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Teaching & Research Faculty

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    Nicole Abaid , bio

    Dr. Abaid's research focuses on networked dynamical systems. She studies diverse biological systems, ranging from animal groups to brain networks, to inspire novel results in mathematical modeling and control.

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    Slimane Adjerid , bio

    Professor Adjerid conducts research on developing new discontinuous finite element methods for solving partial differential equations.

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    Daniel Appelö , bio

    Professor Daniel Appelö is a numerical analyst with an interest in computational techniques for solving differential equations fast and accurately. He is excited about applications in acoustics, electromagnetics, fluids, and more recently in quantum computing.

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    Sarah Arpin (starting Fall 2024) , bio

    Dr. Arpin's research is in algebraic number theory and post-quantum cryptography, including the study of supersingular elliptic curves, isogeny-based cryptography, arithmetic geometry in characteristic p, and code-based cryptography.

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    Christopher Beattie , bio

    The principal research interests of Professor Beattie are in the areas of scientific computing and large scale computational linear algebra, with an emphasis on iterative Krylov methods.

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    Jeff Borggaard , bio

    Professor Borggaard studies the design and control of fluids. This includes computational fluid dynamics, control theory, optimization, sensitivity analysis, uncertainty quantification, and reduced-order models. In each case, the application of these research areas to partial differential equations that describe fluids are of interest.

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    John Burns , bio

    Professor Burns' current research is focused on computational methods for modeling, control, estimation and optimization of complex systems where spatially distributed information is essential. This includes systems modeled by partial and delay differential equations. Recent applications include modeling and control of thermal fluids, design and thermal management systems and optimization of mobile sensor networks.

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    Guher Camliyurt , bio

    Dr. Camliyurt's research interests include mathematical fluid dynamics, nonlinear waves, and unique continuation problems for general elliptic and parabolic PDEs.

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    Paul Cazeaux , bio

    Professor Cazeaux's research deals with multiscale phenomena in mathematical physics and biology, with recent applications in quantum chemistry and condensed matter physics (2D materials).

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    Yingda Cheng , bio

    Professor Cheng's research areas are in scientific computing, applied mathematics and data-driven modeling and computation. She develops numerical methods for partial differential equations, particularly those in higher dimensional space. The application area of Professor Cheng's research includes fusion energy and semiconductor device modeling, to name a few.

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    Lauren M. Childs , bio

    Professor Childs develops and analyzes mathematical and computational models to examine biologically-motivated questions.

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    Stanca M. Ciupe , bio

    Dr. Ciupe's research interest is in the field of applied mathematics, specifically, systems of ordinary and delay differential equations and their application to biology and medicine.

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    Eric de Sturler , bio

    Professor de Sturler's research focuses on numerical analysis for large-scale computational problems with an emphasis on fast solvers for linear and nonlinear systems, inverse problems and parameter estimation, optimization, and design, including iterative solvers and numerical linear algebra, randomization, stochastic methods, model reduction, and high performance computing with applications in computational mechanics, such structural optimization and computational fluid dynamics, tomography and image reconstruction, big data, computational physics, biology, and computer graphics.

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    Andreas Deuchert (starting Fall 2024) , bio

    My main research interests are mathematical quantum mechanics and quantum statistical mechanics. In my work, I develop analytic, functional analytic, and probabilistic methods with a focus on variational techniques to study mathematical problems originating from solid-state physics.

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    Daniel Douglas (starting Fall 2024) , bio

    Dr. Douglas works in the mathematical field of quantum topology. He is particularly interested in interactions with low dimensional geometry and topology, representation theory, combinatorics, and mathematical physics.

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    Alex Elgart , bio

    Professor Elgart primary research area is mathematical physics. The mathematical tools he uses mostly come from analysis and probability.

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    Mark Embree , bio

    CMDA Program Director Professor Embree studies numerical linear algebra and spectral theory, with particular interest in eigenvalue computations for nonsymmetric matrices and transient behavior of dynamical systems.

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    Serkan Gugercin , bio

    Professor Gugercin studies computational mathematics, numerical analysis, and systems and control theory with a focus on data-driven modeling and model reduction of large-scale dynamical systems with applications to inverse problems, structural dynamics, material design, and flow control.

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    Peter Haskell , bio

    Professor Haskell conducts research in index theory, which is the study of the connections between analysis and topological or geometric structures.

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    Leo Herr (starting Fall 2024) , bio

    My work is in algebraic geometry. I study varieties using extra combinatorial data called logarithmic structures which enrich and compactify ordinary varieties as a middleman between schemes and tropical geometry. Log structures help to count curves, study intersections, and construct cohomology theories and invariants that behave well for singular varieties and normal crossings pairs.

