Research in Drexel University's Department of Mathematics builds on a connected community of faculty, graduate and undergraduate students who combine expertise from different disciplines. Mathematics faculty examine broad fields of mathematical theory, technique, and application across a wide range of topic areas, including: partial differential equations, dynamical systems, mathematical neuroscience, numerical analysis, approximation theory, combinatorics, functional analysis, representation theory, geometry and topology, matrix and operator theory, inverse problems, and stochastic analysis.
Our research faculty engage in abstract mathematical training that enables them to apply mathematical techniques to areas such as control theory, mirror design, computer graphics, data compression, fluid mechanics, and modeling biological phenomena. In addition, faculty research receives ongoing support from the National Institutes of Health, the National Science Foundation, and the National Security Agency.
Drexel's Math Department hosts lively research seminars and colloquium series led by top scholars who present innovative mathematical ideas. The Math Department's annual Distinguished Speaker series features a renowned expert who presents on original and ongoing mathematics research.
Faculty Research Areas
Drexel's mathematics faculty scholars conduct leading research at the forefront of a wide range of compelling mathematics and statistics subfields.
Applied and Computational Mathematics
Drexel faculty use mathematics to study problems arising from a wide range of application areas, including –but not limited to– fluid dynamics, electro-magnetics, optics, materials science, neuroscience and other biological problems, and economics and game theory. The Department of Mathematics has many faculty experts in aspects of the theory and application of partial differential equations and dynamical systems, which they bring to bear on problems from these areas. Our faculty engage with all the steps of making mathematics useful for real-world problems, from working closely with applied practitioners, participating in modeling real situations, making theoretical predictions from models, computationally simulating outcomes of the models, and making subsequent refinements. Theoretical work includes proving that models are specified well enough to guarantee that solutions to the model exist, and proving that certain behaviors, desirable or otherwise, occur among the solutions. Computationally, this includes developing, implementing, and analyzing algorithms for the efficient and large-scale computation of these problems.
Seminar: Applied Math/Partial Differential Equation
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mathematical analysis; fluid dynamics; nonlinear partial differential equations; boundary integral methods |
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Application of the Differential Calculus of moving surfaces and Variational Calculus, with heavy emphasis on computation, to problems in Bioengineering, low temperature Physics, Quantum Mechanics and Elasticity |
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Biomathematics, Dynamical Systems, Ordinary and Partial Differential Equations |
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Manifold; Geometric optics; Robotics; Inverse problems; Optical design; Blind spot |
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Dynamical systems, large networks, mathematical neuroscience
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Applied PDEs and numerical analysis, in particular homogenization theory, inverse problems, and related asymptotic and numerical methods |
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Applied Mathematics, Numerical Analysis, Symbolic Computation, Differential Geometry, Modeling of Nonlinear Optical Phenomena, Mathematical Physics |
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Discrete Mathematics; Graph Theory |
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Einstein’s General Theory of Relativity;
Astrophysics;
Cosmology
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nonlinear waves; partial differential equations; dynamical systems; lattice differential equations; coherent structures |
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Inverse problems; partial differential equations; scattering theory; nonlocal operators; non-scattering phenomena
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Applied Analysis, Applied Geometry, Multiscale Methods |
Functional Analysis and Operator Theory
Linear algebra, and its various generalizations in the fields of functional analysis and operator theory, plays a substantial role in contemporary society, including statistics, machine learning and general applications of reproducing kernel Hilbert Spaces. Drexel's Mathematics Department features faculty experts in matrix analysis, singular integral operators, complex variables, Agler model theory, and real algebraic geometry. Our scholars are innovators in the international linear algebra and operator theory communities, having held leadership positions in the International Linear Algebra Society and the International Workshop on Operator Theory and Applications and editorial positions in top-tier peer-reviewed journals such as Journal of Mathematical Analysis and Applications, Complex Analysis and Operator Theory, Annals of Functional Analysis, and Operators and Matrices.
Seminar: Analysis
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mathematical analysis; fluid dynamics; nonlinear partial differential equations; boundary integral methods |
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Passionate about undergraduate teaching;
Core teaching principle is to motivate and inspire students;
Likes to instill mathematical thinking and problem-solving skills in his students;
Aims to prepare them not only for immediate courses but for future success as well
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Function Theory and Operator Theory, Harmonic Analysis, Potential Theory |
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Manifold; Geometric optics; Robotics; Inverse problems; Optical design; Blind spot |
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Functional analysis; complex analysis; noncommutative algebra; matrix analysis |
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Matrix and Operator Theory; Systems Theory; Signal and Image Processing; Harmonic Analysis; Multivariable Interpolation; Factorization; Quantum Computing. |
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Functional Analysis; Operator semigroups; Mathematical Physics
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Combinatorics
Drexel mathematicians who research combinatorics – the study of discrete and finite mathematical structures – explore a broad range of topics, from the properties of graphs and groups to the algebra of symmetric polynomials and power series. Combinatorial objects often have simple-sounding definitions and are intuitive and highly visual, making them a powerful complement to areas with more abstract structures. At Drexel, Mathematics faculty work at the intersection of combinatorics and allied fields, including representation theory, algebra, geometry, and probability theory. Research strengths include symmetric function theory, quantum groups, Hopf algebras, and enumerative combinatorics.
Seminar: Combinatorics, Algebra, and Geometry (CAGE)
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Algebraic Combinatorics, Representation Theory, Complexity Theory |
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Algebraic Combinatorics, Noncommutative Algebra, Symmetric Functions, Hopf Algebras, Enumerative Combinatorics, Invariant Theory |
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Probability Theory and its Applications to Analysis, Combinatorics, Wavelets, and the Analysis of Algorithms |
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Functional analysis; complex analysis; noncommutative algebra; matrix analysis |
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Discrete Mathematics; Graph Theory |
Probability and Statistics
Drexel faculty working in probability and statistics study decision-making under imperfect knowledge across a variety of disciplines, including physics, public health, finance, and data science. Our faculty explores the theoretical, computational, and applied frontiers by conducting research in probabilistic combinatorics, statistical learning, stochastic processes, time series analysis, uncertainty quantification, and variance reduction.
Faculty engage with all stages of the statistical and probabilistic modeling pipeline, from formulating models for complex random systems, to developing and analyzing inference methods, to implementing computational techniques for large-scale data analysis. They work closely with collaborators across disciplines to address challenges such as modeling high-dimensional data, quantifying prediction uncertainty, and designing efficient simulation and sampling methods.
Theoretical research includes establishing rigorous foundations for statistical procedures, understanding the behavior of stochastic systems, and developing new probabilistic tools. On the computational side, faculty develop and analyze algorithms for modern data science and machine learning, including methods for scalable inference, optimization, and simulation. Together, this work equips students and researchers to both understand uncertainty at a fundamental level and apply that understanding to real-world problems.
Seminar: Probability and Statistics
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Time series;
High-frequency data;
Change-point detection;
Wavelet methods;
Fractional/self-similar stochastic processes
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Probability Theory and its Applications to Analysis, Combinatorics, Wavelets, and the Analysis of Algorithms |
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Dynamical systems, large networks, mathematical neuroscience
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Analysis of Partial Differential Equations; Fluid Dynamics; Stochastic Processes |
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Functional analysis; complex analysis; noncommutative algebra; matrix analysis |
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Discrete Mathematics; Graph Theory |
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Applied mathematics; Numerical analysis; Scientific computing; Stochastic simulation |
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Stochastic Calculus, Large Deviation Theory, Theoretical Statistics, Data Network Modeling and Numerical Analysis |