nyu math phd

Mathematics (PhD)

Program description, dual-degree.

The Department of Mathematics is part of the Courant Institute of Mathematical Sciences , an independent division of New York University . Based in Warren Weaver Hall, at the heart of New York University’s Washington Square campus, it is one of the top-ranked Mathematics departments worldwide (#4 in the US and #9 in the world as per the Shanghai rankings ; #6 in the US and #8 in the world as per the QS rankings ).

For more on the Courant Institute and its pioneering history in the field of applied mathematics (our department is consistently ranked #1 in applied mathematics as per USNews), see the history page .

The study of mathematics can lead to a variety of exciting professional careers. Basic research, engineering, finance, business, and government service are among the opportunities open to those with mathematical training.  Moreover, with the increasing importance of basic science and information technology, prospects for careers in the mathematical sciences are very good. Mathematical analysis and computational modeling are important for solving some of the most pressing problems of our time - new energy resources, climate change, risk management, epidemiology, to name a few. We must strive to maintain our technological edge; mathematical skills will be crucial to this effort.

Some more specific business positions include portfolio analysis, design studies, statistical analysis, computer simulation, software design and testing, and other areas of operations research. There are extensive opportunities for mathematics in finance, the actuarial fields, and economic forecasting.

Many laboratories, both government and private, maintain independent research staffs that include mathematicians. Their work often deals with the development of new technology, including research in basic physics and software development, as well as applied mathematics. Numerical simulation, such as weather and climate forecasting, depends heavily on the use of supercomputers.

Practical considerations aside, there is the pleasure of learning, applying, and creating mathematics. Real world issues pose problems that can be studied by formulating and analyzing mathematical models. In some cases applications may lead to new mathematics, and a new branch of the science is born. In other cases abstract theory finds unexpected practical purpose. Working on research problems is exciting; solving difficult problems successfully is, for many, satisfaction enough.

All applicants to the Graduate School of Arts and Science (GSAS) are required to submit the  general application requirements , which include:

• Academic Transcripts
• Test Scores  (if required)
• Applicant Statements
• Résumé or Curriculum Vitae
• Letters of Recommendation , and
• A non-refundable  application fee .

See Mathematics for admission requirements and instructions specific to this program.

The Mathematics Department offers a dual-degree with the NYU School of Law: Mathematics PhD/Law JD.

Program Requirements

Written comprehensive examination, oral preliminary examination, dissertation defense, departmental approval.

The program requires the completion of 72 credits. It is possible, with departmental permission, to take courses relevant to students’ course of study in other departments at NYU or at other universities. A minimum of 32 credits must be completed at the Department of Mathematics.

Additional Program Requirements

The examination tests the basic knowledge required for any serious mathematical study; it is comprised of three individual examinations in Advanced Calculus, Complex Variables, and Linear Algebra, and is given on three consecutive days, twice a year, in early September (or, sometimes, late August) and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. Students may take the written examination twice; a third and final time requires the permission of the Director of Graduate Studies.

This examination is usually taken after two years of full-time study. Its purpose is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. Students may take the oral examination twice; a third and final time requires the permission of the Director of Graduate Studies. All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points. It is recommended that students attempt the examinations well before this deadline.

The oral defense is the final examination on the student’s dissertation. The defense is conducted by a panel of five faculty members (including the student’s advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student’s topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.

All Graduate School of Arts & Science doctoral candidates must be approved for graduation by their department for the degree to be awarded.

Sample Plan of Study

Following completion of the required coursework for the PhD, students are expected to maintain active status at New York University by enrolling in a research/writing course or a Maintain Matriculation ( MAINT-GA 4747 ) course.  All non-course requirements must be fulfilled prior to degree conferral, although the specific timing of completion may vary from student-to-student.

