My research is in the field of algebraic geometry. I focus on applying ideas from physics and noncommutative algebra to study varieties, with examples including homogeneous spaces and their Calabi-Yau relatives, and complex 3-folds and their birational modifications. Mirror symmetry provides much of the motivation for this work, and homological algebra provides many of the tools. Currently, I am working on problems on higher-dimensional varieties, and applying homological algebra to better understand moduli spaces associated to them.