Recent Papers:
Areas of interest and publication:
Professor Bokil's general research interests are in applied mathematics, scientific computing, numerical analysis and mathematical biology. Her primary research interests are in the numerical solution of wave propagation problems. Specifically, she has conducted research on the numerical solution of Maxwell's equations using finite difference and finite element methods. Bokil is also working on several problems in mathematical ecology which involve the construction and analyses of deterministic and stochastic models for applications in population dynamics, epidemiology and spatial ecology.
Dr. Bokil is currently a co-PI on an NSF funded project OP: Collaborative Research: Compatible Discretizations for Maxwell Models in Nonlinear Optics in collaboration with Drs Yingda Cheng at Michigan State and Fengyan Li at RPI. The objective of the collaborative research program is to make significant advances in the understanding and simulations of Maxwell models in nonlinear optics.
In the past, Dr. Bokil was a co-PI on the DOE-NETL funded project Applying Computational Methods to Determine the Electric Current Densities in a Magnetohydrodynamic Generator channel from the External Magnetic Flux Density Measurements,and a co-PI on the NSF-DMS project Residence and First Passage Time Functionals in Heterogeneous Ecological Dispersion.
Dr. Bokil was also PI on the NSF-DMS funded project Time Domain Numerical Methods for Electromagnetic Wave Propagation Problems in Complex Dispersive Dielectrics and a Co-PI on the NSF-CMG funded project, Mathematical and Experimental Analysis of Reactive Transport in Discontinuous Porous Media.
Burton has contributions to ergodic theory and dynamical systems and has worked in various parts of pure and applied mathematics. These include probability theory, percolation and interacting partical systems, neural networks and data mining, number theory and its interactions with dynamics such continued fractions, point processes and random measures, algorithms and coding theory, substitution process, symbolic systems in one and higher dimensions. His current projects include work with the Center for Gene Research and Biotechnology, symbolic and physical models, and coding and search algorithms.
Dascaliuc's research focuses on qualitative properties and long-time behavior of nonlinear PDE. In particular, he is interested in dynamics of the incompressible Navier-Stokes and Euler equations, especially in relation to the turbulence theory. The main goals are to derive the tenets of the heuristic theory of turbulence directly from the physical equations of motion and to understand connections between turbulence in fluids and regularity theory of the 3D Navier-Stokes and Euler equations.
Dick's research interests include the study of factors related to mathematics achievement and participation, cognitive science as applied to the learning of advanced mathematics, uses of technology in the learning of mathematics, and mathematical discourse. He has worked extensively in the calculus curriculum reform movement. He has served on the joint AMS/MAA Committee on Research in Undergraduate Mathematics Education, the National Council of Teachers of Mathematics Research Advisory Committee, and the Advanced Placement Calculus Development Committee. He is a past co-editor of Connecting Research to Teaching for NCTM's Mathematics Teacher journal, associate editor for School Science and Mathematics, an editorial panel member for the Journal for Research in Mathematics Education, and an editorial panel member for the Mathematics Teacher Educator.
Past work has emphasized General Relativity, studying model spacetimes and their properties, as well as the interface between relativity and quantum physics. Current work investigates applications of the Octonions, the unique non-associative division algebra, to the physics of fundamental particles. Other past and present interests include Algebraic Computing, Asymptotic Structure, Non-Euclidean Geometry, Quantum Field Theory in Curved Space, and Signature Change.
Work in Mathematics Education includes directing the Vector Calculus Bridge Project, co-directing the Paradigms in Physics Project, and designing course content for the Oregon Mathematics Leadership Institute, as well as close collaboration with the Physics Education Group at OSU and membership in the ESTEME group of science educators at OSU.
Escher's current work lies in the interaction between algebraic topology and differential geometry, in particular the use of surgery theory to classify spaces of positive sectional curvature. Her previous work is connected to the field of minimal submanifolds; in particular existence and uniqueness questions of minimal isometric immersions of spherical space forms into spheres.
Faridani conducts research in numerical analysis, investigating problems arising in signal processing and tomography. In signal processing he is interested in non-equidistant sampling of bandlimited functions in several variables. His research in tomography comprises questions of optimal sampling and resolution; error estimates for reconstruction algorithms in two and three dimensions; and theory and implementation of local tomography.
For publications and preprints please click here.
Finch works on inverse problems, particularly those arising in medical imaging. He has worked on x-ray computed tomography and vector tomography. He is currently working on problems arising in the medical imaging technique called thermoacoustic tomography and other forms of hybrid imaging.
