Common Research Themes
Our department’s research focus areas and strengths span the disciplines of mathematics, statistics, and mathematics education. Shared research threads include:
- Research Design and Analysis
Biological and Ecological Applications
Faculty Research Interests
Algebraic and Differential and Geometric Topology
Mathematical and computational biology, dynamics in network science (social, epidemiological, and genetic networks), and dynamics in artificial intelligence
Numerical Methods for Partial Differential Equations, Sensitivity Analysis, Mathematical Models of Biological Systems
Numerical Methods, Mathematical Biology, Perturbation Methods, Applied Mathematics
Mathematical Biology; in particular, I am interested in modeling network dynamics in cell biology and systems biology.
Complex analysis, complex dynamics, fractal geometry
Geometry, Topology, & QFT
My work is centered around the field of Geometric Representation Theory, which involves aspects of Representation Theory, Algebraic Geometry, Topology, and Mathematical Physics. Some particular interests include D-modules, topological field theory, skein modules, and (higher) categorical structures.
My background is in Dynamical Systems. I am currently interested in quasi-symmetric renormalization for infinitely ramified fractals, Anosov maps on infra-nil manifolds, non-Meyer substitution Delone sets, and applications of geometry of Stokes space to multi mode fiber-optic communication.
My approach to applied mathematics combines modeling, computation, and analysis to understand problems stemming from general pattern forming systems. Pattern formation is seen in ecological and biological models, chemistry, physics, and even the social sciences. Typical examples are the traveling waves in the Fisher-KPP equation for the transmission of favorable genes or the SIR model for disease epidemics, ringed vegetation patches in desert grasses, hexagon patches in gas discharge experiments, ferrosolitons in ferro-magnetic fluid experiments, and crime hotspot formation. My viewpoint is driven by dynamical systems, and I typically use techniques from spatial dynamics, bifurcation theory, and nonlinear wave propagation.
Applied mathematical techniques in mathematical models of biological problems. Perturbation methods, stability analysis, dynamical systems theory, bifurcation theory, ordinary and partial differential equations, computer simulations.
Number theory, arithmetic geometry, arithmetic statistics
Mathematical modeling of biofilm and material science, Scientific Computation, Numerical Analysis
Affiliate Research Areas
Prasanta Bandyopadhyay (Philosophy)
Statistical/probabilistic notions to long-standing conundrum of methodological issues
Brittany Fasy (School of Computing)
Topological Data Analysis
Kathi Irvine (USGS)
Application-driven method development, particularly for ecological applications; multimodel inference, model combination, and model selection; bayesian methods; promoting the appropriate use of statistical methods in practice; providing accessible computing and visualization tools (e.g., R packages) for practitioners; statistics education
Response surface methodology, experimental design, sampling, quality control
High dimensional data analysis and visualization (especially related to functional data analysis), longitudinal data analysis and hierarchical modeling, measurement error correction methods, philosophy of statistics, and model selection techniques. Application areas include environmental, education, and health related data.
Statistics education, time series analysis, environmental statistics
As an applied Bayesian statistician, much of my work is motivated by working on problems with scientists. From these collaborations come both applied papers and the motivation for more theoretical works. The general focus of my research is Bayesian computation for data analyses with complicated structure, including spatial and spatiotemporal components. Applications of these methods range, but are mainly in the environmental or ecological sciences or related to sports analytics.I am primarily interested in Bayesian modeling, networks, generalized linear models, and specifically applications related to HIV and hard-to-reach, or key, populations like sex workers and drug users. The statistical methods used to estimate population sizes are quite diverse, so my research involves small area estimation and geospatial methods, with a current emphasis on the Network Scale-up Method. I am also broadly interested in anything related to Bayesian computing.
My primary interest is in the development of new statistical theory and methodology in the realm of multiple comparisons. Multiple comparisons is a highly active research area in the broad domain of high dimensional statistical inference. Her current research focuses on development of new methods of multiple comparisons to test complex structures of hypotheses that are frequently obtained from a wide variety of scientific studies including but not limited to genomics, brain-imaging studies, astronomical data, etc.
My main research interest is semi-parametric methodology for missing data settings. More broadly, I apply semi-parametric methods to different statistical domains such as quantile regression and causal inference. I also enjoy collaborative applied and methodological research in diverse scientific areas. Some recent collaborations explored the impacts of restless leg syndrome and genetics on fetal growth and the relationship between sleep patterns and head impacts in football players.Calibration, simulation, and inference of large-scale dynamical systems (especially those related to ecological applications), iterative near-term forecasting, Bayesian hierarchical modeling, application driven methodology, Gaussian process surrogate modeling and optimization.
Mathematical modeling in K-12 mathematics classrooms; connections between the mathematics pre-service teachers study as undergraduates and the mathematics they will teach to school students; mathematics coaching in elementary mathematics classrooms
Teacher learning and teacher change in mathematics; innovative formats for teacher professional development; mathematics teacher leadership; eliciting, understanding and making use of students’ mathematical ideas when teaching; mathematical modeling in formal and informal settings
Effective models of school-based professional learning for pre-service and in-service teachers (e.g., lesson study, coaching, learning communities, classroom action research); overcoming barriers to providing content-focused professional development for rural and otherwise isolated mathematics teachers; effective uses of online and blended learning to develop mathematical and pedagogical knowledge for teaching; construction of knowledge through mathematical discourse in the online learning environment
K-16 students' understanding of geometric measurement; the teaching and learning of mathematical modeling; teachers' understanding and incorporation of research into practice