mit phd thesis

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Thesis Preparation

The following information is provided to assist Chemistry graduate students as they prepare their theses. If graduate students have any questions that are not answered by this guide, they should email the Chemistry Education Office (questions about department policies) or MIT Libraries (for questions about thesis formatting, etc.)

Degree candidates must fill out the Degree Application via WebSIS at the start of the term. Important dates and deadlines (including late fees) for the upcoming academic year are listed below.  It is strongly advised that degree candidates apply for the degree list even if there is uncertainty about completing the thesis defense and submission by the  deadline, as there are no penalties for being removed from the degree list.

Students must successfully complete the thesis defense before submitting their final, signed thesis.

**Please note that the Specifications for Thesis Preparation were updated in November 2022. Please make sure you use these new guidelines.**

Important Dates & Deadlines

May 2024 degree list.

• Degree Application Deadline: February 9, 2024 ($50 late fee if submitted after this date, $85 late fee if submitted after April 12, 2024)
• Thesis Title Deadline: April 12, 2024 ($85 late fee if submitted after this date. If your thesis title is not finalized by this date, please enter your current working title and the final title can be updated later)
• Thesis Submission Deadline: May 10, 2024
• Last day of work in the lab: on or before May 29, 2024. If you plan to end your RA appointment earlier than May 29, 2024, please contact Jennifer to review your timeline.
• Your degree will officially be conferred by MIT on May 30, 2024
• Information about the MIT Health Plan and graduation will be available online here.

September 2024 Degree List

• Degree Application Deadline: June 14, 2024 ($50 late fee if submitted after this date, $85 late fee if submitted after July 21, 2024)
• Thesis Title Deadline:July 19, 2024 ($85 late fee if submitted after this date. If your thesis title is not finalized by this date, please enter your current working title and the final title can be updated later)
• Thesis Submission Deadline: August 16, 2024
• Last day of work in the lab: on or before August 31, 2024. If you plan to end your RA appointment earlier than August 31st, please contact Jennifer to review your timeline.
• Your degree will officially be conferred by MIT on September 18, 2024

February 2025 Degree List

• Degree Application Deadline: September 6, 2024 ($50 late fee if submitted after this date, $85 late fee if submitted after December 13, 2024)
• Thesis Title Deadline: December 13, 2024 ($85 late fee if submitted after this date. If your thesis title is not finalized by this date, please enter your current working title and the final title can be updated later)
• Thesis Submission Deadline: January 17, 2025
• Last day of work in the lab: on or before January 15, 2025. If you plan to end your RA appointment earlier than January 15th, please contact Jennifer to review your timeline.
• Your degree will officially be conferred by MIT on February 19, 2025

May 2025 Degree List

• Degree Application Deadline:February 7, 2025 ($50 late fee if submitted after this date, $85 late fee if submitted after April 11, 2025)
• Thesis Title Deadline: April 11, 2025 ($85 late fee if submitted after this date. If your thesis title is not finalized by this date, please enter your current working title and the final title can be updated later)
• Thesis Submission Deadline: May 9, 2025
• Last day of work in the lab: on or before May 28, 2025. If you plan to end your RA appointment earlier than May 28th, please contact Jennifer to review your timeline.
• Your degree will officially be conferred by MIT on May 29, 2025

Scheduling your Thesis Defense

All PhD candidates must have a Thesis Defense. As soon as your defense is finalized, please email the Chemistry Education Office with the date, time, location, and thesis title . Thesis defenses are strongly encouraged to be in-person.  If there are questions or concerns about an in-person defense, please reach out to Jennifer Weisman. When thesis defenses are on campus, we recommend reserving a room once the defense date is finalized, student can reserve department rooms through the online scheduling system or request a classroom via this form .

Degree candidates should provide their advisor with a copy of the thesis at least two weeks before the defense and provide their thesis committee chair and member with a copy at least one week before the defense. However, degree candidates should talk with their advisor, committee chair, and committee member to find out if they need the thesis further in advance or if there are preferred formats. Degree candidates should allow time in between their thesis defense and the submission deadline to make edits and submit the final copies.

Please note that most receiving a PhD degree are required to present a seminar as part of the thesis defense. This seminar is open to the department. The degree candidate is responsible for providing the Chemistry Education Office with information about their thesis defense at least two weeks ahead of time. Following the seminar, the candidate will meet privately with the thesis committee.

Thesis Formatting

The Institute has very specific requirements for thesis preparation, which were updated in November 2022. Specifications for Thesis Preparation is available on the library’s website and should be read very carefully. The MIT Thesis FAQ may answer additional questions and a helpful checklist is also provided. The specifications also include information about copyright and use of previously published material in a thesis . Do  not  rely on any templates or prior theses from your research group – they may not reflect the most current guidelines. We have highlighted some especially important points below.

Font & Spacing

Title page & committee signature page.

