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Doctor of philosophy (phd), general information.

The term in which you plan to defend, submit your dissertation, and graduate, you must be registered for Thesis (4.THG - 36 units). Your dissertation defense takes place in the presence of your full Dissertation Committee consisting of at least three members including your dissertation supervisor.

Upon satisfactory defense and submission of the dissertation, the supervisor will assign a grade. ("SA" is the final satisfactory grade for PhD.) The grade will not be submitted to the Registrar until the final approved dissertation document is submitted to the department portal by the thesis deadline provided on the departmental thesis deadlines calendar. For help with formatting of your full document, see the Formatting, Specifications & Thesis Submission page for more information.

You are responsible for working directly with your dissertation committee and area administrators to schedule your defense. The defense must not be scheduled for any later than two weeks prior to the thesis submission deadline. Each area may handle the logistics differently, so it is important to touch base with your group early in the defense planning process. For example, many faculty are not available during winter holidays or summer session, and may wish to schedule the defense early in December for a February degree.

Registration Deadline:

• Register for 36 units of   4.THG
• Degree list: Put yourself on the upcoming degree list by applying for a degree .
• Be mindful of the Institute deadline to change your thesis title in WebSIS
• Register your final thesis title: You must return to the online site of your application and add or make a change to your thesis title by this deadline. The title on your final thesis must be an exact match of the one you submit on your Application for Degree. If you add your title after this date, you will be charged a late fee.

One Week Prior to Institute Thesis Deadline:

• Be sure to provide your exact spelling of your name (either legal name or preferred name — whichever you have provided to your degree administrator) when submitting your thesis book to the portal. Using a different name will result in a submission error.
• Max file size: 10MB or less. If file is too large, a submission error will result.

Institute Thesis Deadline:

• All final edits and adjustments to the final dissertation book must be submitted to the department on or before this deadline. Final grade submission by your advisor also must be submitted on or before this deadline. 

One Week After Institute Thesis Deadline:

• Last day to come off the degree list (contact Tessa Haynes )
• Degree conferral date (see Academic Calendar or Department Thesis Deadlines)

Specific Deadlines & Procedure

February 2022 theses deadlines, friday, september 10, 2021.

• Registration Deadline: Fall term registration (4.THG) (Pre-registration for fall deadline is June 17, 2021.
• Degree list: Put yourself on the February degree list by applying for a degree .

Friday, December 10, 2021

• Register your final thesis title: You must return to the online site of your application and add or make a change to your thesis title by this deadline. The title on your final dissertation must be an exact match of the one you submit on your Application for Degree. If you add your title after this date, you will be charged a late fee; but you may still update your thesis title until the actual submission date.

Monday, December 31, 2021

• If you are having difficulty when logged into Office 365 or Sharepoint under a different log in, try clearing your cache on your browser so that you can log in to the form with your MIT Kerberos account.

May 2024 Theses Deadlines

Friday, february 9, 2024.

• Registration Deadline: Fall term registration (4.THG) (Pre-registration for spring deadline is January 19, 2024.
• Degree list: Put yourself on the May degree list by applying for a degree .

Friday, April 12, 2024

Monday, april 29, 2024.

• Your final dissertation book is due by 9am on Monday, April 29 to the Department Thesis Submission Tool ( choose "Single Sign On" and log in with your MIT email address ) for formatting review. This is for the purpose of making certain the document is in compliance with MIT archive requirements. You will be contacted quickly if adjustments are needed. Your signed signature page must also be submitted at this time.

Friday, May 3, 2024

• Final, corrected, approved, electronic version uploaded to the Department Thesis Submission Tool ( choose "Single Sign On" and log in with your MIT email address )

Formatting, Specifications & Thesis Submission

Important : Consult the Formatting, Specifications and Thesis Submission information page for advice and templates on how to format your book. Please pay particular attention to the templates for the frontmatter (Title Page, Committee Page, Abstract, and Table of Contents.) Following the templates now means fewer edits to make later!

PhD Thesis Contacts

• Program Director: Leslie K. Norford
• Director of Computation PhD: George Stiny
• Director of Building Technology PhD: Christoph Reinhart
• Director of HTC PhD: Timothy Hyde
• PhD degree administrator and thesis submission: Tessa Haynes

Curriculum and Thesis

In their first and second years, PhD students are required to complete a series of core classes, coursework in their major and minor fields of study, and an advanced research methods course before proceeding to the thesis-writing stage.

Core courses

Students must satisfy the requirements in at least 10 of 12 half-semester first-year core courses (14.384 and 14.385 are considered second-year courses). The requirements can be met by earning a grade of B or better in the class or by passing a waiver exam.

Waiver exams are offered at the start of the semester in which the course is offered and graded on a pass-fail basis. Students who receive a grade of B- or below in a class can consult the course faculty to determine whether to take the waiver exam or re-take the course the following year. These requirements must all be satisfied before the end of the second year.

Course list

• 14.121: Microeconomic Theory I
• 14.122: Microeconomic Theory II
• 14.123: Microeconomic Theory III
• 14.124: Microeconomic Theory IV
• 14.380: Statistical Methods in Economics
• 14.381: Estimation and Inference for Linear Causal and Structural Models
• 14.382*: Econometrics
• 14.384*: Time Series Analysis (2nd year course)
• 14.385*: Nonlinear Econometric Analysis (2nd year course)
• 14.451: Dynamic Optimization Methods with Applications
• 14.452: Economic Growth
• 14.453: Economic Fluctuations
• 14.454: Economic Crises

*Courses 14.382, 14.384, and 14.385 are each counted as two half-semester courses.

Most students will also take one or more field courses (depending on whether they are waiving core courses) during their first year. Feel free to ask your graduate research officer, field faculty, and advanced students for advice on how you structure your first-year coursework.

Second year students must also successfully complete the two-semester course 14.192: Advanced Research Methods and Communication. The course, which is graded on a pass-fail basis, guides students through the process of writing and presenting the required second-year research paper.

Major field requirement

By the end of year two, PhD students must complete the requirements for two major fields in economics. This entails earning a B or better in two designated courses for each field. Some fields recommend additional coursework or papers for students intending to pursue research in the field.

Major fields must be declared by the Monday following the spring break of your second year. Your graduate registration officer must approve your field selections.

Minor field requirement

PhD students are also required to complete two minor fields, taking two courses in each field and earning a grade of B or better. Your graduate registration officer must approve your field selections.

Minor coursework is normally completed by the end of year two, but in some cases students can defer the completion of one field until after general exams. Students must consult with their graduate registration officer before making a deferment.

Options for minor fields include the eleven economics major fields, plus computation and statistics (from the interdisciplinary PhD in Economics and Statistics).

Students who wish to satisfy one of the minor field requirements by combining two courses from different fields–for example, environmental economics and industrial organization II–can petition the second-year graduate registration officer for permission.

At least one minor field should be from the department’s standard field list.

The fields in which the Department offers specialization and the subjects that will satisfy their designation as a minor field are given in the chart below. Some fields overlap so substantially that both cannot be taken by a student. In any event, the same subject cannot be counted towards more than a single minor field. Students must receive the approval of their Graduate Registration Officer for their designated major and minor fields.

List of fields

• Development
• Econometrics
• Industrial organization
• International
• Macroeconomics
• Organizational
• Political economy
• Public finance
• Computation and statistics (minor only)

Subjects satisfying major and minor requirements

Advanced economic theory.

Minor: Any subset adding up to two full semesters from 14.125, 14.126, 14.127, 14.130, 14.137, 14.147, 14.160, 14.281 and Harvard Ec 2059. Major: At least two of 14.125, 14.126, 14.281, and Harvard Ec 2059. Recommended for major: 14.126, 14.281, and at least one of 14.125, 14.127, 14.130, 14.147, and Harvard Ec 2059.

Econometrics and Statistics

Minor: 14.382 in addition to one of 14.384 or 14.385. Major: Any one of 14.386, 14.387, 14.388 in addition to one of 14.384 or 14.385. Recommended for major: 14.384 and 14.385. *Dual PhD in Economics and Statistics has an additional requirement of 14.386.

Economic Development

Major and minor: 14.771 and 14.772 or 14.773

Minor: Any two of 14.416J, 14.440J, 14.441J, 14.442J, 14.448. Major: 14.416J and 14.441J

Industrial Organization

Minor: 14.271 and 14.272 or 14.273. Major: 14.271 and 14.272 or 14.273. Recommended for major: 14.271, 14.272, and 14.273.

