Areas of research in the Department of Applied and Computational Mathematics and Statistics (ACMS) include:

Mathematical and Computational Biology
Multiscale modeling, using a combination of discrete stochastic systems and differential equations, of biomedical problems including blood clot formation, spread of infection, development, and cancer.

ACMS Faculty: Buechler, Hu, LindsaySommese, Xu, Zhang

Geometry and Statistics
Development of models and theory for inference of non-Euclidean data in particular manifold-valued data such as developing central limit theorems for Frechet means, models for density estimation, regression/classifications on manifolds and other non-Euclidean spaces. Incorporating geometry for statistical learning such as in manifold learning, high-dimensional data analysis, and Big data analysis.

ACMS Faculty: Lin

Network Analysis
Statistical network analysis for large-scale networks; Bayesian network analysis; Development of central limit theorems for large collection of network objects.

ACMS Faculty: Lin

Bayesian Nonparametrics
Bayesian nonparametric modeling for high-dimensional data, complex data or Big data; Bayesian asymptotics or large sample theory for Bayesian models

ACMS Faculty: Lin

Combinatorics, and its applications

ACMS Faculty: Nguyen

Number Theory, and Applied Algebra

ACMS Faculty: Nguyen

Numerical Differential Equations
The design, efficient implementation, and analysis of numerical methods for solving differential equations arising in science and engineering.

ACMS Faculty: Hu, LindsaySommese, Xu, Zhang

Numerical Algebraic Geometry
The discovery, implementation, and application of algorithms to numerically compute and manipulate the solution sets of systems of polynomials.

 ACMS Faculty: HauensteinNguyenSommese

Bioinformatics and Biostatistics
The application of statistical and computational methods to biological and medical data to model, analyze, and predict biological processes.

ACMS Faculty: BuechlerLi, Liu

Applied Partial Differential Equations

Modeling and analysis using partial differential equations tools and theories to study real-world problems arising from the natural and social sciences and engineering.

ACMS Faculty: Hu, LindsaySommese, Zhang

Scientific Computing

The construction and implementation of mathematical algorithms to run on large parallel high-performance computers and their application to problems in science, engineering, and social science.

ACMS Faculty: BuechlerHauensteinHu, LindsaySommese, Xu, Zhang

Bayesian Statistics
Development and application of Bayesian methodology towards data analysis and experimental designs, such as clinical trials, decision making, macrosystem biology, epidemiology modeling, and missing data.

ACMS Faculty: Liu

Data Mining
Modeling, regression, classification, clustering, and testing on modern datasets, especially big datasets generated by high-throughput techniques.

ACMS Faculty: Li

Data Privacy and Statistical Disclosure Limitation
Development of statistical theory and methodology to protect individual data in released data without compromising statistical validity.

ACMS Faculty: Liu