• The title page of the first copy will be digitally signed by the author, advisor, and Professor Adam Willard. The title page should contain the title, name of the author, previous degrees, the degree(s) to be awarded at MIT, the date the degree(s) will be conferred (May, September, or February only), copyright notice, and appropriate names and signatures. Degrees are awarded in Chemistry, regardless of your specific research area. Regardless of when you defend or submit your thesis, the date of degree conferral must be May/June, September, or February.
• As noted above, the title page will be signed by you, your advisor, and Professor Willard. You do not need to have Professor Willard digitally sign the thesis before you submit it, we will arrange to have him sign it. If your advisor has a title (ex., Firmenich Professor of Chemistry) it should also be included under their name. If you are not sure if they have a title, you can consult the Faculty Directory . Professor Willard should have the following listed under his name, on two separate lines: Professor of Chemistry; Graduate Officer
• Each student should place the appropriate copyright notice on the thesis title page. Copyright notice consists of four elements: the symbol “c” with a circle around it © and/or the word “copyright”; the year of publication (the year in which the degree is to be awarded); the name of the copyright owner; the words “All rights reserved” or your chosen Creative Commons license. All theses should have the following legend statement exactly: The author hereby grants to MIT a nonexclusive, worldwide, irrevocable, royalty-free license to exercise any and all rights under copyright, including to reproduce, preserve, distribute and publicly display copies of the thesis, or release the thesis under an open-access license. Please carefully review the copyright information to determine the appropriate copyright ownership.
• The date under Signature of Author should be the date the final thesis is signed and submitted to the department.
• The title page is always considered to be page 1, and every page must be included in the count regardless of whether a number would be physically printed on a page. We recommend that you do not include the page number on the title page.
• There is also a signature page that will be digitally signed by your entire thesis committee. Your advisor will digitally sign your thesis twice, on the title page and signature page. The signature page is right after the title page.
• More details about digital signatures are provided below.

Table of Contents

Final thesis submission, general submission process.

Please carefully review the details below, including the file naming format . There are two steps to the final submissions process:

1. Submit the following documents to the Department of Chemistry:

• An electronic copy of your thesis in PDF/A-1 format (with no signatures)
• A PDF of the digitally signed title page and committee signature page (using DocuSign to obtain signatures)

Please send an email to your advisor, Jennifer Weisman, and William McCoy, which includes the 2 PDFs above and the following text:

“Dear Professor/Dr X: Attached is the final version of my thesis. Please use reply-all to this message to indicate your acceptance of my thesis document and your recommendation for certification by my department.”

**Note: if your thesis document is too large to send via email, your email can include a link to access the document via Dropbox, Google Drive, etc.**

2. Submit your thesis information to MIT Libraries here . Choose to opt-in or opt-out of ProQuest license and publication.  Include the same copyright and license information that is on your thesis title page. Note: this does not involve submitting your actual thesis.

Details for Thesis Submission Process

• After the defense, the student and thesis committee reach agreement on the final thesis document.
• Students should follow the format specifications as stated in the Specifications for Thesis Preparation . Do not print or physically sign pages.
• Students will have the thesis signed electronically through DocuSign. This process is described in detail in the section below.
• The title page is always considered to be page 1, and every page must be included in the count regardless of whether a number is physically printed on a page. The entire thesis (including title page, prefatory material, illustrations, and all text and appendices) must be paginated in one consecutive numbering sequence. Your committee signature page should be page 2. Please see the  Sample Title Page and committee signature page for reference.
• You will still include the title page and committee signature page in the full thesis PDF, they just won’t have any signatures.
• The digitally signed title page and committee signature pages should be in one PDF, separate from the thesis document. This avoids a DocuSign tag at the top of each page of the full thesis. Please use the following naming convention: authorLastName-kerb-degree-dept-year-sig.pdf (ex., montgomery-mssimon-phd-chemistry-2021-sig.pdf).
• Students should save their final thesis document as a PDF using the following file naming convention: authorLastName-kerb-degree-dept-year-thesis .pdf (ex., montgomery-mssimon-phd-chemistry-2021-thesis.pdf).
• Students should not deposit the PDF of their thesis via the Libraries Library’s voluntary submission portal.
• Please send an email to your advisor, Jennifer, and William which includes the final thesis document and file with the digitally signed title/committee signature pages with the following text:

Please also complete the MIT Doctoral Student Exit Survey and your Laboratory Safety Clearance Form .

Digital Signatures

Please see here for a full guide (with screenshots) to using DocuSign to obtain digital signatures

Required Signatures:

These should be everyone’s uploaded digital signatures in their own handwriting, not one of the pre-formatted signatures created by DocuSign.

• Your signature on the thesis title page
• Your advisor’s signature on both the title page and committee signature page
• Your thesis committee chair’s and member’s signatures on the committee signature page
• You do not need to have Adam Willard sign your title page, the Chemistry Education Office will take care of that
• Full thesis with no signatures (including unsigned title page and thesis committee signature page)
• Title page and committee signature page with signatures via DocuSign

Accessing DocuSign

Thesis Hold Requests

Details about requesting a thesis hold are available here and the requests are made to different offices based on the type of request.

Written notification of patent holds and other restrictions must reach the Institute Archives before the thesis in question is received, as under normal circumstances, all theses are open and available for public inspection once they have been received by the Institute Archives.

Graduate Student Exit Interviews

In order to best serve the educational, scientific, and social needs of graduate students in the Chemistry Department, it is critically important that Departmental leadership be appropriately informed of issues of importance to graduate students, ideally on an ongoing basis. Graduate student exit interviews provide information that alert the Department to acute issues that affect graduate students and provide data for longitudinal assessments of graduate student experience within the program.Graduate exit interviews are administered to all graduate students departing the Chemistry Department. The exit interview applies equally to graduate students departing with completed degrees (Ph.D. and M.S.) and without degrees.

• Graduating students will be sent a list of interview questions by the Chemistry Education Office when the student joins the degree list. Instructions about scheduling a time for the in-person or virtual discussion will be included with other informational correspondence from the Chemistry Education Office regarding degree completion. Graduating students will perform their exit interview after the thesis defense so as to avoid making the interview an additional burden.
• For students departing the program without a degree, the interview questions and instructions for scheduling an in-person discussion will be sent by the Chemistry Education Office at the point in time that a date for termination of their appointment in Chemistry is determined.
• For the majority of departing students, this interview coincides with the end of the semester, but a rolling schedule of surveys is anticipated.

