# Research Focus Areas

The Mathematical Sciences department has several research areas that are internationally recognized, with current support coming from the National Science Foundation, the National Institutes of Health, the National Security Agency, as well as several corporations. Below is an outline of the main research areas, with links to webpages of associated faculty.

## Algebra/Discrete Mathematics

- Algebra: Christopher, Martin, Servatius
- Coding Theory and Cryptography: Martin, Servatius
- Combinatorial Geometry: Servatius
- Graph Theory and Combinatorics: Christopher, Martin, Servatius

## Applied Analysis/Differential Equations

- Analysis on Fractals: Mosco
- Calculus of Variations: Larsen, Lurie, Mosco, Vernescu
- Free and Moving Boundary Problems: Bichuch, Fehribach, Larsen, Tang, Tilley, Vernescu
- Mathematical Physics: Humi
- Partial Differential Equations: Capogna, Davis, Farr, Fehribach, Humi, Larsen, Lui, Lurie, Mosco, Sarkis, Tilley, Vernescu, Volkov
- Stochastic Analysis: Bichuch, Blais, Heinricher, Sarkis, Sturm, Vermes

## Mathematical Biology

Mathematical biology is an interdisciplinary area of scientific research focused on solving biological problems. Because of the rapid increase in computing power and the vast amount of data collected over the past half century, mathematicians can now build complex mathematical models to explain biological functions and behavior. At WPI, we have a team of well-connected and dedicated researchers focusing their research in areas such as cardiovascular diseases, computational biofluids, cell movement, and population dynamics. The Departments of Mathematical Sciences, Computer Science, and Biology offer a joint program in bioinformatics and computational biology.

- Cardiovascular Modeling and Biomechanics: Tang
- Cell Motility: Lui
- Flagellar Swimming: Olson
- Tumor Modeling: Weekes

## Financial Mathematics

## Fluids

- Computational Biofluids: Olson
- Computational Fluid Dynamics: Humi, Sarkis, Weekes
- Interfacial Phenomena: Tilley
- Two-Phase Flows: Vernescu
- Viscous Flows: Olson, Tilley, Vernescu

## Mathematics of Materials Science

- Composite Materials/Homogenization: Larsen, Lurie, Mosco, Sarkis, Tilley, Vernescu, Weekes
- Dynamic Materials (materials with properties that change in space and time): Lurie, Weekes
- Fracture and Damage: Larsen
- Mathematical Geophysics: Humi, Volkov
- Porous Electrodes (fuel cells, batteries): Fehribach

## Numerical Analysis/Computational Modeling

- Computational Modeling: Fehribach, Humi, Tang, Tilley, Volkov, Weekes, Yakovlev
- Large Scale and Parallel Computing: Sarkis, Walker
- Numerical Analysis: Sarkis, Walker, Weekes

## Optimization

- Applied Optimization/Operations Research: Davis, Martin, Heinricher
- Computational Methods of Optimization: Sarkis, Walker, Yakovlev
- Optimal Control and Design: Lurie, Heinricher, Vermes
- Stochastic Optimization and Control: Bichuch, Heinricher, Sturm, Vermes

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