International Economics

Major and minor: 14.581 and 14.582

Labor Economics

Major: 14.661 and 14.662A. Minor: Two subjects chosen from 14.193, 14.661, and 14.662

Monetary Economics

Major and minor: Two subjects chosen from 14.461, 14.462, and 14.463

Organizational Economics

Major and minor: 14.282 and one of 14.283-284, 14.441J, or an approved substitute

Political Economy

Major and minor: 14.770 and 14.773

Public Economics

Major and minor: 14.471 and 14.472

General exams

MIT requires doctoral candidates to complete an advanced course of study that includes general exams at its completion. Beginning in 2019-20, the Economics Department will operationalize this requirement to include successful completion of: the core and other required courses; course exams and other requirements of courses in each of a student’s two major and two minor fields; the written research paper and oral presentation components of 14.192. Students may present for the general exams while having one remaining minor field to complete. The faculty will review these components together with the candidate’s overall course record to determine whether students have passed the general exam requirement and can proceed to the thesis writing stage.

Typical course schedule

Math Camp begins on the second Monday in August.

Fall Semester

14.121/14.122 (Micro Theory I/II) 14.451/14.452 (Macro Theory I/II) 14.380/14.381 (Statistical Method in Economics & Applied Econometrics) Field Course (major or minor)

Spring Semester

14.123/14.124 (Micro Theory III/IV) 14.453/14.454 (Macro Theory III/IV) 14.382 (Econometrics) Field Course (major or minor)

2-3 Field Courses 14.192 (Advanced Research and Communication) 14.384  or  14.385 (Advanced Econometrics)

3 Field Courses 14.192 (Advanced Research and Communication)

Years 3 and up

Field workshop Field lunch Thesis writing

Upon satisfying the core and field requirements, PhD candidates embark on original research culminating in a completed dissertation. A PhD thesis normally consists of three research papers of publishable quality. The thesis must be approved by a student’s primary and secondary thesis advisors, and by an anonymous third reader. These three faculty members will be the candidate's thesis committee and are responsible for its acceptance. Collaborative work is acceptable and encouraged, but there must be at least one paper in the dissertation without a co-author who was a faculty member when the research started.

Criteria for satisfactory progress

Third-year students.

• Meet regularly with their advisor
• Participate consistently in their primary field advising lunch, their primary field workshop, and the third-year student research lunch
• Complete their third-year paper
• Participate in third-year meetings organized by the thesis graduate research officer

Students should present on their research in progress at least once in both the third-year student research lunches and their field advising lunch. Presentations provide opportunities for early and broad feedback on research ideas and the chance to develop oral presentation skills. Research ideas or early stage work in progress is encouraged and expected.

Fourth-year and later students

• Participate consistently in their primary field advising lunch and their primary field workshop
• Present at least once per year in their field advising lunch or field workshop. A presentation each semester in the field advising lunch is strongly recommended by most fields; consult your advisors for more information

Satisfactory progress toward a dissertation will be evaluated based on progress assessments by the student’s primary advisor, regular participation in the lunches and workshops, and field lunch or workshop presentations that show continued progress.

The thesis comprises an original investigation, including a written document on a subject approved by a departmental or interdepartmental graduate committee prior to the beginning of the research. Thesis credit cannot be granted for work done prior to registration as a graduate student at the Institute, nor for work initiated without prior approval by the department of registration. The thesis must be completed while in residence, except as noted below.

A thesis may not be presented on research work done at the Institute while on academic, administrative, research staff appointment, or hourly payroll at MIT (including Lincoln Laboratory), the Charles Stark Draper Laboratory, or other affiliated research entities. Supervision by a faculty member of the Institute or a staff member approved by the department is a fixed requirement for doctoral, engineer’s, and master’s theses. Preliminary plans for pursuing an approved thesis may be required by thesis advisors according to the requirements and time schedules of the departments. A thesis advisor may, at his or her discretion, require progress reports in oral or written form as deemed necessary. Before the final written document is submitted, a draft may be required for editorial comment. An oral examination of the doctoral thesis will be held after the thesis has been submitted. The thesis process is not complete until the thesis document is signed, and therefore accepted formally, by the department.

Nonresident doctoral thesis research status

Details and expectations for non-residential doctoral students. Students must have passed the qualifying examination to be eligible to request this status.

Holds and restrictions on thesis publication

Information on thesis hold requests related to patent protection, pursuit of business opportunities, government restrictions, privacy and security, and book publication

Copyright and intellectual property policy

Information on the Institute’s policy concerning ownership of copyrights and rights to intellectual property

Preparation of graduate theses

Information for preparing a thesis

Joint theses

Details and expectations for collaborative research

Thesis research in absentia

Details and expectations for students conducting research off-campus. Students in both master’s and doctoral programs, at any stage in their studies, are eligible to request this status.

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Graduate Program

Pushing the Scholarly Frontier

PhD in Political Science

Our doctoral students are advancing political science as a discipline. They explore the empirical phenomena that produce new scholarly insights—insights that improve the way governments and societies function. As a result, MIT Political Science graduates are sought after for top teaching and research positions in the U.S. and abroad. Read where program alumni are working around the world.

How the PhD program works

The MIT PhD in Political Science requires preparation in two of these major fields:

• American Politics
• Comparative Politics
• International Relations
• Models and Methods
• Political Economy
• Security Studies

We recommend that you take a broad array of courses across your two major fields. In some cases, a single course may overlap across the subject matter of both fields. You may not use more than one such course to "double count" for the course distribution requirement. Keep in mind that specific fields may have additional requirements.

You are free to take subjects in other departments across the Institute. Cross-registration arrangements also permit enrollment in subjects taught in the Graduate School of Arts and Sciences at Harvard University and in some of Harvard's other graduate schools.

Requirements

1. number of subjects.

You will need two full academic years of work to prepare for the general examinations and to meet other pre-dissertation requirements. Typically, a minimum of eight graduate subjects are required for a PhD.

2. Scope and Methods

This required one-semester seminar for first-year students introduces principles of empirical and theoretical analysis in political science.

3. Statistics

You must successfully complete at least one class in statistics.

You must successfully complete at least one class in empirical research methods.

5. Philosophy

You must successfully complete at least one class in political philosophy.

6. Foreign language or advanced statistics

You must demonstrate reading proficiency in one language other than English by successfully completing two semesters of intermediate-level coursework or an exam in that language, or you must demonstrate your knowledge of advanced statistics by successfully completing three semesters of coursework in advanced statistics. International students whose native language is not English are not subject to the language requirement.

7. Field research

We encourage you to conduct field research and to develop close working ties with faculty members engaged in major research activities.

8. Second Year Paper/workshop

You must complete an article-length research paper and related workshop in the spring semester of the second year. The second-year paper often develops into a dissertation project.

9. Two examinations

In each of your two elected fields, you must take a general written and oral examination. To prepare for these examinations, you should take at least three courses in each of the two fields, including the field seminar.

10. Doctoral thesis

As a rule, the doctoral thesis requires at least one year of original research and data collection. Writing the dissertation usually takes a substantially longer time. The thesis process includes a first and second colloquium and an oral defense. Be sure to consult the MIT Specifications for Thesis Preparation as well as the MIT Political Science Thesis Guidelines . Consult the MIT academic calendar to learn the due date for final submission of your defended, signed thesis.

Questions? Consult the MIT Political Science Departmental Handbook or a member of the staff in the MIT Political Science Graduate Office .

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Doctor of philosophy in urban studies and planning, funding and responsibilities for dusp doctoral students, degree requirements, sample schedule by milestones, important early dates (guide by semester), past dissertations, additional resources.

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The Department of Urban Studies and Planning offers a degree in a Doctor of Philosophy in Urban Studies and Planning which is an advanced research degree in planning or urban studies and is focused on training individuals for research and teaching in the areas of applied social research and planning.

Daniel Engelberg

Enjoli Hall

Carmelo ignaccolo.

Aarthi Janakiraman

Justin Kollar

Kevin Lujan Lee

Arianna Salazar Miranda

Chenab Navalkha

Soyoung Park

Lidia Cano Pecharroman

Benjamin Preis

Gokul Sampath

Wonyoung So

Andrew Stokols

Anna Waldman-Brown

Darien Alexander Williams

Lizzie Yarina

The Doctor of Philosophy in Urban Studies and Planning program emphasizes the development of fundamental research competence, flexibility in the design of special area of study, and encouragement of joint student/faculty research and teaching. The program is tailored to the needs of individual students, each of whom works closely with a custom ecosystem of scholars in their field and a mentor in the Department.

DUSP graduates are well prepared for (and go on to work in) a wide range of careers in academia, government, and industry.

Admissions for the doctoral program emphasizes academic preparation, professional experience, and the fit between the student's research interests and the department's research activities. Nearly all successful applicants have previously completed a master's degree. Admission to the doctoral program is highly competitive. 