Postdoctoral/Research Specialist Appointments

If you plan to transition to a postdoctoral/research specialist appointment within the Department of Chemistry at MIT, please contact Jennifer Weisman and  Chemistry HR as soon as possible. Your final signed thesis must be submitted before a postdoc appointment can start. If you are an international student, it is extremely important that you start this process early to allow sufficient timing for visa processing. In addition to talking with Jennifer and HR, please consult with the International Students Office .

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.

Gonzalo Cao

Date: Monday, July 1, 2024 | 10:30am | Room: 2-361 | Zoom Link

Committee: Prof. Gigliola Staffilani (advisor and committee chair), Prof. Semyon Dyatlov and Prof. Larry Guth

Self-similar singularity formation and wellposedness theory for compressible fluids and dispersive PDE

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 | Zoom Link

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.

Shashi Gowda

Date: Thursday, April 25, 2024 | 10:00am | Room: 32-G882 | Zoom Link

Committee: Alan Edelman, Steven Johnson, John Urschel

Symbolic-numeric programming in scientific computing

Scientific programming languages should pursue two goals: closeness to mathematical notation, and the ability to express efficient numerical algorithms. To meet these goals simultaneously, languages use imperative surface syntaxes that mimick mathematical notation. However, mimicking does not make them the same—mathematics is declarative, pliable, and caters to exploratory human nature; but algorithms are imperative and must cater to machines. Hence, there is a fundamental limit to this approach and we leave the expressive power of the symbolic representation on the table.

In this thesis, we ask the question: How can symbolic and numerical modes of computing co-exist, one informing the other? As an answer, we develop a user-extensible system that lifts numerical code into symbolic expressions and can turn symbolic expressions back into high-quality numerical code at staged compilation time, essentially providing the scientific user a way to generate programs and to treat programs as the symbolic artifacts they are. We identified siloing of symbolic software into 3 categories (one can call them “symbolic-only”, “secretly symbolic”, “secretly numerical”) which currently each reproduce similar forms of symbolic capabilities, but cannot share code between each other. Our work demonstrates that this siloing is not essential and an ecosystem of symbolic-numeric libraries can thrive in symbiosis.

Our system is adaptable to any domain: users can define 1) Symbolic variables of any type 2) the set of primitive (symbolically indivisible) functions in the domain, 3) the propa- gation of partial information, and 4) pattern-based rewrites and simplification rules. There is a tendency in scientific computing to create a “compiler for every problem” starting from scratch every time. Every such effort erects its own towers of symbolic and numerical ca- pabilites. A system like ours eliminates this redundancy and lets every scientific user be a “compiler designer” without any prior knowledge of compiler development.

Alasdair Hastewell

Date: Thursday, April 18, 2024 | 10:30am | Room: 2-449 | 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 example of ADHM spaces. 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: Tuesday, April 30, 2024 | 3:30pm | Room: 2-255 | 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.

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Thesis Information

Upcoming thesis defenses.

If you are defending this term and do not see your information listed, please contact Sydney Miller in the APO.

Forming a Thesis Committee

When : Doctoral Students – After completing the written and oral exams and generally by the beginning of their third Year of study. Forming their committees at this stage will allow students to consult with all members of the committee during their studies and can provide additional advice and mentorship for them.

How : Register for thesis research under subject number 8.ThG, form a thesis committee, meet with full committee, and submit a formal thesis proposal to the department.

Thesis Committee Formation

Student should consult with their Research Supervisor to discuss the Doctoral Thesis Committee Proposal Form which will name the 3 required members of the Physics Doctoral Committee and a descriptive preliminary thesis title. 

Doctoral Committee must include 3 members with MIT Physics faculty appointments:

• Committee Chair: Research Supervisor from MIT Physics Faculty or Research Supervisor from outside MIT Physics + Co-Supervisor/Chair from MIT Physics Faculty
• Selected Reader: from MIT Physics Faculty (in the same/similar research area, selected by student and supervisor)
• Assigned Reader: from MIT Physics Faculty (in different research area, selected by the Department’s faculty Graduate Coordinator.)

The Form should include the names of the Student, Chair, and Selected Reader and a Thesis Title, when it is forwarded to the Academic Programs Office via email to [email protected] and Sydney will work with Faculty Graduate Coordinator Will Detmold , who will identify the Assigned Reader.

Following the consultation with their supervisor, the student should reach out to the proposed Selected Reader to secure an electronic signature or email confirmation in lieu of signature to serve on this committee. (Form should include either signature or date of email agreement.) It will take approximately 2-3 weeks before an Assigned Reader will be added and Sydney will provide an introduction to this final member of your Doctoral Committee. Please note: you may not form your committee and defend your thesis in the same semester.

Thesis Committee Meeting and Proposal

Once the Thesis Committee is established, the student should send all members a draft description of the proposed thesis topic and set up the first committee meeting with all members attending together in real time. A formal 2-page written Thesis Proposal should result from this important meeting and be sent to Sydney for the student’s academic record.  

Thesis Proposal

You should discuss your thesis research with your committee members all together in real time at your first committee meeting. Following this full discussion about your thesis topic, please write up your formal Thesis Proposal to reflect the mutually-agreed thesis plans and forward the Proposal to the graduate program at the APO using [email protected] for Sydney to document in the department’s academic records.

Thesis Research

Following the formation of the doctoral committee and submission of the thesis proposal, the student will continue to work on their thesis research in consultation with their Research Supervisor and other members of their Committee. This important communication paves the way for the thesis defense and degree completion.

