yale math phd admissions

Welcome to the Yale Graduate School of Arts and Sciences!  We’re glad you’ve come to our website. If you’re new to Yale, here’s some basic information to help you get started. The Graduate School of Arts and Sciences (GSAS) is one unit within a large, complex, and historic university. In addition to the Graduate School, Yale has an undergraduate school (Yale College) and 13 professional schools that award post-baccalaureate degrees in law, medicine, business, drama, art, architecture, music, nursing, etc. Each school at Yale has its own policies, requirements, and admissions practices. Each grants specific degrees. GSAS is the school that prepares scholars and scientists for careers in research, teaching, and leadership. Note that all programs at the Graduate School of Arts and Sciences have a residency requirement. GSAS does not offer any online degrees. GSAS is home to more than 50 academic departments and programs. The full list of our degrees and programs can be found on the Programs & Departments page. Make sure the program and degree you are interested in is listed there.  If you don’t find what you are looking for on our site, check out Yale’s professional schools . If you are looking for an undergraduate degree, Yale College is the place to apply.

PhD and Master’s Degree Applicants

If you are interested in applying for admission to a PhD or Master’s degree program at GSAS, these web pages will be very useful: 

• PhD/Masters Application Process
• Why Choose Yale Graduate School?
• Tuition, Funding, & Living Costs
• Dates & Deadlines
• Standardized Testing Requirements
• Application Fees & Fee Waiver
• Guidance for International Students

Non-Degree Applicants

In some cases, it is possible to enroll at the Graduate School as a non-degree student. Non-degree students receive a transcript and many of the benefits of being a Yale student, but do not earn a degree upon completion of their enrollment.  We offer three types of non-degree program:

• The Exchange Scholar Program : to be eligible for this program, you must be enrolled at an institution that has a formal exchange program with Yale. Exchange Scholars may enroll in courses or participate in research at Yale. 
• The Visiting Assistant in Research (VAR) Program : if you are an advanced graduate student currently enrolled at another institution and wish to pursue full-time dissertation research at Yale, you may qualify for the VAR program. VARs are not eligible to enroll in courses. 
• The Visiting Student Program : if you have a bachelor’s degree, you may apply to take courses at Yale with the permission of the program.  

Information for All Applicants

• Our application process is entirely online. Your application and all supporting materials, including letters of recommendation, must be submitted online through the application platform. Please do not mail or email any materials to us. 
• Once you initiate an application, your Application Status Portal will keep track of the materials you send, including test scores and recommendations, and will post the admissions decision when it is ready. 
• A complete list of admissions policies and procedures can be found in the Graduate School’s Programs & Policies Bulletin .

We are happy to assist you with your application. If you have questions, please contact us . To ensure that your question is answered as quickly as possible, please note the following: 

• Transactional questions: If your query is about the application process (i.e., the receipt of test scores, a change of name/address, technical problems with the application, etc.), please contact the Graduate School admissions staff at Graduate Admissions . 
• Program-specific questions: Each program evaluates applications differently and independently. If your query is specific to the academic program for which you are applying, please consult their website, where you may find the information you seek. If you still have questions, feel free to contact the director of graduate studies (DGS) or the registrar of the program. They will be able to help you.

Department of Statistics and Data Science

Ph.d. admissions.

The Ph.D. program admits only a small number of new students each year.  We received more than 300 applications for the Fall 2024 cohort; in general, we hope to make 15-18 offers and obtain an entering class of about six to eight students.

All applications for this program should be submitted directly to the Yale Graduate School Office of Admissions through the online application page.

Application requirements and guidelines

Scores from the GRE General Test are now optional.  A GRE Subject Test is also optional, although the Mathematics Subject Test is not recommended for students whose undergraduate major was not Mathematics. 

All applicants should have a strong mathematical background, including advanced calculus, linear algebra, elementary probability theory, and at least one course providing an introduction to mathematical statistics. An undergraduate major may be in statistics, mathematics, computer science, or in a subject in which significant statistical problems may arise.

For those whose native language is not English, the Test of English as a Foreign Language (TOEFL) scores are required. A strong command of English is essential for success at Yale.  This requirement is waived only for applicants who, prior to matriculation at Yale, will have received a baccalaureate degree or its international equivalent with three years of residency from a college or university where English is the primary language of instruction.