Dr. Flahive's work in number theory is principally in Diophantine approximation, with techniques from the geometry of numbers. She is also working with colleagues in computer science on projects in algebraic coding theory and also on developing and analyzing interconnection networks.
Garity's current research is focused on properties of embeddings of Cantor sets in Euclidean spaces, focusing on embeddings in R^3. Cantor sets often arise as limit sets or invariant sets of dynamical systems. The complements of such Cantor sets in R^3 are 3-manifolds with a rich end structure. The possible types of embeddings of these sets in R^n can provide information about possible dynamical systems and about the end structure of manifolds. Recent examples include nonstandard embeddings with simply connected complement, nonstandard embeddings that are rigid, and nonstandard embeddings with both properties.
Gibson's primary research interests are computational electromagnetics, finite element and finite difference methods, and inverse problems. Research topics coinciding with primary interests include: wave propagation modeling, homogenization, direct and indirect (sparse) linear solvers, optimization and regularization techniques, high performance and parallel computing, parameter identification and sensitivity analysis, and modeling uncertainty and variability in PDE's. Current work involves finite element and finite difference methods for time-domain electromagnetics in dispersive media.
Guo is working on circle packing, discrete conformal geometry, hyperbolic geometry, Teichmüller space.
Higdon has worked on open boundary conditions for wave propagation problems and on issues related to the well-posedness of hyperbolic initial-boundary value problems and the stability of their numerical approximations. He is currently working on some mathematical and computational problems related to large-scale, high-resolution numerical modeling of ocean circulation. This modeling involves the solution of a system of partial differential equations that describes fluid flow. Of particular interest are some problems with stability and efficiency that arise from the multiple time scales that are contained in the system.
Casualty and health actuarial mathematics; Workers compensation insurance; Health insurance; Insurance regulatory issues; Reinsurance; Medical professional liability insurance; Loss reserve modeling. Catastrophe modeling. Financial risk modeling, Pricing models and algorithms.
Selction of mathematical interests: Random substitutions, substitution dynamical systems, countable state Markov chains, ergodic theory, compressive sensing, statistical mechanics, entropy.
Selection of biological interests: Genomics, metagenomics, neuroscience, coding sequence prediction, alignment-free genomic analysis techniques.
Yevgeniy Kovchegov works in the field of probability and stochastic processes. His research interests include the mathematical models of statistical mechanics, interacting particle systems, quantum computation, self-similarity, reinforced processes, and percolation. Kovchegov's work is centered around the following topics: mixing times; extending the probabilistic coupling method; orthogonal polynomials in stochastic processes, probability and statistics; quantum walks and quantum computation; occupation times; hitting times; chaos and fractals; applications of probability theory in computer and wireless networks, network coding, biological systems, economics, chemistry, and environmental sciences.
Lee has made contributions to the existence, uniqueness, and continuous dependence theory for solutions to nonlinear boundary value problems. This work, which continues, is joint with R.B. Guenther of Oregon State and A. Granas of the University of Montreal. Lee has also worked on the numerical calculation of solutions to such problems. He has helped develop the extension of Sturm oscillation theory and the properties of Sturm-Liouville eigenvalue problems to higher order equations. This work is closely related to the branch of approximation theory which deals with Tchebycheff systems and with positive operator theory. It led to related work on best quadrature formulas.
Lockwood's primary research interest involves undergraduate mathematics education, particularly studying how students think about and learn combinatorial topics. She has put forth a model of student's combinatorial thinking that especially emphasizes the role of sets of outcomes in effective counting. Other research in this area includes exploring student-generated connections among counting problems through a lens of actor-oriented transfer and determining the effectiveness of systematic listing in counting. Through two NSF-funded grants, She is currently investigating students’ generalizing activity as they solve advanced counting problems, and she is studying ways in which having students engage in computational activity can help them solve counting problems more successfully. Two additional collaborations and areas of research include studying the role of examples in proof and considering the relationship between mathematical content and mathematical practices at all levels.
One focus of Ossiander's research is the development of central limit theorems for sums of random functions. Results in this area are intimately connected with the properties of continuous Gaussian and product-Gaussian processes. The exploration of central limit theory in this general setting has involved the development of exponential bounds for the tail probabilities of sums of random variables. Interesting applications include the calculation of rates of convergence of classes of statistical estimators and the construction of stochastic models for physical systems.
