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, ****Lindsay, Sommese, 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, Lindsay, Sommese, 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: ***Hauenstein, Nguyen, Sommese**

**Bioinformatics and Biostatistics**

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

*ACMS Faculty: ***Buechler, Li, 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,**Lindsay,**Sommese, 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:***Buechler, Hauenstein, Hu,**Lindsay,**Sommese, 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**