The offer of admission typically includes full tuition ($48,300 in 2023-24) and a generous stipend (roughly $40,300 for 2023-24) for five years.  Consult the Graduate School’s financial assistance page (UPDATE NEEDED) for additional detail on living costs and funding.

For incoming students whose TOEFL scores fall below the level required to satisfy the Graduate School’s Oral English Proficiency Standard, the Graduate School provides a stipend for support during a three week Immersive English Program , held late in summer on the Yale campus.

Tuition and Living Costs  (UPDATE NEEDED)

Yale Statistics Ph.D. Program

The Department offers a broad training program comprised of the main areas of statisical theory (with emphasis on foundations, Bayes theory, decision theory, nonparametric statistics), probability theory (stochastic processes, asymptotics, weak convergence), information theory, econometrics, classification, statistical computing, and graphical methods.

With this background, graduates of the program have found excellent positions in universities, industry, and government. Recent graduates have accepted appointments at the Duke University, University of California at Santa Barbara, The City University of New York, Yale University, Bristol-Meyers Squibb, RAND, Federal Reserve Board, New York University, Trinity University, Iowa State University, Merck, and Tulane University.

All applications for this program should be submitted directly to the Yale Graduate School Office of Admissions through the online application page.

• Application requirements and guidelines
• GRE scores for the General Test and for the Subject Test (usually in Mathematics, sometimes in the area of the undergraduate major) should accompany an application.
• All applicants should have a strong mathematical background, including advanced calculus, linear algebra, elementary probability theory, and at least one course providing an introduction to mathematical statistics. An undergraduate major may be in statistics, mathematics, computer science, or in a subject in which significant statistical problems may arise.
• For those whose native language is not English, the Test of English as a Foreign Language (TOEFL) scores are required.
• The Ph.D. program admits only a small number of new students each year. Only 6 initial offers (for a pool of 73 applications) were made for admission in fall 2010.
• The offer of admission typically includes full tuition and a stipend. Consult the Graduate School's financial assistance page for details.
• Tuition and Living Costs

Course of Study

• Fourteen courses are required before students can be admitted to candidacy after the second year. Usually students take four courses in each semester of the first year and three courses in each semester of the second year.
• Ph.D. students are strongly advised to take the courses highlighted in RED , which are taught every year, even if they involve some review of material taken in undergraduate courses. Substitutions are possible with the permission of the DGS.
• The theory qualifying exam is usually based on a combination of advanced undergraduate material (as covered in Stat 241, 242, and 251/551) and graduate material at the level of Stat 600, 610, and 612.
• For the practical qualifying exam, students are expected to be comfortable with R, and have had experience at working with real data. Most students gain that experience from a combination of Stat 661, 625 and participation in the statistical consulting clinic (Stat 627).

Normally during the first two years, fourteen term courses in this and other departments are taken to prepare students for research and practice of statistics. These include courses devoted to case studies and practical work, for which students prepare a written report and give an oral presentation. Specific course requirements .

There is no foreign language requirement.

The SPEAK test

For further details consult that web site.

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Teaching requirements

Qualifying examinations.

• Practical Exam: a written report on an analysis of a data set. Held during a five day period in December, following the end of classes.
• Theory Exam: a written paper on theoretical statistics. A one-day exam (9:00 am -- 4:00 pm) held in early January.
• Oral Exam: held shortly after completion of the Theory Exam.
• A typical theory exam . [Look at http://www.stat.yale.edu/dept-private/Exams/ for copies of other old exams.Yale login required].
• Well prepared students sometimes take one of the Practical or Theory Exams in their first year. No record is kept of an unsuccesful attempt.
• Students who do not pass the exams during January/December of their second year have the option of a retake at the end of the spring semester.

Prospectus and Dissertation

Dissertation research in collaboration with one member of the faculty is begun during the third year. A prospectus for the dissertation should be submitted no later than the first week of March in the third year. The prospectus must be accepted by the department before the end of the third year.

Upon successful completion of the qualifying examination and the prospectus (as well as meeting the Graduate School Honors requirements), the student is admitted to candidacy. Most students complete the dissertation in the fifth year.