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    Traian Iliescu , bio

    At the core of Professor Iliescu's research program is his vision of using both mathematics and computations to provide new knowledge on turbulent fluid flows dominated by coherent structures and create models with practical impact in engineering, climate modeling, and medicine. The ultimate goal of his research program is to transform turbulence modeling as we know it today and use mathematics, computations, physics, and data to discover general laws of turbulent fluid flows.

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    Estrella Johnson , bio

    Professor Johnson's research focuses on the pedagogical practices of mathematicians, with the goal of better understanding and supporting high quality, ambitious teaching in undergraduate mathematics classrooms.

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    Jason LeGrow , bio

    Professor LeGrow's research is in the design, analysis, and optimization of isogeny-based cryptographic protocols.

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    Tao Lin , bio

    Professor Tao Lin's main research interest is the numerical analysis on computational methods related with differential equations. He designs new numerical methods and carry out their convergence analysis. His recent research focuses on immersed finite element (IFE) methods that can solve interface problems of partial differential equation with interface independent meshes. He is also working on applying IFE methods to interface inverse problems via the shape optimization methodology.

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    Honghu Liu , bio

    Professor Liu's research focuses on the design of effective low-dimensional reduced models for nonlinear deterministic and stochastic PDEs as well as DDEs. Applications to classical and geophysical fluid dynamics are actively pursued. Particular problems that are addressed include bifurcation analysis, phase transition, surrogate systems for optimal control, and stochastic closures for turbulence.

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    Nick Loehr , bio

    Professor Loehr conducts research in algebraic combinatorics. His work focuses on the combinatorics of symmetric functions, quasisymmetric functions, lattice paths, and tableau-like structures. These objects encode remarkable algebraic information about group representations, polynomial invariants, and Lie algebras.

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    Hiram López Valdez , bio

    Professor López researches connections of commutative algebra with coding theory and its applications, including quantum error correction, coding for post-quantum cryptography, and distributed storage systems.

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    José Ramón Madrid Padilla , bio

    Professor Madrid works in harmonic analysis and its connections to related fields such as number theory, combinatorics, ergodic theory and PDE.

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    Gretchen Matthews , bio

    Professor Matthews' research is in applications of algebraic geometry to data storage, protection, and security, especially coding theory and cryptography.

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    Agnieszka Miedlar , bio

    Professor Miedlar conducts research in numerical analysis and scientific computing, with a focus on iterative solvers for large-scale linear systems and eigenvalue problems, and adaptive finite element methods (AFEMs).

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    Leonardo Mihalcea , bio

    Associate Professor Mihalcea studies classical and quantum intersection rings for flag manifolds and related algebraic varieties, an area combining techniques from Algebraic Geometry, Combinatorics, and Geometric Representation Theory.

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    Travis Morrison , bio

    Professor Morrison's research is in algorithmic number theory and applications to cryptography.

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    Anderson Norton , bio

    Professor Norton conducts research in mathematics education, building psychological models of students' mathematics and their mathematical development.

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    Daniel Orr , bio

    Daniel Orr conducts research in representation theory and algebraic combinatorics.

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    Eyvindur Ari Palsson , bio

    Associate Professor Palsson conducts research in harmonic analysis, geometric measure theory, combinatorics, number theory and partial differential equations.

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    Mirjeta Pasha (starting Fall 2024) , bio

    Dr. Pasha is an Assistant Professor with research interests on high dimensional (tensor) data analysis, regularization for inverse problems, uncertainty quantification, and high-performance computing. She develops computationally efficient methods and algorithms to solve large-scale problems that arise from an extensive list of applications in data science, medicine, and engineering.

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    Sarah Reznikoff , bio

    Professor Reznikoff is Department Chair and Professor. Her research in analysis currently focuses on groupoid representations of C*-algebras.

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    Michael A. Robert , bio

    Professor Robert builds and analyzes mathematical models to study biological phenomena. He is particularly interested in developing and exploring models to better understand how ecological, meteorological, anthropogenic, and evolutionary processes impact the emergence, spread, and control of infectious diseases.

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    Johann Rudi , bio

    Professor Johann Rudi's research is interdisciplinary and spans large-scale parallel iterative methods for nonlinear and linear systems, development and implementation of algorithms for high-performance computing (HPC) platforms, computational aspects of inverse problems, and quantification of uncertainties in the inferred parameters.

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    Omar Saucedo , bio

    Assistant Professor Saucedo's research is Mathematical Biology with an emphasis on modeling infectious diseases.

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    Mark Shimozono , bio

    Professor Shimozono works on combinatorial problems arising in enumerative algebraic geometry and representation theory.

