The majority of my research focuses on the description, classification and solving of problems in combinatorial optimization. I have especially been involved in problems arising from comparative genomics. A short blurb can be found in my doctoral research proposal. The challenge is to identify a suitable mathematical model in which the problem is well-described, define the formal mathematical problems on them, and find exact or approximate solutions to them.
The long-term goal of each project is to obtain an implementable algorithm which gives a mathematically correct result, while also being biologically consistent. As a result, these projects demand a theoretically sound foundation in algorithms and complexity, but also expect an understanding of basic biology and the tools with which to implement these results.
I have also recently been interested in the role of machine learning to many of these problems, and the applicability and implementation of convex optimization techniques for obtaining efficient solutions to integer programs.