Learning Outcomes

Upon successful completion of the program, graduates will have:

• Mastery of the fundamental methods of basic areas in mathematics broadly related to their future research.
• Deep working knowledge of the theories, concepts and open questions in the selected area of research.
• Mastery in written communication sufficient for writing research articles acceptable for publication in peer-reviewed journals.
• Proficiency in oral communication sufficient to give lectures and presentation at scientific conferences and symposiums.
• Lecturing skills which enables them to teach courses in the future in broad areas in mathematics.
• Mastery of the modern tools and classical methods in the selected area of research.
• The ability to formulate sound research programs and bring a research project to fruition in the form of a peer-reviewed publication.

NYU Policies

Graduate school of arts and science policies.

University-wide policies can be found on the New York University Policy pages .

Academic Policies for the Graduate School of Arts and Science can be found on the Academic Policies page . 

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Mathematics PhD Program

Supervising faculty.

• Program Structure

Current Students

• Application

NYU Shanghai, in partnership with the NYU Graduate School of Arts and Science and the NYU Courant Institute of Mathematical Sciences, invites applications from exceptional students for PhD study and research in Mathematics.

Participating students are enrolled in the NYU GSAS Mathematics PhD program, complete their coursework at the NYU Courant Institute in New York, and then transition to full-time residence at NYU Shanghai where they undertake their doctoral research under the supervision of NYU Shanghai faculty.

Highlights of the Program:

• NYU degree upon graduation
• Graduate coursework at the NYU Courant Institute in New York
• Research opportunities with and close mentorship by NYU Shanghai faculty
• Access to the vast intellectual resources of NYU GSAS and NYU Courant Institute
• Cutting-edge research environment at NYU Shanghai, including the NYU-ECNU Institute of Mathematical Sciences, a thriving community of PhD students, post-doctoral fellows, and research associates, activities such as a regular program of seminars and visiting academics, and links with other universities within and outside China
• Financial aid through the NYU Shanghai Doctoral Fellowship , including tuition, fees, and an annual stipend
• Additional benefits exclusive to the NYU Shanghai program, including international health insurance, housing assistance in New York, and travel funds

Jinzi Mac Huang

Applied Mathematics, Fluid Dynamics, Geophysics, Soft Matter Physics

Mathieu Laurière

Computational Methods, Optimal Control, Game Theory, Partial Differential Equations, Stochastic Analysis, Deep Learning, Reinforcement Learning

Vahagn Nersesyan

Stochastic PDEs, Random Dynamical Systems, Control Theory

Alejandro Ramirez

Probability Theory

Pierre Tarres

Probability Theory, Statistics, Statistical Physics

Probability, Mathematical Physics

Zhuo-Cheng Xiao

Data-Driven Modeling, Applied Dynamical Systems, Coarse-Graining, Spiking Neural Networks