Please see our Alumni page for a sampling of recent Dissertation topics.

Dissertation fellowships

Further information.

Consult the Graduate School's Programs and Policies for general information about Ph.D. study at Yale.

Applied Mathematics Program

Master’s requirements.

Students who withdraw from the Ph.D. program may be eligible for the M.S. degree if they have completed ten graduate-level term courses, maintained a High Pass average, and met the Graduate School’s Honors requirement for the Ph.D. program. Students who are eligible for or who have already received the M.Phil. will not be awarded the M.S.

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Yale University

Admissions Snapshot

19% First-generation students in Class of 2024

53 Countries represented by members of the Class of 2024

6.6% Rate of admissions, Class of 2024

$55,100 Average grant of undergraduate financial aid

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You can earn undergraduate degrees at Yale College, master’s or doctoral degrees at the Graduate School of Arts & Sciences, and specialized degrees at our 13 professional schools. There are also many non-degree programs that allow individuals to study or pursue research without matriculating. Apply directly to the school or program where you wish to enroll.

Yale is committed to ensuring that qualified students are admitted without regard to their financial circumstances, and that they graduate without excessive debt.

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Admissions: Applying to the MD-PhD Program

We seek applicants who are committed to pursuing a career as a physician-scientists. We value students who are curious, creative, compassionate, and resilient, and bring a diverse range of personal experiences, viewpoints, and academic interests to our collaborative and innovative community.

Candidates must submit their application to the Yale School of Medicine which includes the AMCAS and the Yale Secondary Applications and indicate their interest in being considered for the MD-PhD Program. All applications are holistically reviewed to find candidates whose academic and personal experiences indicate exceptional potential and a commitment to pursue MD and PhD training at Yale. Among the things we look for in a candidate's application are:

• Significant research experience(s) with evidence of increasing independence, responsibility, and depth of contributions
• Outstanding letters of recommendation, including those from research mentors who can reflect upon your potential for success as a physician-scientist
• Personal statements that allow us to understand your reasons for training as a physician-scientist
• Activities that reflect your curiosity, compassion, maturity, leadership, grit
• Broad academic excellence, not reflected solely in MCAT scores or GPA

Admissions Timeline

Invitations for interview will be sent via email from September to January. All interviews are virtual and will be scheduled over a two-day period. Candidates have interviews with members of both the MD and MD-PhD Interviewing subcommittees, non-evaluative meetings with MD-PhD program faculty and students, and informational sessions with the program director and current students. Social events and student buddies will help you learn more about the MD-PhD community at Yale and about living in New Haven. As part of the invitation to interview, we will provide a survey link that allows you to request informal meetings with up to five Yale faculty whose research is of interest to you. These informal discussions are not part of the admissions evaluation but are made available to you so that you can get a more complete picture of what Yale has to offer. Applicants who are not invited to interview for the MD-PhD Program will be offered the option to have their application considered for MD-only admission.

Special Instructions for Applicants Interested in “non-traditional” PhD programs

MD-PhD applicants who plan to pursue their PhD in Anthropology, Economics, History of Science & Medicine, Philosophy, Religious Studies or Sociology must submit applications to both the MD-PhD program and to the PhD program. (A link to the PhD program application will be sent to such students when their complete MD-PhD program application is received.) Interview invitations will be made after both applications have been reviewed. Materials required to support the PhD program application are detailed below. Students interested in these programs are encouraged to contact the MD-PhD program to indicate their interest and to obtain the most up-to-date information about specific PhD program requirements. Please note: the completed MD-PhD application must be received by October 15th and the PhD application completed by November 1st to allow full review and consideration for interview.