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    Shu-Ming Sun , bio

    Professor Sun's research interests include the mathematical theory of fluid mechanics, the theory of partial differential equations, and applied nonlinear analysis.

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    Wenbo Sun , bio

    Assistant Professor Wenbo Sun works on the problems lying at the interaction of ergodic theory, combinatorics, and number theory.

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    Peter Wapperom , bio

    Professor Wapperom conducts research in computational fluid dynamics of complex fluids. This involves the mathematical modeling and numerical simulation of the flow of polymeric liquids and fluids reinforced with rigid particles.

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    Tim Warburton , bio

    Professor Warburton holds the John K. Costain Chair in the College of Science at Virginia Tech and is a faculty member of both the Department of Mathematics and the Computational Modeling and Data Analytics program. His research interests include developing new parallel algorithms and methods that are used to solve PDE based physical modes on the largest supercomputers.

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    Megan Wawro , bio

    Professor Wawro's research involves investigating students' reasoning about linear algebra in quantum mechanics and the development of inquiry-oriented instructional materials for linear algebra.

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    Steffen Werner , bio

    Professor Werner conducts research at the intersection of scientific computing and numerical linear algebra with particular focus on scientific machine learning, model order reduction, data-driven modeling, optimization and control of partial differential equations, matrix equations and mathematical software development.

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    Yun Yang , bio

    Assistant professor Yang conducts research in ergodic theory and dynamical systems.

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    Pengtao Yue , bio

    Professor Yue works on the numerical simulation of flow problems with moving boundaries and complex rheology, including multiphase flow, viscoelastic fluids, dynamic wetting, and phase change phenomena.

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    Lizette Zietsman , bio

    Professor Zietsman's research area covers the development and analysis of fundamental numerical algorithms arising in the study of stability, control and estimation of distributed parameter systems typical in structural control, fluid flow control, and thermal systems.

Research Faculty

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    Joseph Antonides , bio

    Dr. Antonides' research focuses on understanding students' mathematical reasoning and learning, with a particular interest in the domains of combinatorics, geometry, and logic.

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    Eduardo Camps Moreno , bio

    Dr. Camps Moreno is a Presidential Postdoctoral Fellow working with Dr. Gretchen Matthews, with a research focus in algebraic coding theory.

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    Giuseppe Cotardo , bio

    Doctor Cotardo's research interest is in algebraic coding theory, with a focus on algebra, geometry, combinatorics, and their applications to the invariant theory of codes endowed with the rank metric.

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    Kyle Dahlin , bio

    Dr. Dahlin is an NSF MPS Ascending Postdoctoral Fellow who uses mathematical tools to answer questions in epidemiology and ecology, particularly those related to the transmission and control of mosquito-borne parasites in human and wildlife populations.

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    Irit Huq-Kuruvilla , bio

    Dr. Huq-Kuruvilla is a postdoctoral scholar working on Gromov-Witten theory and related areas, with a particular focus on quantum K-theory and its relationship with the geometry of the Kontsevich moduli spaces of stable maps.

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    Leah LeJeune , bio

    Dr. LeJeune's research focuses on modeling the spread and control of infectious disease through analysis of mathematical models, particularly deterministic dynamical systems.

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    Shixu Meng , bio

    Dr. Meng’s research interests include computational and analytical methods for solving PDEs and inverse problems, and a major theme is on forward and inverse scattering problems. His most recent interest is on low rank methods and dimension reduction techniques.

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    Petar Mlinarić , bio

    Dr. Mlinarić conducts research in the field of model order reduction, in particular, structure-preserving and optimal methods.

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    Michal Outrata , bio

    Dr. Outrata's research interests include numerical analysis, numerical PDEs and numerical linear algebra with particular focus on Krylow methods, domain decomposition methods and related topics.

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    Jorge Reyes , bio

    Dr. Reyes' research involves the theoretical and computational study of fluid dynamics primarily based on the Navier-Stokes equations (NSE). These studies consist of the finite element analysis of numerical solutions for full-order models and the development of corresponding reduced order models (ROMs).

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    Ping-Hsuan Tsai , bio

    I am a postdoctoral associate working on developing data-driven reduced-order models for turbulent heat transfer applications. Particularly, focusing on developing stabilization strategies and error indicators for turbulent flows to be used in engineering routine and design analysis. In addition to turbulent flows, plasma physics is another application that I have been working on recently.

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    Weihong Xu , bio

    Dr. Xu studies combinatorial algebraic geometry, especially quantum Schubert calculus and questions concerning generalized flag varieties.