When students are ready to defend, they should complete an ‘ Application for Advanced Degree ’ with the Registrar and schedule a thesis defense with all committee members attending in real time, whether in person or by video. Announcements for the defense will be coordinated by the Academic Programs Office and students should be in close contact with Sydney Miller during their final term or study.

Further details about this last stage of your studies will be available separately.

Thesis Defense

If there is even a slight possibility that you may finish this term, please complete an Application for Advanced Degree at the Registrar’s website at the beginning of the term. It is easy to remove your name if your plans change, but this timely step will avoid late fees!

Once you have scheduled your defense, please send this information to Sydney at [email protected] :

• Thesis Title:
• Committee Members:
• Meeting Details: (can be sent in the final week before the defense)

She will create the email notifications for our physics community and the MIT Events and Physics Calendar listings. This information you provide her is also used to generate the defense grade sheet for your defense.

Please send your committee members a thesis draft to help them prepare for your defense and plan to spend around two weeks making thesis revisions after your successful defense. The date you submit your thesis document to the department will determine whether it is for a Fall, Spring, or Summer degree.

Thesis Formatting

Archival copies of all theses must adhere carefully to principles specified by the MIT Libraries for formatting and submission. For complete information about how to format your thesis, refer to the  Specifications for Thesis Preparation .

Graduate Program Coordinator Sydney Miller can review your title page and abstract for accuracy before you submit the thesis. You may send these to her at  [email protected].

Required Signatures and Documentation

• Signatures:  The MIT Archives require an electronic PDF document and the Department needs a separate additional stand-alone title page with electronic/scanned signatures of   the student, research supervisor, and co-supervisor (if applicable). Theses are accepted by Associate Department Head, Professor  Lindley Winslow . Please send your documents to  [email protected]  and the APO staff will forward your thesis submitted to the MIT Library Archives.
• Thesis defense grade sheets:  Before accepting a PhD thesis, the Academic Programs Office must have a signed thesis defense grade sheet from the research supervisor indicating a “Pass” on the thesis defense.
• Thesis letter grade:  Before accepting an SM thesis, Academic Programs must have received a letter or email from the research supervisor, assigning a final thesis grade of A, B, or C.

Finalizing and Submitting your Thesis to MIT

Departments collect the thesis documents on behalf of the MIT Thesis Library Archives and Physics graduate students will submit their thesis to Sydney Miller.  Review overall information from MIT about  thesis specifications and format .

Please see the attached doctoral title page format for Physics and send your draft of the title/cover page and abstract to Sydney for review and any necessary edits. Once these are approved, please prepare the full document, with pagination appropriate for double-sided printing.

Theses may be completed and signed on any date of the year and the degree requirements are completed when the thesis is submitted. This is the final day of student status and payroll. (International students are eligible for Optional Practical Training starting on the following day.)

MIT awards degrees at the end of each term:

• Fall Term degree is in February. (Theses due second Friday in January.)
• Spring Term degree is in May. (Theses due second Friday in May.)
• Summer Term degree is in September. (Theses due second Friday in August.)

Thesis submissions are electronic files and you will submit the following to Sydney:

• A complete thesis document, without signatures
• A title page with electronic signatures from yourself, your supervisor (and co-supervisor, if required). Sydney will work with the Associate Head, Lindley Winslow , whose signature is required for the department and this will be added after you submit your document to the department/Sydney.
• A separate abstract page

Doctoral students also complete and submit the  Proquest/UMI form  (PDF), with attached title page and abstract (no signatures).

In addition to submitting your thesis to the department for the library archives, you may also  add your thesis to DSpace .

Digital Submission Guidelines

All theses are being accepted by the MIT Libraries in  digital form only . Digital theses are submitted electronically to the Physics Department, along with a separate signed title page. Students on the degree list will receive specific guidance about submission from the Academic Programs Office.

General Thesis Policies

All theses are archived in the MIT Libraries. An archival fee must be paid before a student’s final candidacy for a degree can be officially approved.

After all required materials have been submitted to the Academic Programs Office, a thesis receipt will be sent by email.

Thesis Due Dates

Check the MIT Academic Calendar for deadlines to submit your online degree application.

Thesis submission deadlines Graduating in May: Second Friday in May Graduating in September: Second Friday in August Graduating in February: Second Friday in January We strongly recommend that your defense be scheduled at least three weeks prior to the submission date. Consult with Academic Administrator Shannon Larkin to determine your thesis submission timeline.

Thesis FAQs

The information on this page is applicable for both PhD and Masters (with the exception of an Oral defense) degree candidates.

How do I submit a Thesis Proposal? When is it due?

Students register for thesis research units and assemble a thesis committee in the term following passing the Oral Exam.

The first step is for the student and research supervisor to agree on a thesis topic. An initial Graduate Thesis Proposal Cover Sheet (PDF) (Master’s Degree candidates should see process in section below) must be submitted to Academic Programs by the second week of the term.

The form requires

• an initial thesis title
• the name and signature of the research supervisor
• the name of one additional reader for the thesis committee agreed upon by the student and advisor

A third reader from the MIT Physics faculty, who is not in the same research area but whose background makes him or her an appropriate departmental representative on the committee, will be assigned by the Graduate Program Faculty Coordinator. If a student has a co-supervisor (because the main supervisor is from outside the MIT Physics faculty), the thesis committee will consist of four people: research supervisor, co-supervisor, selected reader, and assigned reader.

After the student is notified of the assigned reader, he or she should convene an initial thesis committee meeting within the same term. The student should also register for 8.THG beginning in this term, and in each term thereafter. 8.THG registration should be for up to 36 units, depending on whether the student is also still taking classes and/or receiving academic credit because of a teaching assistantship. All post-qual students should routinely register for a standard total 36 units.

