**Pure mathematics**

Research in pure mathematics at UNH centers on algebra, analysis, and topology, with specific strength in operator theory, functional analysis, categorical algebra, and algebraic topology. There is additional research activity in commutative algebra, complex analysis, and combinatorics.

Professors Don Hadwin, Liming Ge, and Junhao Shen comprise the UNH Operator Algebra group. Hadwin works primarily in functional analysis and operator algebras. Ge's research centers on operator algebras and free entropy, while Shen works in von Neumann and C* algebras.

Professor Dmitri Nikshych is a Fellow of the American Mathematical Society and works in tensor categories, Hopf algebras, and quantum groups. Professor Maria Basterra conducts research in homotopy theory, category theory, and homological algebra.

Professor Rita Hibschweiler works in complex analysis and geometric function theory, Professor Edward Hinson in commutative algebra and linear algebra, and Professor David Feldman in combinatorics and related fields.

**Applied mathematics**

Applied math research at UNH focuses on analytic and computational approaches to complex mathematical problems from science and engineering. Particular areas of strength include partial differential equations, continuum and quantum physics, dynamical systems, and numerical analysis.

Professor Mark Lyon works on numerical methods for partial differential equations, inverse problems, and optimization.

Professor Marianna Shubov's research centers on spectral analysis and non-self-adjoint operators in application to physics and engineering problems.

Professor John Gibson has research interests in dynamical-systems methods for fluid dynamics, numerical methods for very-high-dimensional systems, and computational fluid dynamics.

Professor Kevin Short is a Fellow of the National Academy of Inventors. His work centers on signal processing, secure communications, dynamical systems.

Dr. John McClain performs analytical and computational investigations of Schrodinger's equation, especially in relation to solid state physics.

Interdisciplinary applied math research at UNH is coordinated through the Integrated Applied Mathematics Program, with faculty from Mathematics & Statistics, Physics, Mechanical Engineering, Chemical Engineering, Earth Sciences, and Computer Science.

**Statistics**

Research in Statistics spans a broad spectrum from theoretical to applied to interdisciplinary. Areas of strength include nonparametric function estimation, spatial statistics, environmental statistics, design of experiments, quality and product control.

Professor Linyuan Li’s research is in wavelet and other function approximations, nonparametric smoothing and asymptotic inference for stochastic processes with applications in time series analysis.

Professor Ernst Linder’s work centers on statistical methodology, such as spatial and spatial-temporal statistics, as well as computational solutions primarily for environmental and earth system applications. Examples include statistical downscaling for climate research, inference for point processes for disease mapping, statistical inference in remote sensing, Bayesian methods for precision engineering and hydrology.

Dr. Philip Ramsey’s focus is on statistics and data science methodology for industry. He develops solutions for quality and process control, designs for experimentation and innovation, which includes data mining and high-dimensional nonlinear statistical model-building.

**mathematics Education**

Research in mathematics education at UNH centers on the teaching and learning of mathematics at the secondary level (middle and high school) and the undergraduate level. Particular areas of strength include research on the teaching and learning of calculus and precalculus concepts, mathematics teacher development, the role of reasoning and proof in mathematics learning and teacher development, and the analysis of national educational datasets.

Professor Karen Graham's research focuses on student understanding of calculus and precalculus; the mathematical knowledge needed for teachers at the middle and high school level; and developing and investigating curricula for prospective teachers that draw on both their specialized knowledge of mathematics for teaching and their general knowledge of mathematics content and student learning.

Professor Sharon McCrone's research focuses on the teaching and learning of mathematical proving and reasoning at all levels of school; teacher preparation and knowledge of mathematics for teaching; and the development of mathematical discourse in classrooms as well as how the discourse contributes to the learning process.

Professor Orly Buchbinder's research focuses on teaching and learning of mathematical reasoning and proof at the secondary level; mathematical knowledge for teaching specific to reasoning and proving; and applications of technology for teacher preparation.

Professor Sheree Sharpe's research focuses on the analysis of large nationally representative datasets to explore how factors describing a student and their families, their teachers, and their school relate to mathematics achievement at the secondary level.