Recent Publications by NYU Shanghai Faculty

• Mac Huang, Jinzi, and Nicholas J. Moore. "Morphological attractors in natural convective dissolution." arXiv preprint arXiv:2109.02212 (2021).
• Mac Huang, Jinzi, Michael J. Shelley, and David B. Stein. "A stable and accurate scheme for solving the Stefan problem coupled with natural convection using the Immersed Boundary Smooth Extension method." Journal of Computational Physics 432 (2021): 110162.
• Mac Huang, Jinzi, and Jun Zhang. "Controlling Thermal Convection with Side Heating." arXiv preprint arXiv:2103.04042 (2021).
• Carmona, R., and Laurière, M. Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games: I - the ergodic case. To appear in SIAM Journal on Numerical Analysis (2021)
• Carmona, R., Cooney, D., Graves, C., and Laurière, M. Stochastic Graphon Games: I. The Static Case. To appear in Mathematics of Operations Research (2021)
• Achdou, Y., Laurière, M., and Lions, P.-L. Optimal control of conditioned processes with feedback controls. Journal de Mathématiques Pures et Appliquées (2020)
• Perrin, S., Pérolat, J., Laurière, M., Geist, M., Elie, R., and Pietquin, O. Fictitious play for mean field games: Continuous time analysis and applications. In 34th Conference on Neural Information Processing Systems, NeurIPS 2020 (2020)
• Elie, R., Pérolat, J., Laurière, M., Geist, M., and Pietquin, O. On the convergence of model free learning in mean field games. In 34th AAAI Conference on Artificial Intelligence, AAAI 2020
• V. Jaksic, V. Nersesyan, C.-A. Pillet, A. Shirikyan, Large deviations and entropy production in viscous fluid flows, Arch. Ration. Mech. Anal, 240: 1675-1725, 2021
• V. Nersesyan, Approximate controllability of nonlinear parabolic PDEs in arbitrary space dimension, Math. Control Relat. Fields, 11(2): 1–15, 2021
• V. Nersesyan, A proof of approximate controllability of the 3D Navier-Stokes system via a linear test, SIAM J. Control Optim., 59(4), 2411-2427, 2021
• S. Kuksin, V. Nersesyan, A. Shirikyan, Exponential mixing for a class of dissipative PDEs with bounded degenerate noise, Geom. Funct. Anal., 30(1): 126–187, 2020
• V. Jaksic, V. Nersesyan, C.-A. Pillet, A. Shirikyan, Large deviations from a stationary measure for a class of dissipative PDE’s with random kicks, Comm. Pure Appl. Math., 68(12): 2108–2143, 2015
• Sabot, C., & Tarrès, P. (2021). The*-Vertex-Reinforced Jump Process. arXiv preprint arXiv:2102.08988.
• Bacallado, S., Sabot, C., & Tarrès, P. (2021). The*-Edge-Reinforced Random Walk. arXiv preprint arXiv:2102.08984.
• Merkl, F., Rolles, S. W., & Tarrès, P. (2021, May). Random interlacements for vertex-reinforced jump processes. In Annales de l'Institut Henri Poincaré, Probabilités et Statistiques (Vol. 57, No. 2, pp. 1058-1080). Institut Henri Poincaré.
• Lupu, T., Sabot, C., & Tarrès, P. (2021). Inverting the Ray-Knight identity on the line. Electronic Journal of Probability, 26, 1-25.
• Lupu, T., Sabot, C., & Tarrès, P. (2020). Fine mesh limit of the VRJP in dimension one and Bass–Burdzy flow. Probability Theory and Related Fields, 177(1), 55-90.
• Mac Huang, Jinzi, et al. "Ultra-sharp pinnacles sculpted by natural convective dissolution." Proceedings of the National Academy of Sciences 117.38 (2020): 23339-23344.
• Merkl, F., WW, R. S., & Pierre, T. (2020). Correction to: Convergence of vertex-reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model. Probability Theory and Related Fields, 176(3-4), 1445-1445.
• The Vertex Reinforced Jump Process and a Random Schrödinger operator on finite graph, C. Sabot, P. Tarres * and X. Zeng, Annals of Probability, Volume 45, Number 6A (2017), 3967-3986.
• Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model, C. Sabot and P. Tarres *, Journal of European Mathematical Society, European Mathematical Society (2015), Vol. 17, No. 9, 2353-2378.
• Online learning as stochastic approximation of the regularization paths: optimality and almost-sure convergence, P. Tarres and Y. Yao *, IEEE Transactions in Information Theory (2014), Vol. 60, No. 9, 5716-5735.
• Massless Phases for the Villain model in d ≥ 3, with P. Dario, submitted
• C2 regularity of the surface tension for the ∇ϕ interface model, with S. Armstrong, submitted
• Maximum for Ginzburg-Landau fields, with D. Belius, to appear, Annals of Probability
• Four dimensional loop-erased random walk, with G. Lawler and X. Sun, Annals of Probability 2019, Vol. 47, No. 6
• Critical Percolation and the Minimal Spanning Tree in Slabs, with C. Newman and V. Tassion, Communications on Pure and Applied Math, Volume 70, Issue 11, (2017)
• Zhuo-Cheng Xiao; Kevin K. Lin; Lai-Sang Young; Efficient models of cortical activity via local dynamic equilibria and coarse-grained interactions. Proceedings of the National Academy of Sciences. 2024 Jul 2;121(27):e2320454121.
• Zhuo-Cheng Xiao; Kevin K. Lin; Lai-Sang Young; A data-informed mean-field approach to mapping of cortical parameter landscapes, PLOS Computational Biology, 2021, 17(12): e1009718
• Tianyi Wu; Yuhang Cai; Ruilin Zhang; Zhongyi Wang; Louis Tao; Zhuo-Cheng Xiao; Multiband oscillations emerge from a simple spiking network, Chaos: An interdisciplinary journal of nonlinear science, 2023, 33(4)
• Zhuocheng Xiao; Kevin Lin; Jean-Marc Fellous ; Conjunctive reward–place coding properties of dorsal distal CA1 hippocampus cells, Biological Cybernetics, 2020, 114(2): 285-301
• Zhuo-Cheng Xiao; Kevin K. Lin; Multilevel monte carlo for cortical circuit models, Journal of Computational Neuroscience, 2022, 50: 9-15
• Yuhang Cai; Tianyi Wu; Louis Tao; Zhuo-Cheng Xiao; Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds, Frontiers in Computational Neuroscience, 2021,15