Master’s degree candidates should complete an SM Thesis Proposal Cover Sheet (PDF). A second reader for the Master’s degree thesis committee is assigned by the Graduate Program Faculty Coordinator. Note that there is no public defense required for an SM degree.

See the Doctoral Guidelines for additional information.

I am going to graduate soon–what do I have to do in terms of paperwork etc.?

Please reference the Registrar’s complete graduation checklist . Students should reference this list at the START of the semester prior to graduation. Your research area’s administrative office and the Physics APO will also help you manage the final stage of your degree.

How do I get on/off the Degree List?

Fill out the Degree Application through the student section of WebSIS . Petitioning to be on the degree list for a particular commencement is required. Note that it is easier to be removed from the degree list to be added, so students are encouraged to apply for the degree list if there is any reasonable chance they will complete the PhD in the coming term.

The WebSIS degree list is used to communicate information about thesis defense announcements and grade sheets, thesis formats, and completion dates, so it is important to file a degree application to be on the list in a timely way. The standard deadline for filing a degree application without being assessed a late fee is the Friday of the first week of the term in which a student anticipates graduating. Removing oneself from the degree list requires an email to Academic Programs .

When is my thesis due? Can I get an extension?

Students can defend and submit their thesis on any dates that work for their committees, but MIT confers degrees only 3 times each year: in May, September and February. Thesis submission deadlines Graduating in May: Second Friday in May Graduating in September: Second Friday in August Graduating in February: Second Friday in January We strongly recommend that your defense be scheduled at least three weeks prior to the submission date. Consult with Academic Administrator Shannon Larkin to determine your thesis submission timeline.

Note that these deadlines are already more generous that the Institute thesis deadline. Students desiring extensions should contact the Academic Administrator, Shannon Larkin .

How do I find a room for my Thesis Defense?

Many Divisions have conference and/or seminar rooms which can be used for oral exams and defenses. These locations are recommended to keep your Thesis Defense comfortable and in familiar territory. Students who cannot book a room in their research area should contact Sydney Miller in the Physics APO to check availability of a Physics departmental conference room (often difficult to schedule due to heavy demand) or to help schedule a classroom through the Registrar’s Office.

When I submit my thesis to Physics Academic Programs, what do I need to bring?

Please refer to the Graduate Thesis Submission Guidelines .

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PhD Program

Program overview.

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Rigorous, discipline-based research is the hallmark of the MIT Sloan PhD Program. The program is committed to educating scholars who will lead in their fields of research—those with outstanding intellectual skills who will carry forward productive research on the complex organizational, financial, and technological issues that characterize an increasingly competitive and challenging business world.

Start here.

Learn more about the program, how to apply, and find answers to common questions.

Admissions Events

Check out our event schedule, and learn when you can chat with us in person or online.

Start Your Application

Visit this section to find important admissions deadlines, along with a link to our application.

Click here for answers to many of the most frequently asked questions.

PhD studies at MIT Sloan are intense and individual in nature, demanding a great deal of time, initiative, and discipline from every candidate. But the rewards of such rigor are tremendous:  MIT Sloan PhD graduates go on to teach and conduct research at the world's most prestigious universities.

PhD Program curriculum at MIT Sloan is organized under the following three academic areas: Behavior & Policy Sciences; Economics, Finance & Accounting; and Management Science. Our nine research groups correspond with one of the academic areas, as noted below.

MIT Sloan PhD Research Groups

Behavioral & policy sciences.

Economic Sociology

Institute for Work & Employment Research

Organization Studies

Technological Innovation, Entrepreneurship & Strategic Management

Economics, Finance & Accounting

Accounting  

Management Science

Information Technology

System Dynamics  

Those interested in a PhD in Operations Research should visit the Operations Research Center .  

PhD Program Structure

Additional information including coursework and thesis requirements.

MIT Sloan Predoctoral Opportunities

MIT Sloan is eager to provide a diverse group of talented students with early-career exposure to research techniques as well as support in considering research career paths.

Rising Scholars Conference

The fourth annual Rising Scholars Conference on October 25 and 26 gathers diverse PhD students from across the country to present their research.

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The goal of the MIT Sloan PhD Program's admissions process is to select a small number of people who are most likely to successfully complete our rigorous and demanding program and then thrive in academic research careers. The admission selection process is highly competitive; we aim for a class size of nineteen students, admitted from a pool of hundreds of applicants.

What We Seek

• Outstanding intellectual ability
• Excellent academic records
• Previous work in disciplines related to the intended area of concentration
• Strong commitment to a career in research

MIT Sloan PhD Program Admissions Requirements Common Questions

Dates and Deadlines

Admissions for 2024 is closed. The next opportunity to apply will be for 2025 admission. The 2025 application will open in September 2024. 

More information on program requirements and application components

Students in good academic standing in our program receive a funding package that includes tuition, medical insurance, and a fellowship stipend and/or TA/RA salary. We also provide a new laptop computer and a conference travel/research budget.

Funding Information

Throughout the year, we organize events that give you a chance to learn more about the program and determine if a PhD in Management is right for you.

PhD Program Events

June phd program overview.

During this webinar, you will hear from the PhD Program team and have the chance to ask questions about the application and admissions process.

July PhD Program Overview

August phd program overview, september 12 phd program overview.

Complete PhD Admissions Event Calendar

Unlike formulaic approaches to training scholars, the PhD Program at MIT Sloan allows students to choose their own adventure and develop a unique scholarly identity. This can be daunting, but students are given a wide range of support along the way - most notably having access to world class faculty and coursework both at MIT and in the broader academic community around Boston.