Core criteria and guidelines for doctoral admission decisions:

• Application strength: cohesiveness of statement, compelling research topics, preparedness for doctoral level work.
• Alignment with Departmental research priorities: achieving racial justice, tackling the climate change, enhancing democratic governance, and closing the wealth gap
• Could an applicant work with more than one DUSP faculty on their committee?
• Does applicant have a strong match with at least one lead faculty?

11.001J    Introduction to Urban Design & Development

11.002    Making Public Policy

11.005    Introduction to International Development

11.200    Gateway I

11.201    Gateway II

11.202/203    Microeconomics

11.205/11.188    Introduction to Spatial Analysis

11. 220   Quantitative Reasoning  

11.222    Introduction to Critical Qualitative Methods 

• Cross-cutting substantive areas – research of interest to multiple DUSP program groups and strategic priorities
• If you reach out to a faculty member directly and they have not responded before you complete your application, please note that no response does not reflect a judgement. Faculty have many time commitments and may be unable to answer your request quickly.
• Please do note DUSP students offer Peer Application Support Services (PASS) , supporting students who may face structural barriers in applying, including (but not limited to) international applicants, first generation college students, and applicants who identify as Black, Indigenous, Latinx, queer, disabled, and/or a person of color. 
• Faculty members do on occasion recruit students for their externally funded research, but those student's admission is still decided by committee.  

Learn more via the Admissions page, here.

Each doctoral student has an assigned faculty academic advisor with whom they should develop a plan of study. All faculty are concerned with promoting good personal and academic relationships between students and advisors. Faculty advisors are responsible for: approving the registration for the doctoral student at the beginning of each semester, reviewing the student's progress, meeting with their advisee on a regular basis, and alerting the student and Department Headquarters if any issues arise concerning satisfactory progress towards completing the student's degree requirements.

If the student is nonresident, the student and faculty should communicate on a regular basis with each other concerning the progress being made, the timing to be determined jointly by the student and faculty member.

Advisees may request switching advisors. Initiating a change in advisors is the responsibility of the student. The student should:

• Talk to the other faculty member about her/his willingness to serve as a doctoral advisor;
• Inform the current advisor about the desired change in advisors (ideally the decision would be made in discussions with the current and future advisor);
• If the issue becomes complicated, discuss the move with the Head of the PhD Committee;
• Inform the Doctoral Program Academic Advisor .

Addition resources for roles, relationships, and advising best practices may be found here . Student support resources may be found here . Additional information on doctoral student advisee/advisor relationship may be accessed via the DUSP Handbook.

The Department admits five to seven students a year to the doctoral program. All admitted students receive funding for five academic years, including the option of summer work. In addition, some students are admitted with five academic years of funding as part of a research project sponsored by a faculty member and/or external funding.

Departmentally-funded students commit to completing five teaching assistantships and three research assistantships during their time as students at DUSP. The department also issues a call for optional funded summer work during the spring term. 

For more detailed information regarding the cost of attendance, including specific costs for tuition and fees, books and supplies, housing and food as well as transportation, please visit the SFS website .

Required Coursework

In their first (fall) semester, students are required to take 11.233. There are no exceptions nor substitutions to this requirement. The output of this class is a research proposal that can form the basis for the required first-year research paper.

The Doctoral Research Seminar focuses on writing a research paper - the first year paper (FYP) - on a subject of the student's choice. The paper's purpose is to assess the student's ability to independently make a reasoned argument based on evidence that they have collected and to allow the student to work closely with a faculty advisor.

Students are expected to finish the paper in the spring of their first year, and students CANNOT register for their third semester of courses until this paper has been completed.

Methods Courses

All PhD students must complete one graduate-level class in quantitative methods and one graduate-level class in qualitative methods from a list of approved subjects by the end of their fourth semester. Enrolled doctoral students may consult the PhD Wiki pages for community collected information on methods courses of interest to DUSP PhD students:

• Quantitative Methods Courses
• Qualitative Methods Courses

In addition, students are strongly encouraged to enroll in DUSP's Advanced Seminar on Planning Theory (11.930).

Field Exams (General Exams)

General Exams will ordinarily be taken either in late spring of the second year or in early fall of the third year. These examinations contain a written and an oral component. All PhD students are expected to prepare for an examination in two fields. The first field is theory oriented and must be a discipline or equivalent systematic approach to social inquiry. The second field is typically customized to student specializations.

• City Design & Development
• International Development
• Urban Information Systems
• Public Policy and Politics
• Health and Global Communities
• Urban History
• Urban and Regional Economics
• Urban Sociology
• Environmental Planning and Natural Resource Management
• Housing and Real Estate Development
• Labor and Employment Policy
• Neighborhood and Community Development
• Negotiation and Dispute Resolution
• Planning in Developing Countries
• Regional Development
• Transportation and Land Use

Dissertation  

Summary and Full Dissertation Proposal

Within three months after successful completion of the general examinations, each PhD candidate is expected to submit to the PhD Committee a five-to six-page preliminary dissertation research proposal summary.

• The proposal should include the dissertation topic, the importance of the topic, the research method, the types of information to be used, the means of obtaining the required information (surveys, statistical testing, literature, etc.), and a selected bibliography.
• The preliminary dissertation proposal must be approved and signed by the dissertation advisor on the student's committee. The dissertation committee must be chaired by a member of DUSP and include at least one other member of the MIT faculty.
• Membership of the general examination and dissertation committees need not overlap.

Within one year after passing the general examinations, the student must submit a full proposal to their dissertation committee and for approval by the PhD Committee. Full proposals should expand upon the topics covered in the preliminary proposals and must be signed by all members of the student's dissertation committee. An external reviewer will be invited to provide feedback as well.

• In this proposal (usually 25-30 pages in length), the student should provide details on the research design and preliminary ideas (e.g., hypotheses) that will guide the research effort. They should also discuss the relevant literature and potential data sources.
• All students are expected to organize a colloquium in which they discuss their dissertation proposal before their full committee, the external reviewer, and other interested members of DUSP and MIT more generally. The student is expected to notify all DUSP members of the time and place of the colloquium and the dissertation proposal cannot be approved until the colloquium has been held. No colloquia will be held during the last two weeks of the semester, or final exam week, or during the summer. 

Oral Dissertation Defense

After the dissertation committee and the student indicate that the dissertation is completed, the committee chair will ask for the student to appear for an oral examination. The oral examination will customarily last for two hours and will be attended by all members of the dissertation committee. Other faculty and/or students may be allowed to attend the oral examination at the discretion of the dissertation committee. If revisions, normally slight, to the dissertation are suggested by the committee, the committee chair may be solely in charge of approving the revised document. If major revisions are needed, all members of the committee need to review the revised document, and, in some cases, another oral examination may be required. 

Guidelines for preparation of the dissertation document are available from DUSP's PhD Academic Administrator. The student must follow these guidelines carefully. All final dissertation document are submitted electronically. Students will be removed from the degree list for graduation if the appropriate dissertation documents are not met by the deadline set each semester by DUSP. All PhD dissertations are graded on a satisfactory basis. 

Written Dissertation Options 

In addition to the traditional monograph (i.e. a book-length manuscript), students may opt for a three-paper dissertation. 

The three-paper option is based on three related publishable papers and is designed to be used in situations where the thesis material is better suited to three papers on the same general topic rather than turning the dissertation into a book. A dissertation cannot be comprised of essays on three totally separate topics.

• Both the summary and full dissertation proposal are still required, with a dissertation committee consisting of a chair and two readers. The three-papers option should represent different aspects of the same topic.
• A student wishing to submit a three-paper dissertation should propose this plan at the time they submit the initial dissertation summary proposal or, if a decision to do so is made only subsequently, the student should indicate this plan as part of the full dissertation proposal that is submitted to the PhD Committee in advance of the Dissertation Proposal Colloquium.
• One paper in a three-paper dissertation may be co-authored. In such cases, as part of the full Dissertation Proposal, the student should explain the rationale for the proposed co-authorship. The PhD committee representative charged with evaluating the dissertation proposal will be asked to review this to determine the significance of the student's role in the collaborative paper. If there is a change in the plan for co-authorship after the Dissertation Proposal Colloquium has taken place, this must be cleared with the PhD Committee.
• In meeting the criterion of “publishable papers,” the dissertation may include a paper that has been previously published, as long as this paper has been completed as part of the student's doctoral program at MIT.
• A student's First Year Paper may not be used for one of the three papers submitted for the dissertation, unless it has been significantly revised and updated.
• Finally, the three-paper dissertation itself must contain a section that explains how the three papers are related.

