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Core Faculty
Kim Ruane
Professor and Department Chair of Mathematics
Geometric Group Theory/Topology
James Adler
Professor
Scientific computing and numerical analysis: Efficient computational methods for complex fluids, plasma physics, electromagnetism and other physical applications.
Jasmine Bhullar
Norbert Wiener Fellow
Bruce Boghosian
Professor
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.
Christoph Borgers
Professor
Anomalous diffusion, mathematical neuroscience
Corey Bregman
Assistant Professor
Geometric group theory, low-dimensional topology, CAT(0) spaces
Christopher Coscia
Lecturer
Enumerative and probabilistic combinatorics, graph theory, Markov chain Monte Carlo
Christopher Dock
Norbert Wiener Fellow
I work primarily in harmonic analysis, matrix analysis, and frame theory, with applications to signal processing, compressed sensing, machine learning, and the measurement of quantum systems.
Moon Duchin
John DiBiaggio Professor of Citizenship and Public Service
Geometry of groups and surfaces
Zachary Faubion
Senior Lecturer
Set Theory, specifically forcing elementary embeddings and large cardinal axioms
Fulton Gonzalez
Professor
Noncommutative harmonic analysis, representations of Lie groups, integral geometry, and Radon transforms
Boris Hasselblatt
Professor
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.
Xiaozhe Hu
Associate Professor
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.
Misha Kilmer
William Walker Professor of Mathematics
Numerical Linear and Multilinear Algebra, Scientific Computing, Image Reconstruction and Restoration
Arkadz Kirshtein
Norbert Wiener Fellow
PDE analysis and computations, complex fluids, numerical analysis, mathematical modeling in physics and engineering, mathematical modeling in biology and medicine, bioinformatics, fluid dynamics, finite difference schemes.
Robert Lemke-Oliver
Associate Professor
Number theory
Carl Lian
Norbert Wiener Fellow
Ian Manly
Lecturer
George McNinch
Professor
The structure and representations of algebraic groups
James Murphy
Assistant Professor
Machine learning, harmonic analysis, statistical learning, graph theory, data science, computational mathematics, image processing, signal processing
Kasso Okoudjou
Professor
Time-frequency analysis, pure, applied, and numerical harmonic analysis; analysis and differential equations on fractals and graphs.
Abani Patra
Director of the Data Intensive Studies Center and Stern Family Professor
computational sciences, data driven modeling
Samantha Petti
Assistant Professor
Eric Quinto
Robinson Professor of Mathematics
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.
Lorenzo Ruffoni
Norbert Wiener Fellow
Geometry and Topology, Geometric Group Theory
David Smyth
Associate Professor
Algebraic Geometry
Abiy Tasissa
Assistant Professor
Matrix completion, compressive sensing, distance geometry
Montserrat Teixidor I Bigas
Professor
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.
Loring Tu
Professor
Algebraic geometry, topology, and differential geometry
Genevieve Walsh
Professor
Hyperbolic manifolds and orbifolds, low-dimensional topology, group actions
Affiliate Faculty
Shuchin Aeron
Associate Professor
data science, statistical signal processing, inverse problems, compressed sensing, information theory, convex optimization, machine learning, algorithms for geophysical signal processing, compressed sensing architectures and evaluation, video and image data acquisition and processing
Lenore Cowen
Professor
data science, graph algorithms, distributed algorithms, approximate routing, classification and clustering for high-dimensional data, coloring and its generalizations, computational molecular biology
Luis Dorfmann
Professor
Mathematical models of material behavior; Nonlinear magneto- and electromechanical interactions; Biomechanics of soft materials; Rubber elasticity and inelasticity
Andrew Izsak
Professor and Department Chair of Education
The psychology of mathematical thinking, teachers' and students' understanding and use of inscriptions, multiplicative reasoning, applications of psychometric modeling for assessment and research in mathematics education.
Eric Miller
Professor
Signal and image processing, tomographic image formation and object characterization, inverse problems, regularization, statistical signal and imaging processing, and computational physical modeling. Applications explored include medical imaging and image analysis, environmental monitoring and remediation, landmine and unexploded ordnance remediation, and automatic target detection and classification.
Vladimir Podolskii
Associate Professor
Computational complexity, logical foundations of computer science, tropical geometry
Paola Sebastiani
Professor
Diane Souvaine
Professor
computational geometry, design and analysis of algorithms, computational complexity
Part-time Faculty
Joshua Enxing
Lecturer
Linda Garant
Lecturer
Curtis Heberle
Lecturer
Emeriti Faculty
Mary Glaser
Senior Lecturer Emerita
Undergraduate education; Discrete Mathematics
Marjorie Hahn
Professor Emerita
Zbigniew Nitecki
Professor Emeritus
Dynamical systems, especially in dimensions 1 and 2; braids; combinatorial/geometric group theory; graphs
Richard Weiss
William Walker Professor of Mathematics Emeritus
Group theory, especially buildings and other geometric aspects of group theory