# Research: Interests

## Electric Power Grid Modeling

As the U.S. dependence on networks—such as the electric power, communication, and transportation systems—grows, the need for secure and reliable operational standards becomes vital to economic, energy, and national security. A striking example is the August 2003 blackout in the Northeast, which demonstrated the catastrophic consequences of a few broken links in a critical infrastructure. This research project is focused on developing mathematical algorithms for analyzing vulnerabilities in the electric power grid and computing the severity of blackouts.

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## Antibiotic Resistance

Antibiotic resistance due to the overuse of drugs has become a global challenge even as the development of new antibiotics has steadily declined. Another promising approach is the development of reliable methods for restoring susceptibility after antibiotic resistance has arisen. A greater understanding of the relationship between antibiotic administration and the evolution of resistance is key to solving this problem. This research is focused on developing data-driven mathematical approaches for developing antibiotic treatment plans that can reverse the evolution of antibiotic resistance determinants.

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## Machine Learning

The advent of big data has provided us with the promise of being able to detect new patterns in data, optimize policies, and discover new science. This research is focused on the development of new mathematical algorithms applicable to machine learning for pattern detection and feature extraction of large data sets.

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## Optimization

I am interested in many areas generally related to nonlinear optimization with a particular emphasis on methods for solving problems arising in simulation-based optimization, which are typically non-smooth and lack derivative information.

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## Density Functional Theory

One of the most widely used techniques in computational chemistry and material simulations is based on density functional theory (DFT). Using DFT, you can calculate many material properties, including the electronic structure, the charge density, and the total energy of electronic systems. This research is focused on the development of new mathematical algorithms that can be used to study many thousand-atom systems, with applications including the study of solar cells for renewable energy, biomedical imaging, and the design of novel materials.

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## Numerical Linear Algebra

I have been interested in numerical linear algebra since my original foray into this area for my Ph.D. dissertation. As interesting problems arise in other research projects, I will collaborate with other PIs to investigate these problems, especially if it involves parallel computations.

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