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Profiles of our current students

MIT Sloan produces top-notch PhDs in management. Immersed in MIT Sloan's distinctive culture, upcoming graduates are poised to innovate in management research and education.

Academic Job Market

Doctoral candidates on the current academic market

Academic Placements

Graduates of the MIT Sloan PhD Program are researching and teaching at top schools around the world.

view recent placements 

MIT Sloan Experience

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The PhD Program is integral to the research of MIT Sloan's world-class faculty. With a reputation as risk-takers who are unafraid to embrace the unconventional, they are engaged in exciting disciplinary and interdisciplinary research that often includes PhD students as key team members.

Research centers across MIT Sloan and MIT provide a rich setting for collaboration and exploration. In addition to exposure to the faculty, PhD students also learn from one another in a creative, supportive research community.

Throughout MIT Sloan's history, our professors have devised theories and fields of study that have had a profound impact on management theory and practice.

From Douglas McGregor's Theory X/Theory Y distinction to Nobel-recognized breakthroughs in finance by Franco Modigliani and in option pricing by Robert Merton and Myron Scholes, MIT Sloan's faculty have been unmatched innovators.

This legacy of innovative thinking and dedication to research impacts every faculty member and filters down to the students who work beside them.

Faculty Links

• Accounting Faculty
• Economic Sociology Faculty
• Finance Faculty
• Information Technology Faculty
• Institute for Work and Employment Research (IWER) Faculty
• Marketing Faculty
• Organization Studies Faculty
• System Dynamics Faculty
• Technological Innovation, Entrepreneurship, and Strategic Management (TIES) Faculty

Student Research

“MIT Sloan PhD training is a transformative experience. The heart of the process is the student’s transition from being a consumer of knowledge to being a producer of knowledge. This involves learning to ask precise, tractable questions and addressing them with creativity and rigor. Hard work is required, but the reward is the incomparable exhilaration one feels from having solved a puzzle that had bedeviled the sharpest minds in the world!” -Ezra Zuckerman Sivan Alvin J. Siteman (1948) Professor of Entrepreneurship

Sample Dissertation Abstracts - These sample Dissertation Abstracts provide examples of the work that our students have chosen to study while in the MIT Sloan PhD Program.

We believe that our doctoral program is the heart of MIT Sloan's research community and that it develops some of the best management researchers in the world. At our annual Doctoral Research Forum, we celebrate the great research that our doctoral students do, and the research community that supports that development process.

The videos of their presentations below showcase the work of our students and will give you insight into the topics they choose to research in the program.

Attention To Retention: The Informativeness of Insiders’ Decision to Retain Shares

2024 PhD Doctoral Research Forum Winner - Gabriel Voelcker

Watch more MIT Sloan PhD Program  Doctoral Forum Videos

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• CSE PhD Overview
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• Program Overview and Curriculum
• For New CCSE Students
• Terms of Reference

A listing of CSE PhD and SM thesis titles and authors can be found at DSpace@MIT . Note, SM theses completed before September 2020 will be classified under Computation for Design and Optimization (CDO), CSE’s original program name.

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Graduate Theses

Theses by department.

• Comparative Media Studies
• Computation for Design and Optimization
• Computational and Systems Biology
• Department of Aeronautics and Astronautics
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• Department of Urban Studies and Planning
• Engineering Systems Division
• Harvard-MIT Program of Health Sciences and Technology
• Institute for Data, Systems, and Society
• Media Arts & Sciences
• Operations Research Center
• Program in Real Estate Development
• Program in Writing and Humanistic Studies
• Science Writing
• Sloan School of Management
• Supply Chain Management
• System Design & Management
• Technology and Policy Program

Recent Submissions

Heat transfer coefficients in a falling film condenser 

A criminal courts, prison and hospital building , wave length measurements in the spectrum of the neodymium arc .

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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 .

Events Calendar

Physics PhD Thesis Defense: Silviu-Marian Udrescu

Friday, June 14, 2024 at 9:00am

Building 26, Kolker Room (26-414) 60 VASSAR ST, Cambridge, MA 02139

Dear Colleagues,

''Radioactive atoms and molecules for fundamental physics '' Presented by Silviu-Marian Udrescu

Date: Friday, June 14, 2024 Time: 9 am Location: Kolker Room #26-414

Committee:   Ronald Fernando Garcia Ruiz, Martin Zwierlein, Long Ju

Best of luck to Silviu!

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Through econometrics, Isaiah Andrews is making research more robust

When you read about a new study, you may wonder: How accurate are these results? MIT economist Isaiah Andrews PhD ’14 often asks that as well, especially about social sciences research. Unlike most of us, though, Andrews’ job involves answering that question.

Andrews, a professor in MIT’s Department of Economics, is an expert in econometrics, the study of the methods used in economics. But the purpose of his specialty defies simple boundaries. After all, the point of refining research methods is to make applied studies better — and to better grasp their limits.

“There are many fields in economics that answer socially significant questions,” Andrews says. “There are things it would be good for us to understand, but I often find myself interested in how sure we are about them. To what extent do we know the things we think we know? To what extent is there more to know, based on the uncertainty and degree of confidence? These issues of uncertainty matter because the answers to the substantive questions matter.”

Andrews’ core contributions to economics very much involve uncertainty and confidence. He first became known for research on “weak identification,” settings where key variables do not yield much information about the issues being studied. And he has published notable work about the challenges of building economic models.

Andrews’ work also illuminates larger ideas about how we use data. His most recent published paper examines the “winner’s curse” in the social sciences — the idea that programs testing well one time are too often chosen for implementation, when sometimes they performed well purely by chance, and are likely to perform worse the next time they are tried out.

