Doctorate

Application Deadlines

Fall: Dec 15
Spring: n/a

Summer: n/a

School/Department

Mathematics
Program Director

Fulton Gonzalez
Contact

gradadmissions@tufts.edu
Format

On-campusCommitment Options

Full-timeAverage Duration

Varies
Credits

Varies
All our professors are active in research, which provides many choices of research areas for our doctoral students. The department has numerous research clusters constituting particular areas of strength, including:

- Algebra, Representation Theory, Algebraic Geometry
- Analysis and PDEs
- Computational and Applied Mathematics
- Dynamical Systems
- Geometric Group Theory and Topology
- Probability

At the same time, our faculty is devoted to teaching and mentoring of students. Our graduate courses and research seminars provide a great atmosphere for collaborative learning and research.

Our PhD in Mathematics consists of preliminary coursework and study, qualifying exams, a candidacy exam with an advisor, and creative research culminating in a written dissertation and defense. All doctoral students must also do some teaching on the way to the PhD.

Upon graduation, you will have an in-depth understanding and mastery of the literature in at least one particular subfield of mathematics (and applied mathematicians will also demonstrate mastery of their area of application). You will also have the skills to develop research proposals, carry out independent research and present and defend your research work in oral, written and graphic forms. Our students also gain valuable teaching experience and learn how to conduct a classroom and grade undergraduate work. Perhaps most importantly, you will develop an understanding of your professional and ethical responsibilities as well as an appreciation of the impact of mathematics in the social context.

Graduates of the PhD Program have gone on to work in the following positions: staff scientist, senior software engineer, technical writer, and research engineer. Others have gone on to academic positions such as postdocs and tenure-track professor positions.

- Application fee
- Resume/CV
- Personal Statement (750 words or less): This statement should include your reasons for wanting to pursue graduate study at Tufts and within the Department of Mathematics. Discuss what makes mathematics exciting to you. In addition, please include a description of a math problem or topic that challenged you early in your undergraduate experience. Discuss how you, perhaps with the help of others, overcame those difficulties to understand the problem better and how you presently understand it. Do not be afraid to choose something from a "basic" class like calculus. Your application materials already speak to your achievements; here instead we are interested in hearing about how you have developed your interest in mathematics. Please limit your statement to 750 words or fewer.
- Official TOEFL, IELTS, or Duolingo English Test, if applicable
- Transcripts
- Three letters of recommendation

**Please note that our department alternates recruiting in-coming classes that are focused on either applied or pure mathematics. For the Fall 2023 admissions (matriculation in September 2023), we are focusing on students interested in areas of pure mathematics.**

See Tuition and Financial Aid information for GSAS Programs.

Average Salary: **$90K - $110K**

Average Age: **27**

*Sources: GSAS-SOE Graduate Exit Survey 2020 - 2021 and Academic Analytics (Alumni Insights)

Research Interests:
Noncommutative harmonic analysis, representations of Lie groups, integral geometry, and Radon transforms

Research Interests:
Scientific computing and numerical analysis: Efficient computational methods for complex fluids, plasma physics, electromagnetism and other physical applications.

Professor, Mathematics

Professor, Computer Science

Professor, Physics & Astronomy

Research Interests:
Applied dynamical systems, applied probability theory, kinetic theory, agent-based modeling, mathematical models of the economy, theoretical and computational fluid dynamics, complex systems science, quantum computation
Current research emphasis is on mathematical models of economics in general, and agent-based models of wealth distributions in particular. The group's work has shed new light on the tendency of wealth to concentrate, and has discovered new results for upward mobility, wealth autocorrelation, and the flux of agents and wealth. The group's mathematical description of the phenomenon of oligarchy has also shed new light on functional analysis in general and distribution theory in particular.
Secondary projects include new directions in lattice Boltzmann and lattice-gas models of fluid dynamics, kinetic theory, and quantum computation.

Professor, Mathematics

Research Interests:
Anomalous diffusion, mathematical neuroscience

Research Interests:
Geometric group theory, low-dimensional topology, CAT(0) spaces

Professor, Mathematics

Professor, Tisch College

John Dibiaggio Professor of Citizenship and Public Service, Mathematics

Research Interests:
Geometry of groups and surfaces

Professor, Mathematics

Research Interests:
Dynamical systems: Hyperbolicity, invariant foliations, geodesic flows, contact flows, and related topics
—
Hasselblatt's research, undertaken with colleagues from several continents, is in the modern theory of dynamical systems, with an emphasis on hyperbolic phenomena and on geometrically motivated systems. He also writes expository and biographical articles, writes and edits books, and organizes conferences and schools. His publication profile can be viewed at https://mathscinet.ams.org/mathscinet/author?authorId=270790 (with a subscription). Former doctoral students of his can be found in academic positions at Northwestern University, George Mason University, the University of New Hampshire, and Queen's University as well as among the winners of the New Horizons in Mathematics Prize.

Research Interests:
Scientific computing and numerical analysis; Parallel multigrid and multilevel methods for large-scale coupled systems; Efficient numerical methods for reservoir simulation, fluid-structure interaction, and other applications.

Professor, Mathematics

William Walker Professor of Mathematics, Mathematics

Professor, Computer Science

Research Interests:
Numerical Linear and Multilinear Algebra, Scientific Computing, Image Reconstruction and Restoration

Research Interests:
The structure and representations of algebraic groups

Professor, Mathematics

Chair, Mathematics

Research Interests:
Geometric Group Theory/Topology

Professor, Mathematics

Robinson Professorship in Mathematics, Mathematics

Research Interests:
Tomography is an inverse problem, and the goal of tomography is to map the interior structure of objects using indirect data such as from X-rays. Integral geometry is the mathematics of averaging over curves and surfaces, and it is the pure math behind many problems in tomography. Integral geometry combines geometric intuition, harmonic analysis, and microlocal analysis (the analysis of singularities and what Fourier integral operators do to them). I have proven support theorems and properties of transforms integrating over hyperplanes, circles and spheres in Euclidean space and manifolds.
Because of the mentorship of Tufts physics professor and tomography pioneer, Allan Cormack (Tufts' only Nobel Laureate) I developed X-ray tomography algorithms for the nondestructive evaluation of large objects such as rocket bodies, and this motivated my research in limited data tomography
In limited data tomography problems, some tomographic data are missing. I developed a paradigm to describe which features of the object will be visible from limited tomographic data and which will be invisible (or difficult to reconstruct). I proved the paradigm using microlocal analysis. Often artifacts are added to tomographic reconstructions from limited data, and colleagues and I recently used microlocal analysis to prove the cause of these added artifacts and to predict where they will occur.
Collaborators and I have developed local algorithms for electron microscopy, emission tomography, Radar, Sonar, and ultrasound. In each case we use microlocal analysis to determine the strengths and weaknesses of the problem and to refine and improve the algorithms.

Professor, Mathematics

Research Interests:
To each point on a curve, one can often associate in a natural way a line or plane (or higher dimensional linear variety) that moves with the point in the curve. This set of linear spaces is called a vector bundle. Vector bundles appear in a variety of questions in Physics (like the computation of Gromov-Witten invariants) . Moreover, they provide new insights into old mathematical problems and have been used to give beautiful proofs to long standing conjectures as well as striking counterexamples to some others.

Research Interests:
Algebraic geometry, topology, and differential geometry

Research Interests:
Hyperbolic manifolds and orbifolds, low-dimensional topology, group actions

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