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- Optimal Modeling
- Modeling is the first step for solving real-world problems and understanding complex phenomena via a mathematical approach. However, there could be enormous different models to the same phenomenon. Furthermore, even in essentially equivalent models, the difficulty of the numerical computation varies due to variable choices and freedom in mathematical expressions in these models. Exploiting techniques from discrete mathematics, optimization, and statistics, we aim to establish a systematic methodology for selecting an optimal model from enormous possible models.
- Discrete Computational Geometry
- Computational geometry studies algorithms for solving geometric problems. Our particular interest is to understand the discrete structures behind geometric graphs and networks in engineering topics such as robotics, structural mechanics, and bioinformatics, and establish mathematical foundations for efficient algorithms.
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