A note on completing your dissertation during the summer:

Please be aware that most DUSP faculty are on nine-month contracts, and are not paid to teach or work with students during June, July, and August. Accordingly, any student seeking to complete PhD thesis work over the summer in order to be placed on the September degree list must be certain about the willingness of the advisor and readers to take on this responsibility. Any student seeking this arrangement must submit a form signed by all members of the advising team, attesting to their willingness and summer availability. This form should be submitted to the PhD Academic Administrator no later than the Spring thesis due date. Failure to do so may result in removal from eligibility for the September degree list. If this happens, a student would need to submit their thesis and hold the defense during the fall term, and would need to pay the pro-rated fall semester's tuition if beyond the funded five academic years.

• Advisor sign-off required
• Advisor sign-off required 
• With members of PhD Committee required 
• Determine first and second field exams interests
• Assemble general exams committee
• General exam committee sign-off required
• Complete course work p reparation for general exams
• Complete second-year review statement and meeting
• Dissertation committee and external reviewer sign-off required

Year Three+

• Complete further coursework - if helpful to dissertation 
• Research and write dissertation
• Dissertation chair and committee members
• Revise dissertation as necessary  
• Dissertation chair and/or committee sign-off required
• Revise dissertation as necessary 
• Submit completed dissertation to department

First Semester

• Meet with your assigned faculty advisor
• Determine who will be your faculty advisor for your First-Year Paper (FYP)
• Complete FYP research proposal 

Second Semester

• Work on FYP, including fieldwork during IAP if necessary 
• Submit your First-Year Paper
• Schedule your First-year Review
• At least two weeks before First-year Review at the end of second semester.
• Take any recommended actions after First-year Review meeting   

Third Semester

• OPTIONAL schedule a presentation of your First-Year paper in the PhD Colloquium series
• Determine your first and second field exams interests
• Your chair must be a member of DUSP faculty
• at least another two faculty members, at least one of whom must be a member of the MIT faculty

Fourth Semester

• Schedule your first and second field examinations 
• sent to the members of your exam committee
• sent to DUSP's PhD Academic Administrator at least one month before taking your general exams
• with PhD Committee member and your advisor 
• take any necessary actions following meeting
• Take   your first and second field examinations
• within three months of finishing general exams
• Explore and decide who will chair your Dissertation Committee
• Think about and discuss with your Dissertation Chair who else will sit on your Dissertation Committee

Fifth Semester

• If exams are not completed in your second year, please note you must complete your general exams by the end of your fifth semester. Please refer to semester four for more details.
• Meet with your Dissertation Committee chair to discuss your dissertation proposal
• Write a draft dissertation proposal for feedback from your Dissertation Committee
• ​​​​​​​Circulate your dissertation proposal to your Dissertation Committee
• Schedule a colloquium on your dissertation proposal

This embedded table shows recent dissertation research by the doctoral community. A more complete listing of DUSP dissertation work can be found here.

Additional resources for DUSP doctoral students may be found in DUSP's Resources, Policies, and Procedures page under general ,  funding sources , professional development , students , and doctoral students .  

We welcome any questions you have about the DUSP doctoral program. 

• Questions, concerns, and/or complaints regarding registration, enrollment, leaves, exams and/or other student requirements should be addressed to Sandra Elliot  .
• Questions, concerns, and/or complaints regarding regarding the doctoral student process should be addressed to the PhD Committee co-Chairs ( see DUSP Governance )

Thesis Defenses

Julius baldauf.

Date: Thursday, March 28, 2024 | 2:10pm | Room: 2-449 | Zoom Link

Committee: Bill Minicozzi (Thesis Advisor and Examination Committee Chair), Tristan Collins, Tristan Ozuch

The Ricci Flow on Spin Manifolds

This thesis studies the Ricci flow on manifolds admitting harmonic spinors. It is shown that Perelman's Ricci flow entropy can be expressed in terms of the energy of harmonic spinors in all dimensions, and in four dimensions, in terms of the energy of Seiberg-Witten monopoles. Consequently, Ricci flow is the gradient flow of these energies. The proof relies on a weighted version of the monopole equations, introduced here. Further, a sharp parabolic Hitchin-Thorpe inequality for simply-connected, spin 4-manifolds is proven. From this, it follows that the normalized Ricci flow on any exotic K3 surface must become singular.

Date: Tuesday, April 30, 2024 | 3:00pm | Room: 4-149 | Zoom Link

Committee: Alexander Rakhlin (advisor), Yury Polyanskiy, Martin Wainwright, Ankur Moitra (chair)

Smoothed Online Learning: Theory and Applications

Many of the algorithms and theoretical results surrounding modern machine learning are predicated on the assumption that data are independent and identically distributed. Motivated by the numerous applications that do not satisfy this assumption, many researchers have been interested in relaxations of this condition, with online learning being the weakest such assumption. In this setting, the learner observes data points one at a time and makes predictions, before incorporating the data into a training set with the goal of predicting new data points as well as possible. Due to the lack of assumptions on the data, this setting is both computationally and statistically challenging. In this thesis, we investigate the statistical rates and efficient algorithms achievable when the data are constrained in a natural way motivated by the smoothed analysis of algorithms. The first part covers the statistical rates achievable by an arbitrary algorithm without regard to efficiency, covering both the fully adversarial setting and the constrained setting in which improved rates are possible. The second part of the thesis focuses on efficient algorithms for this constrained setting, as well as special cases where bounds can be improved under additional structure. Finally, in the third part we investigate applications of these techniques to sequential decicions making, robotics, and differential privacy. We introduce a number of novel techniques, including a Gaussian anti-concentration inequality and a new norm comparison for dependent data.

Murilo Corato Zanarella

Date: Tuesday, April 23, 2024 | 11:00am | Room: 4-370

Committee: Wei Zhang, Zhiwei Yun and Spencer Leslie (Boston College)

First explicit reciprocity law for unitary Friedberg—Jacquet periods

In the early 2000's, Bertolini and Darmon introduced a new technique to bound Selmer groups of elliptic curves via level raising congruences. This was the first example of what is now termed a "bipartite Euler system", and over the last decade we have seen many breakthroughs on constructing such systems for other Galois representations, including settings such as twisted and cubic triple product, symmetric cube, and Rankin—Selberg, with applications to the Bloch—Kato conjecture and to Iwasawa theory.

This thesis studies the case of Galois representations attached to automorphic representations on a totally definite unitary group U(2r) over a CM field which are distinguished by the subgroup U(r) x U(r). We prove a new "first explicit reciprocity law" in this setting, which has applications to the rank 0 case of the corresponding Bloch—Kato conjecture.

Date: Wednesday, April 24, 2024 | 3:00pm | Room: 2-142

Committee: Wei Zhang, Julee Kim, Zhiwei Yun

Local newforms and spherical characters for unitary groups

We first prove a smooth transfer statement analogous to Jacquet–Rallis’s fundamental lemma and use it to compute the special value of a local spherical character that appears in the Ichino–Ikeda conjecture at a test vector. Then we provide a uniform definition of newforms for representations of both even and odd dimensional unitary groups over p-adic fields. This definition is compatible with the one given by Atobe, Oi, and Yasuda in the odd dimensional case. Using the nonvanishing of the local spherical character at the test vector, we prove the existence of the representation containing newforms in every tempered Vogan L-packet. We also show the uniqueness of such representations in Vogan L-packets and give an explicit description of them using local Langlands correspondence.

Patrik Gerber

Date: Friday, April 26, 2024 | 9:30am | Room: 2-361

Committee: Philippe Rigollet (advisor), Yury Polyanskiy, Martin Wainwright

Likelihood-Free Hypothesis Testing and Applications of the Energy Distance

The first part of this thesis studies the problem of likelihood-free hypothesis testing: given three samples X,Y and Z with sample sizes n,n and m respectively, one must decide whether the distribution of Z is closer to that of X or that of Y. We fully characterize the problem's sample complexity for multiple distribution classes and with high probability. We uncover connections to two-sample, goodness of fit and robust testing, and show the existence of a trade-off of the form mn ~ k/ε^4, where k is an appropriate notion of complexity and ε is the total variation separation between the distributions of X and Y. We demonstrate that the family of "classifier accuracy" tests are not only popular in practice but also provably near-optimal, recovering and simplifying a multitude of classical and recent results. We generalize our problem to allow Z to come from a mixture of the distributions of X and Y, and propose a kernel-based test for its solution. Finally, we verify the existence of a trade-off between m and n on experimental data from particle physics.