Another major Andrews paper, from 2019, analyzed how much publication bias exists in academic journals — which can lean toward publishing dramatic findings rather than equally valid null results, as replication studies, in part, can reveal.

At times, Andrews’ work seems like the social science equivalent of an X-ray machine: He scans studies to look for problems under the surface. But Andrews does not only look for problems; he develops techniques to prevent them in the first place. In typical Andrews fashion, his papers on the winner’s curse and on replication bias both offer new methods for avoiding these pitfalls. 

“It’s important to work on these tools because the tools are going to be used on important things,” Andrews says. “If you have a beautiful tool and it’s never used, is it a tool, or a work of art?”

Andrews is recognized as a leading-edge practitioner in his field. In 2021, he was given the John Bates Clark Medal, awarded annually by the American Economic Association to the best economist under the age of 40. In 2020, he was granted a prestigious MacArthur Fellowship. With his career flourishing, Andrews rejoined the MIT faculty last year.

Career-changing conversation

Andrews grew up in the Boston area, in a family where both of his parents had earned PhDs in economics. While Andrews was not always set on becoming an economist, he did take advanced courses in the subject as an undergraduate at Yale University, where he graduated summa cum laude. He then entered the doctoral program at MIT.

At the time, in 2009, after the financial-sector meltdown and related recession, a lot of attention in economics was directed toward finance and macroeconomics, but Andrews did not feel compelled to study those topics.

“I didn’t feel they were such a good fit in terms of the style of work that appealed to me,” Andrews says. “I was finding econometrics-y questions very interesting.”

At one MIT Department of Economics function, Andrews started talking to Anna Mikusheva, an econometrician on the Institute faculty. By the end of the event, Mikusheva had suggested Andrews help with some research she was working on.

“The research assistant role for Anna turned into a joint project and I found my interest continuing to be drawn to these questions,” Andrews says. “So by virtue of that, that’s where my work went.”

Mikusheva and Andrews co-authored a high-profile series of papers on weak identification that wound up getting published soon after he received his PhD from the Institute in 2014. After spending a couple of years as a junior fellow in the Harvard Society of Fellows, Andrews joined the MIT faculty in 2016. He moved to Harvard University in 2018, then returned to MIT last summer.

As Andrews’ career has evolved, his wide-ranging work has often involved productive research partnerships, including papers co-authored Mikusheva, Matthew Gentzkow and Jesse M. Shapiro, Toru Kitagawa and Adam McCloskey, and Maximilian Kasy.

At all turns, Andrews stays focused on questions about the certainty (or uncertainty) involved in economic analysis and the degree of confidence (or lack thereof) we might have as a result.

“The worst scenario is when the data tells us very little, but we’re wrongly overconfident and think the data is telling us a lot,” Andrews says.

Making numbers more useful

To a consequential degree, Andrews also finds motivation in particular research problems. His recent paper (with Kitagawa) and McCloskey on the “winner’s curse” both introduces a new technique for estimating results and then applies it to a major research project on the social mobility of different U.S. neighborhoods, initiated by economists Raj Chetty and Nathaniel Hendren. Andrews’ conclusion: The Chetty/Hendren findings hold up well, suggesting social programs can productively use those results.

“The thing that matters for society is what is it we all do with those numbers,” Andrews says. “If we can think about what makes numbers more useful for people downstream, it’s important.”

Research is hardly all Andrews spends his time on. He has a long-running commitment to teaching, working with both undergraduates and graduate students, and as a PhD candidate in 2014, won MIT’s Robert M. Solow Prize for Excellence in Reasearch and Teaching.

“MIT students are very smart, so if you can help them frame a question the right way, it’s important,” Andrews says. “Ten years down the road, they may not retain the exact answer, but if they retain the framing of the question, they can work their way to the correct answer.”

In the MIT Department of Economics, where working productively with graduate students is a point of emphasis, Andrews now finds himself in the position Mikusheva was in, a decade ago, when she was encouraging him to follow his core intellectual interests.

“The graduate mentoring piece is very, very important,” Andrews says. “If you look at the social impact of an hour of my time, I feel the highest marginal product things I do are around advising. These are extremely capable people where a little bit of input or redirect can have big benefits down the road for them, and then hopefully the things they are doing are useful, and will benefit society.”

On all fronts, then, Andrews keeps trying to refine our knowledge about the extent of our knowledge. Summing up his work, Andrews offers his own epigram about the nature of his research.

“I would like to understand the extent to which we understand things,” Andrews says. 

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This architect is cutting up materials to make them stronger and lighter

Emily Baker hopes her designs can make it cheaper and easier to build stuff in disaster zones or outer space.

• Sofi Thanhauser archive page

As a child, Emily Baker loved to make paper versions of things: cameras, a spaceship cockpit, buildings for a town in outer space.

It was a habit that stuck. Years later, studying architecture in graduate school at the Cranbrook Academy of Art in Michigan, she was playing around with some paper and scissors. It was 2010, and the school was about to buy a CNC plasma cutter, a computer-controlled machine capable of cutting lines into sheets of steel. As she thought about how she might experiment with it, she made a striking discovery.

By making a series of cuts and folds in a sheet of paper, Baker found she could produce two planes connected by a complex set of thin strips. Without the need for any adhesive like glue or tape, this pattern created a surface that was thick but lightweight. Baker named her creation Spin-Valence . Structural tests later showed that an individual tile made this way, and rendered in steel, can bear more than a thousand times its own weight. 

In chemistry, spin valence is a theory dealing with molecular behavior. Baker didn’t know of the existing term when she named her own invention—“It was a total accident,” she says. But diagrams related to chemical spin valence theory, she says, do “seem to have a network of patterns that are very similar to the tilings I’m working with.” 