Selected Faculty and Student Features

" Is Modeling the Brain Too Time-Consuming? See How Math Can Help " (Zhuo-Cheng Xiao)

" NYU Shanghai Awards First PhD in Mathematics " (Shuo Qin)

" Dialogue with Pierre Tarrès, Co-Director of the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai " (Pierre Tarres, Mathieu Laurière, Mac Huang, Vahagn Nersesyan, Alejandro Ramírez)

" Three Faculty Members Receive NYU Shanghai Tenure " (Vahagn Nersesyan, Alejandro Ramírez)

" Controlling Heat with Heat: New Approach Proposed to Tame Thermal Convection " (Mac Huang)

" Institute Members Participate in Research Funded by NSFC Major Research Plan " (Mac Huang)

" Math Mini-Course: Introduction to Mean Field Games " (Mathieu Laurière)

" NYU Shanghai Hosts International Forum of Fluid Physics " (Mac Huang)

" NYU Shanghai Professor Identifies Final Shape of Stone Forest Pinnacles " (Mac Huang)

" How Do Stone Forests Get Their Spikes? New Research Offers Pointed Answers " (Mac Huang)

“ NYU Shanghai Launches New Mathematics PhD ” (Pierre Tarres)

" Faculty Spotlight: Pierre Tarres " (Pierre Tarres)

Structure of Program

Participating students complete the PhD degree requirements set by the NYU Courant Institute and in accordance with the academic policies of NYU GSAS. Each student develops an individualized course plan in consultation with the Director of Graduate Study at the NYU Courant Institute and the student’s NYU Shanghai faculty advisor. A typical sequence follows:

Begin program with funded research rotation, up to 3 months preceding first Fall semester, to familiarize with NYU Shanghai and faculty as well as lay a foundation for future doctoral study.

Complete PhD coursework at NYU Courant Institute alongside other NYU PhD students.

Return to Shanghai for second funded research rotation to solidify relationships with NYU Shanghai faculty and make further progress in research.

Under supervision of NYU Shanghai faculty advisor, pursue dissertation research and continue coursework. Depending on each student’s individualized course of study, return visits to New York may also occur. Complete all required examinations and progress evaluations, both oral and written, leading up to submission and defense of doctoral thesis.

To learn more about the NYU Mathematics PhD program degree requirements, please visit this page .

Application Process and Dates

Applications are to be submitted through the NYU GSAS Application portal , within which students should select the Mathematics PhD as their program of interest, and then indicate their preference for NYU Shanghai by marking the appropriate checkbox when prompted. Applicants will be evaluated by a joint admissions committee of New York and Shanghai faculty. Application requirements are set by the NYU Courant Institute and are the same as those for all NYU PhD applicants, no matter their campus preference; however, candidates are recommended to elaborate in their application and personal statements about their specific interests in the NYU Shanghai program and faculty. 

For admission in Fall 2025, the application deadline is January 4, 2025.

Interested students are welcome to contact  Vivien Du , PhD Program Manager, at  [email protected]  with any inquiries or to request more information.