In the second part we study applications of the energy distance to minimax statistics. We propose a density estimation routine based on minimizing the generalized energy distance, targeting smooth densities and Gaussian mixtures. We interpret our results in terms of half-plane separability over these classes, and derive analogous results for discrete distributions. As a consequence we deduce that any two discrete distributions are well-separated by a half-plane, provided their support is embedded as a packing of a high-dimensional unit ball. We also scrutinize two recent applications of the energy distance in the two-sample testing literature.

Alasdair Hastewell

Date: Thursday, April 18, 2024 | 12:30pm | Room: 4-153 | Zoom Link

Committee: Jörn Dunkel (chair), John Bush, Alexander Mietke

Robust spectral representations and model inference for biological dynamics

Current developments in automated experimental imaging allow for high-resolution tracking across various scales, from whole animal behavior to tissue scale single-cell trajectories during embryogenesis to spatiotemporal gene expression dynamics or neural dynamics. Transforming these high-dimensional data into effective low-dimensional models is an essential theoretical challenge that enables the characterization, comparison, and prediction of the dynamics within and across biological systems. Spectral mode representations have been used successfully across physics, from quantum mechanics to fluid dynamics, to compress and model dynamical data. However, their use in analyzing biological systems has yet to become prevalent. Here, we present a set of noise-robust, geometry-aware mathematical tools that enable spectral representations to extract quantitative measurements directly from experimental data. We demonstrate the practical utility of these methods by applying them to the extraction defect statistics in signaling fields on membranes of starfish, the inference of partial differential equations directly from videos of active particle dynamics, and the categorization of emergent patterns in spatiotemporal gene expression during bacterial swarming.

An additional challenge occurs for complex biophysical processes where the underlying dynamics are yet to be entirely determined. Therefore, we would like to use the experimental data to infer effective dynamical models directly that can elucidate the system's underlying biological and physical mechanisms. Building on spectral mode representations, we construct a generic computational framework that can incorporate prior knowledge about biological and physical constraints for inferring the dynamics of living systems through the evolution of their mode representations. We apply this framework first to single-cell imaging data during zebrafish embryogenesis, demonstrating how our framework compactly characterizes developmental symmetry breaking and reveals similarities between pan-embryo cell migration and Brownian particles on curved surfaces. Next, we apply the framework to the undulatory locomotion of worms, centipedes, robots, and snakes to distinguish between locomotion behaviors. Finally, we present an extension of the framework to the case of nonlinear dynamics when all relevant degrees of freedom are only partially observed, with applications to neuronal and chemical dynamics.

Arun Kannan

Date: Tuesday, April 23, 2024 | 1:00pm | Room: 1-273 | Zoom Link

Committee: Pavel Etingof (advisor), Roman Bezrukavnikov, Victor Kac

On Lie Theory in the Verlinde Category

A symmetric tensor category (STC) can be thought of as a “home” to do commutative algebra, algebraic geometry, and Lie theory. They are defined by axiomatizing the basic properties of a representation category of a group (or affine supergroup scheme). Are these the only examples of STCs? In characteristic zero, a famous theorem of Deligne states that, assuming a natural growth condition, representation categories of affine supergroup schemes are the only examples. However, the situation is totally different in positive characteristic, and the Verlinde category Verp is the most fundamental counterexample and appears to play a key role in generalizing the theorem of Deligne to positive characteristic. Moreover, Verp contains the category of supervector spaces. The upshot is that the study of Verp provides new algebraic structures and phenomena beyond that afforded by superalgebra and supergeometry but must also generalize what is already known.

In this thesis defense, we will first survey the theory of symmetric tensor categories. Then, we will discuss new algebraic structures that arise from the Verlinde category, including new constructions of exceptional Lie superalgebras and a generalization of Jordan algebras unique to characteristic 5. Finally, we will turn to progress made on generalizing useful algebraic techniques and machinery from the super setting to the Verp setting, like the Steinberg tensor product theorem and notions of polynomial functors.

Daniil Kliuev

Date: Tuesday, April 16, 2024 | 2:30pm | Room: 2-131

Committee: Pavel Etingof, Roman Bezrukavnikov and Ivan Loseu (Yale)

Positive traces and analytic Langlands correspondence

I will describe my results with co-authors in two directions.

The first direction is the problem of classification of positive traces on quantized Coulomb branches. In the most general setting, this problem generalizes the classical problem of describing irreducible unitary representations of real reductive Lie groups. We consider the case of Kleinian singularities of type $A$ and provide a complete classification of positive traces.

The second direction is analytic Langlands correspondence, which is the following. Let $X$ be a smooth irreducible projective curve over $\mathbb{C}$, $G$ be a complex reductive group. On one side of this conjectural correspondence there are $G^{\vee}$-opers on $X$ satisfying a certain topological condition ({\it real} opers), where $G^{\vee}$ is Langlands dual group. On the other side there is joint spectrum of certain operators on $L^2(Bun_G)$, called Hecke operators, where $Bun_G$ is the variety of stable parabolic $G$-bundles on $X$ and $L^2(Bun_G)$ is a Hilbert space of square-integrable half-densities. We prove most of the main conjectures of analytic Langlands correspondence in the case when $G=\operatorname{PGL}_2(\mathbb{C})$ and $X$ either a genus one curve with points or $X$ is $\mathbb{P}^1$ with higher structures at points.

Vasily Krylov

Date: Monday, April 29, 2024 | 9:30am | Room: 2-143

Committee: Roman Bezrukaunikov (advisor), Zhiwei Yun, and Ivan Loseu (Yale)

Geometry and representation theory of symplectic singularities in the context of symplectic duality

This thesis studies the geometry and representation theory of various symplectic resolutions of singularities from different perspectives. Specifically, we establish a general approach to attack the Hikita-Nakajima conjecture and illustrate this approach in the examples of ADHM spaces and parabolic Slodowy varieties. We also study minimally supported representations of the quantizations of ADHM spaces and provide explicit formulas for their characters. Lastly, we describe the monodromy of eigenvalues of quantum multiplication operators for type A Nakajima quiver varieties by examining Bethe subalgebras in Yangians and linking their spectrum with Kirillov-Reshetikhin crystals.

Jae Hee Lee

Date: Monday, April 1, 2024 | 3:00pm | Room: 2-361 | Zoom Link

Committee: Prof. Paul Seidel (thesis advisor), Prof. Pavel Etingof, Prof. Denis Auroux (External, Harvard)

Equivariant quantum connections in positive characteristic

Date: Tuesday, April 23, 2024 | 1:30pm | Room: 13-1143

Committee: Davesh Maulik, Michael Hopkins, Haynes Miller, and Jeremy Hahn

The algebraic K-theory of the chromatic filtration and the telescope conjecture

Chromatic homotopy theory gives a conceptual framework with which to understand the stable homotopy theory, by decomposing the stable homotopy category into monochromatic pieces. There are two variants of these monochromatic pieces, the K(n) and T(n)-local categories, the former of which is often quite understandable in terms of formal groups of height n, and the latter of which detects the so-called v_n-periodic part of the stable homotopy groups of spheres. I will explain how algebraic K-theory has refined our understanding of these monochromatic pieces. On one hand, algebraic K-theory is an important structural invariant of these categories that 'stably' classifies objects and their automorphisms, and I will explain some tools we have to computationally access the K-theory of these categories. On the other hand, the algebraic K-theory of such categories are interesting as spectra: they detect a lot of information about the stable homotopy groups of spheres and have helped us understand the difference between the T(n) and K(n)-local categories.

Calder Morton-Ferguson

Date: Friday, April 26, 2024 | 1:30pm | Room: 2-449 | Zoom Link

Committee: Roman Bezrukavnikov (advisor), Zhiwei Yun, Ivan Loseu

Kazhdan-Laumon categories and representations

In 1988, D. Kazhdan and G. Laumon constructed the \emph{Kazhdan-Laumon category}, an abelian category $\mathcal{A}$ associated to a reductive group $G$ over a finite field, with the aim of using it to construct discrete series representations of the finite Chevalley group $G(\mathbb{F}_q)$. The well-definedness of their construction depended on their conjecture that this category has finite cohomological dimension. This was disproven by R. Bezrukavnikov and A. Polishchuk in 2001, who found a counterexample for $G = SL_3$.

Since the early 2000s, there has been little activity in the study of Kazhdan-Laumon categories, despite them being beautiful objects with many interesting properties related to the representation theory of $G$ and the geometry of the basic affine space $G/U$. In the first part of this thesis, we conduct an in-depth study of Kazhdan-Laumon categories from a modern perspective. We first define and study an analogue of the Bernstein-Gelfand-Gelfand Category $\mathcal{O}$ for Kazhdan-Laumon categories and study its combinatorics, establishing connections to Braverman-Kazhdan's Schwartz space on the basic affine space and the semi-infinite flag variety. We then study the braid group action on $D^b(G/U)$ (the main ingredient in Kazhdan and Laumon's construction) and show that it categorifies the \emph{algebra of braids and ties}, an algebra previously studied in knot theory; we then use this to provide conceptual and geometric proofs of new results concerning this algebra.