Requested additional materials:

• Anthropology
• History of Science and Medicine
• Religious Studies
• Please upload a current resume/CV.
• Applicants to Economics (Only) – GRE Test Scores required

Important information to keep in mind:

• The " personal statement of academic purpose " is carefully evaluated by PhD program faculty; when requested, it should be prepared with this audience in mind. This document should be a succinct statement of 500-1,000 words explaining why you are applying to Yale for graduate study, describing your past research, your preparation for the intended field of study, your academic plans for graduate study at Yale (e.g. your proposed research project), and your subsequent career objectives. Explain how the faculty, research, and resources at Yale would contribute to your future goals.
• You may submit a letter of recommendation from the same individual as part of both the AMCAS and GSAS applications; we encourage you to ask the recommenders most capable of speaking to your preparation for the PhD program of study to submit their letters to both AMCAS and GSAS. Once you identify a recommender in the GSAS Admissions Portal, they will receive an email providing instructions and access information.
• No application fee to GSAS will be required to submit these additional materials.
• The MCAT will be accepted in lieu of the GRE except for candidates to Economics.

Gap years are not necessary for applicants . Nationally, >75% of MD-PhD students have taken at least one gap year after college 1 . Gap years can help applicants gain research or clinical experience necessary for deciding whether dual-degree training is right for them. Or they can provide time to travel, work, or take the MCAT and apply. But gap years per se are not necessary to be admitted to MD-PhD programs! The distribution of gap years taken by Yale MD-PhD applicants, interviewed or accepted candidates, and matriculated students for 2019-2023 shows a median “gap” of 2 years for interviewed, accepted, and matriculated applicants But 18% of our current students joined the program immediately after graduating from college.

Diversity and inclusion are central to our mission; our goal is to train students with a wide range of backgrounds, personal identities, and research interests to become physician-scientists. MD-PhD students who matriculated in the past five years completed their undergraduate degrees at accredited four-year institutions all over the United States and territories, and include students who have attended community colleges, historically black colleges and universities (HBCUs) and small, non-research-intensive colleges. Demographics of current students, as self-identified in their AMCAS medical school applications, are shown below. We encourage individuals with disabilities or who may be from economically, socially, culturally and/or educationally disadvantaged backgrounds to apply to our Program. Yale is committed to providing an accessible and inclusive environment to individuals with disabilities by ensuring that appropriate academic and technical accommodations are available to students. Please contact the MD-PhD Office and Student Accessibility Services for further information. U.S. citizens, permanent residents, refugees, asylees, DACA recipients and international students are all eligible to apply for admission to the MD-PhD Program.

1 Brass LF, Fitzsimonds RM, Akabas MH. Gaps between college and starting an MD-PhD program are adding years to physician-scientist training time. JCI Insight. 2021;e156168 [ PMC free article ] [ PubMed ] [ Google Scholar ]

Yale's MD-PhD Program grants full consideration to students who plan to pursue a PhD program in departments that are part of the Biological and Biomedical Sciences (BBS) , the School of Public Health (YSPH) , School of Engineering and Applied Sciences (SEAS) , and some departments of the Graduate School of Arts and Sciences (GSAS ). Please click on the links for more information on specific PhD programs. Current students are pursuing their PhD training in the following programs and departments.

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Bringing an investigator’s eye to complex social challenges

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Anna Russo likes puzzles. They require patience, organization, and a view of the big picture. She brings an investigator’s eye to big institutional and societal challenges whose solutions can have wide-ranging, long-term impacts.

Russo’s path to MIT began with questions. She didn’t have the whole picture yet. “I had no idea what I wanted to do with my life,” says Russo, who is completing her PhD in economics in 2024. “I was good at math and science and thought I wanted to be a doctor.”

While completing her undergraduate studies at Yale University, where she double majored in economics and applied math, Russo discovered a passion for problem-solving, where she could apply an analytical lens to answering the kinds of thorny questions whose solutions could improve policy. “Empirical research is fun and exciting,” Russo says.

After Yale, Russo considered what to do next. She worked as a full-time research assistant with MIT economist Amy Finkelstein . Russo’s work with Finkelstein led her toward identifying, studying, and developing answers to complex questions. 

“My research combines ideas from two fields of economic inquiry — public finance and industrial organization — and applies them to questions about the design of environmental and health care policy,” Russo says. “I like the way economists think analytically about social problems.”

Narrowing her focus

Studying with and being advised by renowned economists as both an undergraduate and a doctoral student helped Russo narrow her research focus, fitting more pieces into the puzzle. “What drew me to MIT was its investment in its graduate students,” Russo says.

Economic research meant digging into policy questions, identifying market failures, and proposing solutions. Doctoral study allowed Russo to assemble data to rigorously follow each line of inquiry.