Soon, Baker began experimenting with linking individual tiles together to produce a larger plane. There are perhaps thousands of geometric cutting patterns that can create these multiplane structures, and she has so far discovered only some of them. Certain patterns are stronger than others, and some are better at making curved planes. 

Baker uses software to explore each pattern type but continues to work with cut paper to model possibilities. The Form Finding Lab at Princeton is now testing various tiles under tension and compression loads, and the results have already proved incredibly strong. 

Baker is also exploring ways to use Spin-Valence in architecture and design. She envisions using the technique to make shelters or bridges that are easier to transport and assemble following a natural disaster, or to create lightweight structures that could be packed with supplies for missions to outer space. (Closer to home, her mother has begun passing along ideas to her quilting group; the designs bear a strong resemblance to quilt patterns.)

“What I find most exciting about the system is the way it adds stiffness to something that was previously very flexible,” says Isabel Moreira de Oliveira, a PhD candidate in civil engineering at Princeton, who is writing her dissertation on Spin-Valence and testing which shapes work best for specific applications. “It entirely changes the behavior of something without adding material to it.” Plus, she adds, “you can ship this flat. The assembly information is embedded in how it’s cut.” This could help reduce transportation costs and lower carbon emissions generated from shipping. 

Baker grew up in Alabama and Arkansas, the daughter of a librarian and a chemical engineer at Eastman Kodak. Everybody in the family made things by hand—her mother taught her how to sew, and her father taught her how to work with wood. In high school, she took some classes in the school’s agricultural program, including welding, where she had a particularly supportive teacher. “I’ll tell you who the best two welders in the class are gonna be right now,” she recalls him saying, as he pointed at her and the only other female student. And, she says, “it was true. We picked it up a little faster than the guys. It was really empowering.”

Baker went on to study chemical engineering at the University of Arkansas in Fayetteville before she switched to architecture, drawn to the more tactile work. After five years at a small architecture firm in Jackson, Mississippi, she enrolled at Cranbrook, where she sensed she would have the space and tools to experiment. She now teaches in the architecture program at the University of Arkansas.

No doubt her experience in high school welding class aided in a more recent collaboration. Together with her UA colleague Edmund Harriss, an assistant professor of mathematics and art, she has developed Zip-Form —a system for welding and bending two sheets of steel together to make complex 3D curves using low-cost tools and easily learned skills. 

As a process, it is “a physical manifestation of integrating differential properties of the curve,” Harriss says. “The way the mathematical theory links to manufacturing process in Zip-Form is incredibly clean and elegant.” He explains that Baker’s willingness to engage seriously with the mathematics sets her apart from other architects he has worked with: “I think often people get intimidated by the mathematics and try to fall back on their expertise to say where the mathematics isn’t working.” Baker wasn’t like that. 

Like Spin-Valence, Zip-Form has potential applications in construction. Shortly after developing the technique, Baker met Mohamed Ismail, now an assistant professor of architecture at the University of Virginia, who was then a PhD student at MIT. He was working on low-cost, low-­carbon structural systems for housing in developing countries. When Ismail learned that Baker and Harris had found a way to make complex 3D structures out of flat sheets, his mind immediately went to concrete. A system like this, he says, is “exactly the kind of thing that is necessary when you’re trying to build complex concrete formwork [molds to pour the concrete into] in places where you don’t have a robotic arm or 3D printer.” 

In a project they worked on together, Baker and Ismail used Zip-Form to create a mold for a 16-foot prototype curved beam that’s more environmentally sustainable than a traditional beam, reducing the total carbon emissions associated with resource extraction, production, transport and other stages in the typical life cycle of a beam by 40%. 

While most concrete buildings use vastly more material than is structurally necessary, curved beams save concrete by using material only where it is needed to bear a structural load. Concrete is responsible for approximately 8% of total global carbon emissions, but it is also desperately needed to build housing, especially in places like India and Africa, where the population is forecast to grow rapidly in the next 20 years. Zip-Form demands more labor than more automated processes, but the equipment it uses is more affordable. 

Ismail and Baker are now working with a fabrication company in Kenya to demonstrate to real estate developers and an African housing nonprofit that this technology is competitive on price with traditional methods, and thus has a key role to play in affordable construction. The construction industry in the US can be mind-numbingly slow to adopt new techniques, Baker and Ismail both say, but they believe Zip-Form can easily be brought into building projects, using tools and materials that are already available. 

Zip-Form has creative potential, too. Danielle Hatch , an artist known for large-scale fabric installations, is using the system to make a public sculpture in Arkansas inspired by the movement of ribbons on the dancers she saw at a Hispanic cultural festival. “How could I evoke that sense of lightness and play, with metal?” she wondered. Zip-Form allowed her to make steel that she describes as “lyrical.” 

Baker has been inspired by the work of R. Buckminster Fuller, the polymath known for popularizing the geodesic dome—and for turning his mind to everything from affordable housing and transportation to renewable energy. She has studied his story closely, especially reflecting on the gaps between the broad scope of his thought—which often sought to revolutionize entire systems—and the limited real-world changes that resulted from his ideas. “Is there something I should have learned from his life and experience?” she wonders. 

Like Fuller, whose work extended far beyond architecture to consider the ways people relate to one another and to materials, Baker doesn’t think just about physical forms but about how people build, live, and manufacture—and the hierarchies that determine who does what. She thinks of architecture as always being in conversation with the body of the builder. A brick, she points out, is an excellent example because it’s the perfect size for a worker to hold while slathering it with mortar. Baker wants the tools she creates to be just as practical.

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