After Bezrukavnikov and Polishchuk's counterexample to Kazhdan and Laumon's original conjecture, Polishchuk made an alternative conjecture: though this counterexample shows that the Grothendieck group $K_0(\mathcal{A})$ is not spanned by objects of finite projective dimension, he noted that a graded version of $K_0(\mathcal{A})$ can be thought of as a module over Laurent polynomials and conjectured that a certain localization of this module is generated by objects of finite projective dimension. He suggested that this conjecture could lead toward a proof that Kazhdan and Laumon's construction is well-defined, and he proved this conjecture in Types $A_1, A_2, A_3$, and $B_2$. In the final chapter of this thesis, we prove Polishchuk's conjecture for all types, and prove that Kazhdan and Laumon's construction is indeed well-defined, giving a new geometric construction of discrete series representations of $G(\mathbb{F}_q)$.

Matthew Nicoletti

Date: Monday, April 29, 2024 | 2:30pm | Room: 2-361 | Zoom Link

Committee: Alexei Borodin (Advisor, chair), Scott Sheffield, Lauren Williams (Harvard)

Title: Stochastic Dynamics on Integrable Lattice Models

The purpose of this thesis is to present some new results related to the six-vertex and dimer model. One theme is the construction and analysis of Markov processes which are naturally associated to these lattice models. Certain integrability properties of the six-vertex and dimer model, often related to the Yang--Baxter equation, allow for the construction of associated Markov chains. In some cases, these are measure preserving Markov chains on configurations of the lattice model. In other cases, they arise via transfer matrices, after choosing a distinguished time coordinate, as a continuous time degeneration of the "time evolution" of the lattice model itself. It is often the case that the integrability of the underlying lattice model provides powerful tools to study the associated Markov chains or their marginals, which are sometimes Markov chains themselves.

In particular together with coauthors, we construct and analyze Markov chains on six-vertex configurations and on dimer model configurations, both of which are models for surface growth in the (2+1)-dimensional "Anisotropic KPZ" (or "AKPZ") universality class; we construct a Markov chain generalizing "domino shuffling" which samples exactly from a recently introduced probability measure on tuples of interacting dimer configurations; using a version of the usual domino shuffling algorithm, we construct and analyze deterministic "t-embeddings" of certain dimer graphs, which discretize minimal surfaces carrying the conformal structure of the limiting Gaussian free field; we construct stationary measures for several colored interacting particle systems using the Yang—Baxter equation.

Alexander Ortiz

Date: Wednesday, April 24, 2024 | 1:15pm | Room: 2-449 | Zoom Link

Committee: Larry Guth (advisor), David Jerison, Gigliola Staffilani

Sparse Fourier restriction for the cone

If the Fourier transform of F(x) is supported near a segment of the light-cone in R^3, what is the shape of the level sets U(N) = {x in R^3 : |F(x)| > N} for large values of N? In 2000, Thomas Wolff had a creative idea to study a related question based on the method of point-circle duality, and used it in a pivotal way to prove the first sharp L^p-decoupling estimates for the cone in R^3 for large values of p.

I will discuss new weighted L^2 estimates of F(x) which give us insight into the shape of level sets. I will explain how we use some of the same key ideas introduced by Wolff, together with a few new ones in the same spirit. By Wolff's method, our main theorem will partly be an application of a recent circular maximal function estimate due to Pramanik—Yang—Zahl in 2022 from their study of Kaufman-type restricted projection problems.

Date: Wednesday, April 3, 2024 | 3:30pm | Room: 2-449

Committee: Prof. Yufei Zhao (advisor and chair), Prof. Dor Minzer, and Prof. Philippe Rigollet

Random and exact structures in combinatorics

We aim to show various developments related to notions of randomness and structure in combinatorics and probability. One central notion, that of the pseudorandomness-structure dichotomy, has played a key role in additive combinatorics and extremal graph theory. In a broader view, randomness (and the pseudorandomness notions which resemble it along various axes) can be viewed as a type of structure in and of itself which has certain typical and global properties that may be exploited to exhibit or constrain combinatorial and probabilistic behavior.

These broader ideas often come in concert to allow the construction or extraction of exact behavior. We look at three particular directions: the singularity of discrete random matrices, thresholds for Steiner triple systems, and improved bounds for Szemerédi's theorem. These concern central questions of the areas of random matrices, combinatorial designs, and additive combinatorics.

Mehtaab Sawhney

Date: Wednesday, April 17, 2024 | 2:00pm | Room: 2-449

Committee: Yufei Zhao, Dor Minzer, and Philippe Rigollet

Probabilistic and Analytic Methods in Combinatorics

The defense will center on fast algorithms for discrepancy theory. Discrepancy theory is broadly concerned with the following problem; given a set of objects, we aim to partition them into pieces which are “roughly equal”. We will focus specifically on vector balancing: given a set of vectors, one seeks to divide them into two parts with approximately equal sum.

Important results in this area, including Spencer’s six standard deviations suffice and Banaszczyk's results towards the Komlós conjecture, were originally purely existential. However, since work of Bansal from 2010, it has become clear that such existential results can often be made algorithmic. We will explain a pair of such results. The first concerns bounds for online vector balancing obtained via a certain Gaussian fixed point random walk. The second gives an algorithmic form of Spencer's theorem that runs in near input sparsity time.

George Stepaniants

Date: Thursday, April 25, 2024 | 2:30pm | Room: 4-149 | Zoom Link

Committee: Philippe Rigollet, Jörn Dunkel, Sasha Rakhlin

Inference from Limited Observations in Statistical, Dynamical, and Functional Problems

Observational data in physics and the life sciences comes in many varieties. Broadly, we can divide datasets into cross-sectional data which record a set of observations at a given time, dynamical data which follow how observations change in time, and functional data which observe data points over a space (and possibly time) domain. In each setting, prior knowledge of statistical, dynamical systems, and physical theory allow us to constrain the inferences and predictions we make from observational data. This domain knowledge becomes of paramount importance when the data we observe is limited: due to missing labels, small sample sizes, unobserved variables, and noise corruption.

This thesis explores several problems in physics and the life sciences, where the interplay of domain knowledge with statistical theory and machine learning allows us to make inferences from such limited data. We begin in Part I by studying the problem of feature matching or dataset alignment which arises frequently when combining untargeted (unlabeled) biological datasets with low sample sizes. Leveraging the fast numerical methods of optimal transport, we develop an algorithm that gives a state-of-the-art solution to this alignment problem with optimal statistical guarantees. In Part II we study the problem of interpolating the dynamics of points clouds (e.g., cells, particles) given only a few sparse snapshot recordings. We show how tools from spline interpolation coupled with optimal transport give efficient algorithms returning smooth dynamically plausible interpolations. Part III of our thesis studies how dynamical equations of motion can be learned from time series recordings of dynamical systems when only partial observations of these systems are captured in time. Here we develop fast routines for gradient optimization and novel tools for model comparison to learn such physically interpretable models from incomplete time series data. Finally, in Part IV we address the problem of surrogate modeling, translating expensive solvers of partial differential equations for physics simulations into fast and easily-trainable machine learning algorithms. For linear PDEs, our prior knowledge of PDE theory and the statistical theory of kernel methods allows us to learn the Green's functions of various linear PDEs, offering more efficient ways to simulate physical systems.

Date: Wednesday, April 3, 2024 | 2:00pm | Room: 2-255

Committee: Scott Sheffield (advisor), Alexei Borodin, Nike Sun

Conformal welding of random surfaces from Liouville theory

Liouville quantum gravity (LQG) is a natural model describing random surfaces, which arises as the scaling limit for random planar maps. Liouville conformal field theory (LCFT) is the underlying 2D CFT that governs LQG. Schramm-Loewner evolution (SLE) is a random planar curve, which describes the scaling limits of interfaces in many statistical physics models. As discovered by Sheffield (2010), one of the deepest results in random geometry is that SLE curves arises as the interfaces under conformal welding of LQG surfaces.

In this thesis, we present some new results on conformal welding of LQG surfaces as well as their applications towards the theory of SLE. We first define a three-parameter family of random surfaces in LQG which can be viewed as the quantum version of triangles. Then we prove the conformal welding result of a quantum triangle and a two-pointed quantum disk, and deduce integrability results for chordal SLE with three force points.