Announcing the loss of Profesor Henry McKean

Sylvia Serfaty Awarded the 2024 Maryam Mirzakhani Prize in Mathematics

Lai-​Sang Young Awarded the 2023 Heinz Hopf Prize

Vlad Vicol Named a 2023 Simons Investigator in Mathematics

Nina Holden Awarded the Rollo Davidson Prize for 2023

Shizhu Liu Wins NYU Golden Dozen Teaching Award

Fang-Hua Lin Receives NSF Research Award

Jinyoung Park Awarded the 2025 Levi L. Conant Prize

Professor Raghu Varadhan Awarded 2023 Padma Vibhusan

NYU Courant Mathematics Department

Gérard Ben Arous Wins NeurIPS Outstanding Paper Award

Jonathan Niles-Weed Wins the SIAG/DATA Early Career Prize

Sad News of the Passing of our Colleague and Friend, Professor Marco Avellaneda 1955 - 2022

Guido DePhilippis named 2021 Simons Investigator. Congratulations!

Jeff Cheeger has been awarded the 2021 Shaw Prize in Mathematical Sciences

Nader Masmoudi Elected to the American Academy of Arts & Sciences.

NYU Courant Mourns the Loss of Professor Andrew J. Majda

NYU Courant Mourns the Loss of Professor Jerry Percus

NYU Courant Mourns the Loss of Professor Louis Nirenberg

Sylvia Serfaty elected to the European Academy of Sciences

Jeff Cheeger to receive an honorary degree from the University of Chicago

Gerard Ben Arous and Lai-Sang Young elected to the National Academy of Sciences.

Eric Vanden-Eijnden named a Vannevar Bush Faculty Fellow

Serfaty, Shelley, and Zeitouni elected to AMACAD

Marsha Berger awarded Norbert Wiener Prize

Jeff Cheeger receives 2019 Steele Prize for Lifetime Achievement

Percy Deift awarded the 2018 Henri Poincare Prize

Congratulations to Sylvia Serfaty on being named a 2018 Simons Investigator!

Sylvain Cappell elected to American Academy of Arts & Sciences

Nader Masmoudi has been awarded the 2017 Fermat Prize

Leslie Greengard Elected to American Academy of Arts & Sciences

Louis Nirenberg awarded the 2015 Abel Prize

News & Announcements

--> lai-sang young awarded the 2024 rolf schock prize in mathematics.

Lai-Sang Young, Professor of Mathematics and Neural Science , has received the 2024 Rolf Schock Prize in Mathematics from the Royal Swedish Academy of Sciences. Read More

--> Eyal Lubetzky Named a 2025 Fellow of the American Mathematical Society

Eyal Lubetzky,  Chair and Professor of Mathematics , has been named a 2025 Fellow of the American Mathematical Society. Read More

--> Percy Deift Invested as a Member of the American Academy of Sciences and Letters

Percy Deift, Silver Professor of Mathematics , has been invested as a Member of the American Academy of Sciences and Letters in recognition of intellectual excellence and courage.  Read More

--> Jinyoung Park Awarded the 2025 Levi L. Conant Prize

Jinyoung Park, Assistant Professor of Mathematics , has received the 2025 Levi L. Conant Prize from the American Mathematical Society.  Read More

--> Announcing the loss of Profesor Henry McKean

It is with profound sadness that we inform you of the passing of our esteemed friend and colleague Henry McKean,  Professor Emeritus of Mathematics . Read More

Upcoming Seminars

Tuesday, november 26, 2024, direct simulation of projection-based thalamocortical connectome reproduces spatiotemporal patterns of sensory-evoked activity, the non-abelian hodge locus, optimal transport metrics on fiber bundles by disintegration, euclidean distortion of quasisymmetrically hilbertian metric spaces, monday, december 2, 2024, tuesday, december 3, 2024, dynamic independent range sampling in 3d, thursday, december 5, 2024, 20-min flash talks, friday, december 6, 2024.

