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.
Professor Adjerid conducts research on developing new discontinuous finite element methods for solving partial differential equations. His interest was on studying the superconvergence properties of discontinuous Galerkin methods that can be used to estimate discretization errors. Lately he his working on high-order immersed finite elements for interface problems.
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. His primary focus is on model reduction of large scale dynamical systems with a goal of developing practical and rigorous computational algorithms for efficient manipulation and simulation of systems arising from physical models frequently described by systems of partial differential equations.
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.
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.
Professor Chung's research concerns computational methods in the intersection of computational modeling, machine learning, data analytics with an emphasis on inverse problems. Driven by its application, he and his group develop and analyze efficient numerical methods for inverse problems. Applications of interest are, but not limited to, systems biology, medical and geophysical imaging, and dynamical systems.
Assistant professor Martin Fraas works in mathematical physics, studying mathematical structures of quantum mechanics. His research interests include topological phases of matter, open quantum systems, and the adiabatic theory.
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.
Professor Hewett's research interests lie at the intersection of inverse problems, deep learning, and high-performance computing. His research is motivated by problems in science with extreme data and compute scales, for example geoscience and space physics. Research in these areas also involves developments in numerical differential equations, optimization, estimation, and statistics.
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.
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.
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.
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.
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.
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.
Dr. Martin is an assistant professor doing research focused on computational mathematics, particularly with applications to geosciences. Her interests include data-intensive high performance computing, signal processing, imaging science, inverse problems, and working with large-scale sensor networks collecting streaming data.
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.
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.
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.
Associate 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.
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.
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.
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.
Dr. Teffera Asfaw conducts research in nonlinear analysis. The main research areas are degree and variational inequality theories and applications. The goal of the research is to derive existence theorems for inclusion and inequality problems and their applications to operator equations and inequalities in appropriate function spaces.
Math Emporium Academic Manager.
Dr. Clemons does research in the overlapping ares of complex dynamical systems, ergodic theory, and topology and teaches a wide variety of traditional courses in differential equations and combinatorics.
Shelley Farmer is a mathematics instructor who teaches 1000 and 2000 level courses. She serves as an advisor to freshman and sophomore mathematics majors. Shelley is also a member of the K-12 Outreach Committee.
Jessica Hurdus, Advanced Instructor, teaches undergraduate math courses, chairs the lower-division math advising team, coordinates math transfer credit evaluations, and is a team member for Math Emporium online quiz and test development.
Dr. Malik's interests lie in nonlinear partial differential equations; specifically the asymptotic behavior, orbital stability, and effective dynamics, of dark solitons that arise from defocusing nonlinear Schrodinger equations.
Dr. Truman conducts research in mathematics education, studying mathematical problem-solving of college students and other adults in areas such as linear algebra with a particular focus on adults on the autism spectrum.
Dr. Wells thinks about most things related to complex hyperbolic geometry. In particular, he is interested in (non-)arithmetic subgroups of SU(n,1) and, lately, spherical CR-uniformizations of 3-manifolds.
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.
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.
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.