The second main result is regarding the conformal welding of a multiple number of LQG surfaces, where under several scenarios, we prove that the output surfaces can be described in terms of LCFT, and the random moduli of the surface is encoded in terms of the partition functions for the SLE curves.

The third part is about the conformal welding of the quantum disks with forested boundary, where we prove that this conformal welding gives a two-pointed quantum disk with an independent SLE$_\kappa$ for $\kappa\in(4,8)$. We further extend to the conformal welding of a multiple number of forested quantum disks, where as an application, for $\kappa\in(4,8)$, we prove the existence of the multiple SLE partition functions, which are smooth functions satisfying a system of PDEs and conformal covariance. This was open for $\kappa \in (6,8)$ and $N\ge 3$ prior to our work.

The conformal loop ensemble (CLE) is a random collection of planar loops which locally look like SLE. For $\kappa \in (4,8)$, the loops are non-simple and may touch each other and the boundary. As a second application, we derive the probability that the loop surrounding a given point in the non-simple conformal loop ensemble touches the domain boundary.

Danielle Wang

Date: Tuesday, April 23, 2024 | 1:00pm | Room: 4-265

Committee: Wei Zhang (advisor/chair), Julee Kim, Spencer Leslie (Boston College)

Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions

The global twisted GGP conjecture is a variant of the Gan-Gross-Prasad conjecture for unitary groups, which considers the restriction of an automorphic representation of GL(V) to its subgroup U(V), for a skew-Hermitian space V. It relates the nonvanishing of a certain period integral to the central value of an L-function attached to the representation.

Catherine Wolfram

Date: Wednesday, April 24, 2024 | 4:00pm | Room: 2-449 | Zoom Link

Committee: Scott Sheffield (thesis advisor), Alexei Borodin, Curtis McMullen

Random geometry in two and three dimensions

A central theme in random geometry is the interplay between discrete models and continuum ones that appear in scaling limits. Surprising structure and symmetry often arises in these scaling limits, leading to an interplay between combinatorics, probability, complex analysis, and geometry.

The dimer model is one of the classical lattice models of statistical mechanics and can be defined in any dimension. In the first half of this thesis, we prove a large deviation principle for dimer tilings in three dimensions. This generalizes a two-dimensional result of Cohn, Kenyon, and Propp, and is one of the first results for dimers in any dimension $d>2$. Many ideas and constructions used to study dimers are specific to two dimensions, so our arguments start from a smaller set of tools including Hall's matching theorem, the qualitative description of the Gibbs property, and a double dimer swapping operation.

In the second half of this thesis, we study discrete, geometrically-motivated coordinates called shears on the space of circle homeomorphisms up to M\"obius transformations. The Weil-Petersson Teichm\"uller space is a subspace of this which has been of long-term interest in geometry and string theory and has recent connections to SLE curves in probability. We introduce and study natural $\ell^2$ spaces in terms of shears, and obtain sharp results comparing them to H\"older classes of circle homeomorphisms and the Weil-Petersson class. We also give some preliminary results about i.i.d. Gaussian random shears.

MEMP PhD Thesis Defense (10:00am): Sydney E. Sherman

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Koch Institute, Luria Auditorium 500 Main Street, Cambridge MA, Room 76-156 and Zoom (See below for full information)

Single-sided magnetic resonance sensors for clinical detection of volume status

Several pathological processes affect the body's ability to regulate volume status. In each of these disease states, the body loses some ability to regulate fluid balance and maintain an euvolemic state. Deviations from euvolemia have been shown to increase morbidity and mortality. The ability to detect pre-symptomatic changes in volume status would allow for more responsive management of these conditions and prevention of higher-mortality complications. Direct evaluation and quantification of early-stage changes in volemic state is not currently a clinical measure. T 2  relaxometry, a magnetic resonance imaging technique, may offer a feasible method to quantify volume status. In this work we explore the design of single-sided magnetic resonance sensors for the quantification of volume status, evaluate the clinical performance of the sensor, and elucidate further physiological considerations for fluid diagnostics.

The primary research question that motivated this thesis is: can a point-of-care relaxometer sensitively distinguish muscle interstitial fluid shifts in a single measurement? Several approaches are used to answer this question including instrumentation development, signal acquisition studies, and human subject studies. We describe the design of a point-of-care, single-sided magnetic resonance relaxometer. The constructed sensor can acquire slice-selective signal from 8mm above the instrument’s surface with a high signal-to-noise ratio. We review instrument performance on phantoms, ex-vivo tissue, and human subjects. Preliminary observational clinical studies of two cohorts, healthy athletes and in-patient hemodialysis patients, were conducted and validate the instrument is able to detect signal selectively from the muscle interstitial compartment and distinguish healthy adults and those with end stage renal disease with a single measurement. We discuss the implementation of multi-exponential fitting of acquired data. This enables analysis of individual muscle tissue compartments. We demonstrate strategies to double signal acquisition and improve T2 fitting accuracy through the simulation and implementation of linear frequency swept adiabatic radio frequency pulses.  These decrease the sensitivity of applied RF pulses to B 1  and B 0  inhomogeneity and reduce the effects of stimulated echoes. Finally, we explore physiological considerations for the instrument’s clinical implementation with an MRI study of chronic kidney disease and healthy control subjects. This allows for the evaluation of physiological factors which may affect the device’s accuracy and offer further future areas for study.

The single-sided magnetic resonance sensor and signal acquisition and processing techniques described demonstrate high potential for quantitative clinical assessment of volume status. This work focuses exclusively on healthy subjects or adults with chronic kidney disease, but the principles demonstrated are agnostic to many underlying disease pathologies.

Thesis Supervisor: Michael J. Cima, PhD  David H. Koch Professor of Engineering; Professor of Materials Science and Engineering, Massachusetts Institute of Technology

Thesis Committee Chair: Elfar Adalsteinsson, PhD Eaton-Peabody Professor, Electrical Engineering and Computer Science and Institute for Medical Engineering and Computer Science, Massachusetts Institute of Technology

Thesis Readers: Matthew Rosen, PhD Associate Professor of Radiology, Harvard Medical School; Associate Investigator, Athinoula A. Martinos Center for Biomedical Imaging, Mass General Research Institute; Kiyomi and Ed Baird MGH Research Scholar, Mass General Research Institute, Massachusetts General Hospital  Sagar Nigwekar, MD Physician Investigator, Nephrology, Mass General Research Institute; Assistant Professor of Medicine, Harvard Medical School; Assistant Physician, Nephrology, Massachusetts General Hospital ------------------------------------------------------------------------------------------------------

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Topic: Sydney Sherman MEMP PhD Thesis Defense Time: April 18, 2024, 1:00 PM Eastern Time (US and Canada)

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QS World University Rankings rates MIT No. 1 in 11 subjects for 2024

QS World University Rankings has placed MIT in the No. 1 spot in 11 subject areas for 2024, the organization announced today.

The Institute received a No. 1 ranking in the following QS subject areas: Chemical Engineering; Civil and Structural Engineering; Computer Science and Information Systems; Data Science and Artificial Intelligence; Electrical and Electronic Engineering; Linguistics; Materials Science; Mechanical, Aeronautical, and Manufacturing Engineering; Mathematics; Physics and Astronomy; and Statistics and Operational Research.

MIT also placed second in five subject areas: Accounting and Finance; Architecture/Built Environment; Biological Sciences; Chemistry; and Economics and Econometrics.

For 2024, universities were evaluated in 55 specific subjects and five broader subject areas. MIT was ranked No. 1 in the broader subject area of Engineering and Technology and No. 2 in Natural Sciences.

Quacquarelli Symonds Limited subject rankings, published annually, are designed to help prospective students find the leading schools in their field of interest. Rankings are based on research quality and accomplishments, academic reputation, and graduate employment.

MIT has been ranked as the No. 1 university in the world by QS World University Rankings for 12 straight years.

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Stanford alum, business school dean Jonathan Levin named Stanford president

Jonathan Levin has been appointed the 13th president of Stanford University. (Image credit: Aubrie Pick)

Jonathan Levin, a distinguished economist and Stanford alumnus who has led the Stanford Graduate School of Business as dean for the last eight years, has been appointed the next president of Stanford University, the Board of Trustees announced today.

Jerry Yang, BS, MS ’90, chair of the Board of Trustees, thanked the 20-member Presidential Search Committee (PSC) for their work, and said Levin was the unanimous choice of the search committee and of the trustees. The PSC conducted a comprehensive search for Stanford’s next president. Levin will become president effective Aug. 1, 2024.