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Online Application for the Graduate School of Arts and Science (GSAS) at New York University

To start a new application:   Click "Start New Application" at the bottom of this screen. To continue an application:   Click "(year) Application" on the left side of the screen below. Submitting your online application, including all required supporting materials, must be completed by no later than the application deadline of the program to which you are applying. This includes not only documents you are required to upload, but also materials that are sent by others such as official test scores and letters of recommendation.  Please refer to the Instructions section of your online application for our complete policies and procedures. You may submit only one application to the Graduate School of Arts and Science (GSAS) for consideration in a given term. If you submit more than one application to GSAS for a term, all applications submitted after the first one will be held and will not be considered for admission. Thus, please determine carefully the one GSAS program to which you will apply.  Applicants are permitted to submit admissions applications to two (or more) programs if they are within different schools at NYU . For example, you may apply to a program in GSAS and to a different program at the Steinhardt School. However, you may not apply to both Computer Science and Economics at the same time because both are within GSAS. If you choose to apply to programs that are in different schools, it will be necessary to complete and submit separate applications and pay each school a separate application fee. The following NYU graduate schools are separate from GSAS: Tandon (Engineering), Tisch (Arts), Vilcek (Medicine), School of Law, Steinhardt (Culture, Education and Human Development), Stern (Business), Public Health, Wagner (Public Service), Silver (Social Work) and Gallatin (Individualized Study).

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Mathematics Education

Phd in teaching and learning concentration.

Prepare to conduct mathematics education research at the elementary, secondary, and postsecondary level.   You will work closely with faculty on all aspects of the research process, including designing a research proposal, honing your methodology, implementing a research agenda, and disseminating findings.

What You'll Learn

• Strategies for designing and analyzing research studies in mathematics education
• Qualitative and quantitative research methods 
• Current issues in mathematics pedagogy, teacher education, curriculum, and integration of educational technology 

How You'll Learn

Pedagogy and content courses.

As a student in this doctoral program, you will take a series of courses focused on issues of teaching and learning and complete mathematics courses appropriate to the level of interest (elementary, secondary, post-secondary) in your research. If you're interested in doing work at the secondary or above level, you will take mathematics courses in the mathematics department.

Research Methods Courses

Take courses designed to prepare you for all aspects of the research process. You will gain mastery of a wide range of qualitative and quantitative research methods in mathematics education, then work closely with faculty members to develop your own research interests and a research proposal. 

Exceptional Faculty Resources

Mathematics Education faculty work closely with College of Arts and Sciences faculty in NYU's  Courant Institute for Mathematical Sciences . These collaborations provide you with opportunities to draw on content knowledge and pedagogical expertise from a diverse range of sources.

You'll graduate prepared to work as a researcher or teacher educator in mathematics education in colleges and universities. You'll also have the skills needed to excel as a mathematics education specialist or consultant in government organizations and multinational corporations.

Jasmine Y. Ma

Associate professor.

• Admissions and Financial Support
• Degree Requirements

PhD Program Overview

Our center offers an interdisciplinary PhD in Atmosphere Ocean Science and Mathematics (AOSM) . The program shares many exciting features with the PhD in Mathematics . Our goal is to train mathematically talented students both in the tools of modern applied mathematics and disciplinary atmosphere-ocean science. By drawing students from new pools of talent, our program seeks to be a significant channel for the recruitment and training of excellent students into the important and highly interdisciplinary fields of atmosphere, ocean, and climate science. We are committed to the education and training of our graduate students.

The Courant Institute at New York University  has a world-leading reputation in applied mathematics and scientific computation and the placement of the Center within the Courant Institute provides a unique platform for interdisciplinary research. Our students greatly benefit from being part of the broader NYU community, and the NYC area.

NYU Graduate Admissions

A graduate education brings the work you did as an undergrad to the next level and provides you with the opportunity to focus on the topics and ideas that you care about most. Expectations increase in graduate school. So do the chances to strengthen the skills and expertise that will help you cement yourself as a thought leader and innovator in your chosen field. When you pursue a graduate degree at New York University, you are part of a diverse, dynamic, dedicated community that pushes you every step of the way and supports you at every turn—in a city where resources and opportunities are second to none.

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