“Doctoral study means you get to write about something you’re really interested in,” Russo notes. This led her to study policy responses to climate change adaptation and mitigation. 

“In my first year, I worked on a project exploring the notion that floodplain regulation design doesn’t do a good job of incentivizing the right level of development in flood-prone areas,” she says. “How can economists help governments convince people to act in society’s best interest?”

It’s important to understand institutional details, Russo adds, which can help investigators identify and implement solutions. 

“Feedback, advice, and support from faculty were crucial as I grew as a researcher at MIT,” she says. Beyond her two main MIT advisors, Finkelstein and economist Nikhil Agarwal — educators she describes as “phenomenal, dedicated advisors and mentors” — Russo interacted regularly with faculty across the department. 

Russo later discovered another challenge she hoped to solve: inefficiencies in conservation and carbon offset programs. She set her sights on the United States Department of Agriculture’s Conservation Reserve Program because she believes it and programs like it can be improved. 

The CRP is a land conservation plan administered by USDA’s Farm Service Agency. In exchange for a yearly rental payment, farmers enrolled in the program agree to remove environmentally sensitive land from agricultural production and plant species that will improve environmental health and quality.

“I think we can tweak the program’s design to improve cost-effectiveness,” Russo says. “There’s a trove of data available.” The data include information like auction participants’ bids in response to well-specified auction rules, which Russo links to satellite data measuring land use outcomes. Understanding how landowners bid in CRP auctions can help identify and improve the program’s function. 

“We may be able to improve targeting and achieve more cost-effective conservation by adjusting the CRP’s scoring system,” Russo argues. Opportunities may exist to scale the incremental changes under study for other conservation programs and carbon offset markets more generally.  

Economics, Russo believes, can help us conceptualize problems and recommend effective alternative solutions.

The next puzzle

Russo wants to find her next challenge while continuing her research. She plans to continue her work as a junior fellow at the Harvard Society of Fellows, after which she’ll join the Harvard Department of Economics as an assistant professor. Russo also plans to continue helping other budding economists since she believes in the importance of supporting other students.   

Russo’s advisors are some of her biggest supporters. 

Finklestein emphasizes Russo’s curiosity, enthusiasm, and energy as key drivers in her success. “Her genuine curiosity and interest in getting to the bottom of a problem with the data — with an econometric analysis, with a modeling issue — is the best antidote for [the stress that can be associated with research],” Finklestein says. “It's a key ingredient in her ability to produce important and credible work.”

“She's also incredibly generous with her time and advice,” Finklestein continues, “whether it's helping an undergraduate research assistant with her senior thesis, or helping an advisor such as myself navigate a data access process she's previously been through.”

“Instead of an advisor-advisee relationship, working with her on a thesis felt more like a collaboration between equals,” Agarwal adds. “[She] has the maturity and smarts to produce pathbreaking research.

“Doctoral study is an opportunity for students to find their paths collaboratively,” Russo says. “If I can help someone else solve a small piece of their puzzle, that’s a huge positive. Research is a series of many, many small steps forward.” 

Identifying important causes for further investigation and study will always be important to Russo. “I also want to dig into some other market that’s not working well and figure out how to make it better,” she says. “Right now I’m really excited about understanding California wildfire mitigation.” 

Puzzles are made to be solved, after all.

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Microlocal sheaves and affine Springer fibers

The resolutions of Slodowy slices $\widetilde{\mathcal{S}}_e$ are symplectic varieties that contain the Springer fiber $(G/B)_e$ as a Lagrangian subvariety.In joint work with R. Bezrukavnikov, M. McBreen and Z. Yun, we construct analogues of these spaces for homogeneous affine Springer fibers. We further understand the categories of microlocal sheaves in these symplectic spaces supported on the affine Springer fiber as some categories of coherent sheaves.In this talk I will mostly focus on the case of the homogeneous element $ts$ for $s$ a regular semisimple element and will discuss some relations of these categories with the small quantum group providing a categorification of joint work with R.Bezrukavnikov, P. Shan and E. Vasserot.If I have time I will then mention some recent application of this result to the Breuil-Mezard conjecture by T. Feng and B. Le Hung.