Parks has developed and implemented a computational technique for computing parametric area minimizing surfaces. He derived an existence and regularity theory for a class of constrained variational problems. Parks has discovered, and characterized, a type of minimal surface with surprising properties, defined in terms of the Jacobi elliptic functions.
Malgo Peszynska's research interests are in applied and computational modeling of real life phenomena. Originally trained in pure mathematics, she came to applied mathematics projects through her interest in parallel and high performance computing. Since her PhD she has worked on models of flow and transport using mathematical and numerical analysis as well as computer simulations to understand these phenomena better across the various time and spatial scales. She is involved in a variety of interdisciplinary projects with academic, national lab, and industry collaborators from hydrology, oceanography, statistics, environmental, petroleum, civil and coastal engineering, physics, and materials science. Her research projects were funded by NSF, DOE-NETL and by DOE; her current projects include NSF-DMS 1115827 "Hybrid modeling in porous media" and NSF-DMS 1522734 "Phase transitions in porous media across multiple scales". She believes in "paying it forward" and is engaged in external and university service via editorial work and conference organization: she is the Vice-President of Pacific Northwest SIAM Section; she also served as Chair (2011-12) and Program Officer (2009-10) of SIAM Activity Group on Geosciences and on the Organizing Committee for SIAM Annual 2014.
Petsche's research program involves the study of the iteration of self-maps on varieties and analytic spaces, as well as the arithmetic theory of height functions over global fields.
Pohjanpelto works on the theory and applications of generalized symmetries of differential equations. He has studied the structure of symmetries of the electromagnetic field and applied symmetries in the construction of conservation laws and classification of group invariant solutions. He has also used variational bicomplexes to study the correspondence of generalized symmetries of equations in physical and potential formulation.
Applied and computational mathematics, in two distinct research tracts: (1) the application of statistical physics ideas, data sciences, and dynamics on probability distributions, to the understanding complex non-equilibrium physical and human systems and to the development of forecasting tools for these systems; (2) the role of ocean and ocean transport in climate dynamics and in nearshore processes. Example research problems in tract 1: resilience and uncertainty quantification in natural and human complex systems, using data and physical models. Adaptive time series methods for climate and financial data. Extreme/rare events. Dimension and uncertainty reduction in complex systems. Example research problems in tract 2: oil spill dynamics, wave breaking dynamics, wave-generated transport, the role of oceans in global climate. Sediment dynamics. Outside of these tracts he has also done research on wavelets, bone dynamics, blood cell dynamics, public choice and elections, solitary waves, high performance computing.
Schmidt is currently most interested in: natural extensions for continued fractions for various Fuchsian groups (with C. Kraaikamp, and various third co-authors: I. Smeets, H. Nakada, and W. Steiner; with K. Calta; and, most recently with P. Arnoux) and connections between the ergodic theory of billards and 1-forms on algebraic curves and, with the ergodic theory and arithmetic of generalized continued fractions. Recent results include diophantine approximation results for flow directions on translation surfaces (with Y. Bugeaud and P. Hubert, and more recently again with P. Hubert); a new proof with A. Fisher of a beautiful result of Moeckel.
The research interests of Showalter include singular or degenerate nonlinear evolution equations and partial differential equations, variational inequalities and free-boundary problems, and related applications to initial-boundary-value problems of mechanics and diffusion. His current work is focused on the development of multiscale mathematical models of coupled fluid-solid dynamics, deformable porous media, and upscaled models of transport and flow in heterogeneous media. - Panta Rhei
With the advent of modern computers, mathematical techniques can be used to combine information from x-ray pictures of a three-dimensional object, taken from a large number of different directions, and to reconstruct the internal structure of the object. This leads to mathematical questions of practical importance concerning a class of integral transforms known as x-ray and Radon transforms. Solmon has established uniqueness, nonuniqueness, stability and range characterization results for these integral transforms.
Swisher's research interests lie in number theory and combinatorics. Particular interests include modular and mock modular forms, integer partitions (including multipartitions and overpartitions), hypergeometric series, and supercongruences.
Thomann's research is primarily in problems in partial differential equations arising from fluid mechanics. He also collaborates with colleagues in other departments, as well as in the Mathematics Department, in the development of mathematical models to problems in Ecology, Oceanography, Hydrology and management of Natural Resources.
Waymire's primary research concerns applications of probability and stochastic processes to problems of contemporary applied mathematics. His publications cover a wide range of theory and applications, including random fields, heterogeneous dispersion, multiplicative cascades, Markov processes and their applications to surface and groundwater hydrology, fluid turbulence, statistical physics, financial mathematics and mathematical biology.