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    Fangchi Yan , bio

    Dr. Yan studies partial differential equations (PDEs) that are motivated from the modeling of physical phenomena and real-world problems in general. His research focuses on the problem of well-posedness for nonlinear dispersive equations, including the Korteweg-de Vries (KdV) equation and the nonlinear Schrödinger (NLS) equation.

Collegiate & Visiting Faculty

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    Gazi Mahmud Alam , bio

    Dr. Alam's research interests are focused on the development of methods and algorithms for solving control and inverse problems on quantum graphs.

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    Rachel Arnold , bio

    Dr. Arnold conducts research on mathematical teaching and learning in upper-level mathematics courses, such as Introduction to Proofs and Advanced Calculus.

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    Arunabha Biswas , bio

    Visiting Assistant Professor Biswas works in number theory.

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    Brian Cook , bio

    Visiting Assistant Professor Cook's research focuses on arithmetic harmonic analysis, extremal combinatorics & additive/analytic number Theory.

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    Kyle Flanagan , bio

    Visiting Assistant Professor Kyle Flanagan conducts research in mathematics education with a primary focus on professional mathematicians' mathematical practices and mathematical understanding.

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    Artem Hulko , bio

    Dr. Hulko conducts research in mathematical analysis, particularly in the area of non-self-adjoint operators on Hilbert spaces. He is also interested in Game Theory.

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    Palanivel Manoharan , bio

    Research interest in Geometry of Manifolds and geometry of quantum states.

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    Sanja Pantic , bio

    Professor Pantic has done research in nonlinear partial differential equations and numerical simulations of wave propagation.

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    John Pratt , bio

    Visiting Assistant Professor' John Pratt's research focuses on nuclear magnetic and nuclear quadrupole resonance in solids.

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    Michael T. Schultz , bio

    Dr. Schultz conducts research in the intersection of algebraic geometry and mathematical physics.

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    Turker Topcu , bio

    Dr. Topcu works in the field of computational science. His research involves developing algorithms and codes to solve partial and ordinary differential equations to simulate quantum dynamical systems.

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    Eric Ufferman , bio

    Collegiate Assistant Professor Ufferman teaches classes in both Computational Modeling and Data Analytics and Discrete Mathematics.

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    Jason R. Wilson , bio

    Collegiate Assistant Professor Wilson teaches Math and CMDA classes. His research interests include large scale linear algebra, high performance computing, and the mathematical foundations of data science.

Instructional Faculty

Retired & Emeritus Faculty

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    Joseph Ball , bio

    Professor Ball conducts research in Hilbert-space operator theory and operator algebras, exploring connections with multivariable function theory and engineering systems theory.

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    Ezra (Bud) Brown , bio

    Bud Brown does research in number theory (mainly algebraic number theory, quadratic forms, and elliptic curves), combinatorics (mainly combinatorial designs), expository mathematics (two dozen articles on a variety of topics), and cryptography.

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    Martin Day , bio

    Professor Day's research focused on applications of the large deviations analysis of stochastic processes, specifically the classical exit problem for diffusions. Later work involved fluid limit analysis of queueing processes.

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    William Floyd , bio

    Professor Floyd conducts research in geometric group theory, complex dynamics, and discrete conformal geometry.

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    George Hagedorn , bio

    Professor Hagedorn works in mathematical physics. He specializes in molecular quantum dynamics.

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    Jong Uhn Kim , bio

    Professor Kim's research has been in analysis of partial differential equations which arise in fluid mechanics and elasticity.

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    Martin Klaus , bio

    Professor Klaus' research mainly concerns the spectral theory of linear operators and their connection with nonlinear evolution equations. This research has applications in the study of optical pulse propagation.

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    Peter A. Linnell , bio

    Professor Linnell conducts research in pure mathematics, especially algebra, with a little analysis and topology.

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    Michael Renardy , bio

    Professor Renardy's research is in partial differential equations and applications to fluid mechanics, in particular viscoelastic flows.

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    Yuriko Renardy , bio

    Professor Renardy's research concerns the modeling, analysis and computation of fluid motion, in particular fluids with interfaces and non-Newtonian fluids. She has worked in particular on problems of stability, pattern formation, deformation of drops, and thixotropic yield stress fluids.

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    Bob Rogers , bio

    Professor Rogers studies continuum mechanics and nonconvex problems in partial differential equations. He also studies models of acoustics.

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    John Rossi , bio

    Professor Rossi conducts research in complex function theory with specialties in value distribution theory and potential theory.

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    Layne T. Watson , bio

    Dr. Watson's research interests include numerical analysis; nonlinear programming; mathematical software; solid mechanics; fluid mechanics; image processing; parallel computation; bioinformatics.