“Jon brings a rare combination of qualities: a deep understanding and love of Stanford, an impressive track record of academic and leadership success, the analytical prowess to tackle complex strategic issues, and a collaborative and optimistic working style,” Yang said. “He is consistently described by those who know him as principled, humble, authentic, thoughtful, and inspiring. We are excited about Stanford’s future under Jon’s leadership.”

Levin, 51, has been a member of the Stanford faculty since 2000. The winner in 2011 of the John Bates Clark Medal, an award recognizing the most outstanding American economist under the age of 40, Levin today is the Philip H. Knight Professor and dean of the Stanford Graduate School of Business. He also serves as a member of President Biden’s Council of Advisors on Science and Technology.

“I am grateful and humbled to be asked to lead Stanford – a university that has meant so much to me for more than three decades,” Levin said. “When I was an undergraduate, Stanford opened my mind, nurtured my love for math and literature, and inspired me to pursue an academic career. In the years since, it has given me opportunities to pursue ideas in collaboration with brilliant colleagues, teach exceptional students, and bring people together to achieve ambitious collective goals around the university.”

“As I look to Stanford’s future, I’m excited to strengthen our commitment to academic excellence and freedom; to foster the principles of openness, curiosity, and mutual respect; and to lead our faculty and students as they advance knowledge and seek to contribute in meaningful ways to the world.”

Levin will succeed Richard Saller, who has served as Stanford’s president on an interim basis since September 2023.

“I want to thank President Richard Saller for his exemplary leadership this year,” Levin said. “He, along with Provost Martinez, have demonstrated deeply principled academic values and uncommon thoughtfulness as they have navigated a unique set of challenges. I look forward to working with them in the months ahead, and continuing that work with Provost Martinez and leaders across the university to envision an even better Stanford.”

Presidential search process

The PSC, composed of diverse stakeholders across the university, conducted an extensive and rigorous seven-month search for the university’s 13th president. Read more about the search process .

Leaders of the search highlighted Levin’s impressive academic credentials, strong track record as dean of the Graduate School of Business, and extensive knowledge of Stanford and its culture. They also noted that he has the personal qualities that members of the community emphasized were important in Stanford’s next president, including integrity, humility, aspiration, and emotional and intellectual intelligence.

“Jon is a leader who drives change in a way that engages faculty, students, and other stakeholders,” said Bonnie Maldonado, MD ’81, co-chair of the Presidential Search Committee and senior associate dean for faculty development and diversity in the Stanford School of Medicine. “Moreover, Jon’s academic background, analytical skills, and experience have provided him with the skillset and ability to oversee this incredibly complex institution.”

“Jon exhibits a perspective that blends optimism, intellect, ideas, and experience,” said Lily Sarafan, BS ’03, MS ’03, co-chair of the Presidential Search Committee and trustee. “Jon has a deep understanding of Stanford and its role in the world, including the need to expand the university’s educational reach, support emerging areas of research, and renew trust and goodwill both internally and externally.”

“We interviewed an impressive slate of candidates, individuals with excellent credentials and experience,” Sarafan continued. “From that outstanding group, Jon emerged as the person best suited to lead Stanford into the future.”

Academic career and public service

Levin attended Stanford as an undergraduate, completing a BA in English and a BS in mathematics in 1994. He then completed an MPhil in economics from Oxford University and a PhD in economics from MIT.

Image credit: Aubrie Pick

He joined the economics faculty at Stanford in 2000 and later was awarded an endowed chair, becoming the Holbrook Working Professor of Price Theory in the School of Humanities and Sciences.

He served as chair of the Stanford economics department from 2011 to 2014. As chair, Levin established a vision and strategy to elevate the department and helped recruit two future Nobel laureates and four Clark medalists to Stanford.

Levin is widely recognized for his scholarship in industrial organization and market design. His research has spanned topics ranging from incentive contracts to game theory to e-commerce, consumer lending, and health care competition. He helped design the first Advance Market Commitment that accelerated the global adoption of pneumococcal vaccine. He also helped design the Federal Communication Commission’s $20 billion incentive auction to convert broadcast television spectrum to broadband wireless licenses. He has advised technology companies building online marketplaces and advertising systems.

Levin has also been active in public service. In 2021, Levin was invited by President Biden to serve on the President’s Council of Advisors on Science and Technology. In this role, he has studied problems ranging from the modeling and predicting of extreme weather to the prospects of AI for scientific discovery, and from cyber-physical resilience to the future of the social sciences.

Levin became dean of the Graduate School of Business in 2016. Under his leadership, the school made important advances in multiple strategic areas.

First, it made significant investments in its research and teaching mission, including the creation of the GSB Research Hub to provide shared resources for empirical and experimental work, and the Teaching and Learning Hub to support curriculum development, educational technology, and experiential learning. The school significantly increased faculty research funding, redesigned student fellowships to be need-based, and expanded its distinctive academic-practitioner teaching model, among other efforts.

Second, the school expanded its educational reach. It has extended its footprint in executive and online education, including significant growth of the flagship online LEAD program for mid- to senior-level professionals. The school has made significant strides with Stanford Seed, which educates entrepreneurial leaders in the developing world; the King Center on Global Development, established in 2017 in partnership with the Stanford Institute for Economic Policy Research; and by initiating Stanford Global Economic Forums in Beijing and Singapore. This year, the GSB introduced the new Stanford Pathfinder classes for undergraduates across the university.

Third, during Levin’s tenure as dean, the school launched a major new initiative around Business, Government, and Society. The initiative addresses how business intersects with societal issues, such as sustainability, the effects of technology, the strength of democratic institutions, and global politics. It has led to new classes, research grants, workshops for students, a faculty-led effort on artificial intelligence, and new partnerships between the GSB and Stanford’s other schools and institutes.

A commitment to different perspectives has also been a core tenet of the school. The GSB degree programs increased their outreach efforts and significantly increased the representation of women and historically under-represented groups. Today, the GSB student population is the most diverse in the school’s history. Specific programs have also been created, including the Building Opportunities for Leadership Diversity (BOLD) Fellows Fund for students of backgrounds with financial hardship, and the Stanford Latino Entrepreneurship Initiative, which has educated more than 1,000 entrepreneurial business leaders.

“Stanford is a place of unbridled optimism, of exploration and innovation,” said Jennifer Aaker, PhD ’95, a member of the Presidential Search Committee and the General Atlantic Professor at the GSB. “It’s a place where anything is possible – where you can excel in academics and athletics, pursue entrepreneurship with integrity, combine intellectual rigor with irreverence. Jon loves Stanford, and he understands this central truth about the university: that it is a place of possibility. He is the right person to not only envision where Stanford should go, but to take us there. He’s also pro-fun.”

With Levin’s appointment as president, a search will be undertaken by the provost for his successor as dean of the Graduate School of Business.

Depth of knowledge, breadth of experience

Levin’s career as a student, faculty member, and academic leader touches many disciplines across the university. He was both an undergraduate, and faculty member, in Stanford’s School of Humanities & Sciences. During his 16 years in Stanford’s Department of Economics, he worked closely with undergraduates, and advised nearly 50 PhD dissertations. He chaired the university committee on undergraduate admissions and financial aid, served on the university budget group, and in both 1994 and 2012 participated in major university reviews of undergraduate education. As dean of the business school, he adds a deep knowledge of professional education and student life, along with overseeing a highly interdisciplinary faculty, search committee members said.

Image credit: Saul Bromberger

“Jon embodies the character and values I aspire to emulate as a future Stanford graduate,” said Senkai Hsia, the undergraduate member of the Presidential Search Committee. “As an undergraduate alum himself, Jon gets the irreverent spirit of exploration and exuberance that makes Stanford special. He is admired by students at the Graduate School of Business, and I know he will love engaging with students across the university. Jon will boldly lead Stanford into a bright future.”

Levin’s awards and honors include membership as a fellow of the American Academy of Arts and Sciences; Fulbright Scholar; Sloan Research Fellow; recipient of a Guggenheim Fellowship; winner of the John Bates Clark Medal, recognizing the outstanding American economist under the age of 40; and recipient at Stanford of the Dean’s Award for Distinguished Teaching and the Department of Economics Teaching Prize.

Levin is married to Amy Levin, a physician. They have three children.

A list of previous Stanford presidents is available here .

Stanford University is a place of discovery, creativity, innovation, and world-class medical care. Dedicated to its founding mission of benefitting society through research and education, Stanford strives to create a sustainable future for all, catalyze discoveries about ourselves and our world, accelerate the societal impact of its research, and educate students as global citizens. Its main campus holds seven schools along with interdisciplinary research and policy institutes, athletics, and the arts. More than 7,000 undergraduate and 9,000 graduate students pursue studies at Stanford each year. Learn more at stanford.edu.