d’Ingenieur Civil en Mathématiques Appliquées 1995, Catholic (Louvain).
Climate and the general circulation of the atmosphere; moist convection; tropical meteorology; numerical modeling.

Jerome K. Percus, Professor, Mathematics, Physics. Ph.D. 1954 (physics), M.A. 1948 (mathematics), B.S. 1947 (electrical engineering), Columbia.
Chemical physics; mathematical biology.

Charles S. Peskin, Professor, Mathematics, Neural Science; Silver Professor. Ph.D. 1972 (physiology), Yeshiva; B.A 1968 (engineering and applied physics), Harvard.
Applications of mathematics and computing to problems arising in medicine and biology; fluid dynamics of the heart; molecular machinery within biological cells; mathematical/computational neuroscience.

Richard M. Pollack, Professor, Mathematics, Computer Science. Ph.D. 1962 (number theory), New York; B.A. 1956 (philosophy and mathematics), Brooklyn College (CUNY).
Algorithms in real algebraic geometry; discrete geometry; computational geometry.

Aaditya Rangan, Assistant Professor. Ph.D. 2003 (mathematics), California (Berkeley); B.A. 1999 (mathematics and physics), Dartmouth.
Large-scale scientific modeling of physical, biological, and neurobiological phenomena.

Weiqing Ren, Assistant Professor. Ph.D. 2002 (mathematics), New York; B.S. 1994 (mathematics), Nanjing.
Applied mathematics; scientific computing; multiscale modeling of fluids.

John Rinzel, Professor, Neural Science, Mathematics. Ph.D. 1973 (applied mathematics), M.S. 1968 (applied mathematics), New York; B.S. 1967 (engineering science), Florida.
Computational neuroscience; nonlinear dynamics of neurons and neural circuits; sensory processing.

Sylvia Serfaty, Associate Professor. Ph.D. 1999 (mathematics), Paris XI (Orsay); M.S. 1995 (mathematics), Ecole Normale Supérieure (Paris).
Partial differential equations; variational problems with applications to physics.

Jalal Shatah, Professor. Ph.D. 1983 (applied mathematics), M.S. 1981 (applied mathematics), Brown; B.S. 1979 (mathematics and engineering science), Texas (Austin).
Partial differential equations; analysis.

Scott Sheffield, Associate Professor. Ph.D. 2003 (mathematics), Stanford; B.A./M.A. 1998 (mathematics), Harvard.
Probability and mathematical physics.

Michael J. Shelley, Lilian and George Lyttle Professor of Applied Mathematics; Professor, Mathematics, Neural Science. Ph.D. 1985 (applied mathematics), M.S. 1984 (applied mathematics), Arizona; B.A. 1981 (mathematics), Colorado.
Mathematical modeling and simulation; biophysical fluid dynamics; fluid-body interactions; locomotion; visual neuroscience; neuronal networks.

K. Shafer Smith, Assistant Professor, Mathematics (Atmosphere Ocean Science). Ph.D. 1999 (physics), California (Santa Cruz); B.S. 1992 (physics and mathematics), Indiana.
Large-scale atmospheric and oceanic dynamics; climate dynamics; geostrophic turbulence; waves and instabilities; balanced dynamics.

Joel H. Spencer, Professor, Mathematics, Computer Science. Ph.D. 1970 (mathematics), Harvard; B.S. 1965 (mathematics), Massachusetts Institute of Technology.
Discrete mathematics; theoretical computer science.

Daniel L. Stein, Professor, Physics, Mathematics; Dean for Science, Faculty of Arts and Science. Ph.D. 1979 (condensed matter theory), M.S. 1977 (physics), Princeton; B.S. 1975 (physics), Brown.
Quenched disorder in condensed matter systems; stochastic escape phenomena; fluctuations in mesoscopic systems.

Esteban G. Tabak, Professor. Ph.D. 1992 (mathematics), Massachusetts Institute of Technology; Civ.Eng. 1988 (hydraulics), Buenos Aires.
Atmosphere and ocean science; fluid dynamics; data analysis.

Anna-Karin Tornberg, Assistant Professor, Mathematics, Computer Science. Ph.D. 2000 (numerical analysis), Licentiate 1998 (numerical analysis), Royal Institute of Technology (Stockholm); M.S. 1997 (engineering physics), Uppsala; M.S. 1996 (mechanical engineering), Houston.
Numerical analysis; computational fluid dynamics; moving boundary problems.

Daniel Tranchina, Associate Professor, Biology, Mathematics, Neural Science. Ph.D. 1981 (neurobiology), Rockefeller; B.A. 1975 (neurobiology), SUNY (Binghamton).
Mathematical modeling in neuroscience; biostatics.

Yuri Tschinkel, Professor; Chair, Department of Mathematics. Ph.D. 1992 (mathematics), Massachusetts Institute of Technology; M.A. 1990 (mathematics), Moscow State.
Algebraic geometry; number theory; automorphic forms.

Eric Vanden Eijnden, Professor. Ph.D. 1997 (physics), B.S. 1992 (physics), Free (Brussels).
Applied mathematics; stochastic processes; statistical physics.

S. R. Srinivasa Varadhan, Frank Jay Gould Professor of Science; Professor, Mathematics. Ph.D. 1963 (statistics), Indian Statistical Institute; M.A. 1960 (statistics), B.Sc. 1959 (statistics), Madras.
Probability theory; stochastic processes; partial differential equations.

Akshay Venkatesh, Associate Professor. Ph.D. 2002 (mathematics), Princeton; B.S. 1997 (mathematics and physics), Western Australia.
Automorphic forms; number theory; analysis and dynamics on homogenous spaces.

Harold Weitzner, Professor. Ph.D. 1958 (physics), M.A. 1955 (physics), Harvard; B.A. 1954 (mathematics and physics), California (Berkeley).
Plasma physics; fluid dynamics; differential equations.

Olof B. Widlund, Professor, Mathematics, Computer Science. Habilitation 1966 (mathematics), Uppsala; Ph.D. 1964, M.S. 1960 (mathematics), Royal Institute of Technology (Stockholm).
Numerical analysis; partial differential equations; parallel computing.

Lai-Sang Young, Lucy and Henry Moses Professor of Science; Professor, Mathematics. Ph.D. 1978 (mathematics), M.S. 1976 (mathematics), California (Berkeley); B.A. 1973 (mathematics), Wisconsin (Madison).
Nonlinear dynamics and mathematical physics.

Jun Zhang, Assistant Professor, Physics, Mathematics. Ph.D. 1994 (physics), Copenhagen; M.S. 1990, Hebrew; B.S. 1985 (physics), Wuhan.
Fluid dynamics; biophysics; complex systems.

ASSOCIATED FACULTY IN OTHER DEPARTMENTS

Marsha J. Berger, Computer Science; Kit Fine, Philosophy; Bhubaneswar Mishra, Computer Science; Michael L. Overton, Computer Science; Nikolaus Rajewsky, Biology; Tamar Schlick, Chemistry, Computer Science.

AFFILIATED FACULTY IN OTHER DEPARTMENTS

Robert Shapley, Neural Science; Eero P. Simoncelli, Neural Science; Alan Sokal, Physics; George Zaslavsky, Physics.

FACULTY EMERITI

Martin D. Burrow, Martin D. Davis, Harold M. Edwards, Melvin Hausner, Warren W. Hirsch, Eugene Isaacson, Frank Karal, Samuel N. Karp, Peter D. Lax, Cathleen S. Morawetz, Louis Nirenberg, Jacob T. Schwartz, Harold N. Shapiro, Lu Ting, Peter Ungar.