Researcher in mathematics with focus on complex geometry and partial differential equations.
Most of my research is focused on complex geometry. Two important topics in this field are (1) canonical metrics on complex manifolds and their relationship to moduli spaces and stability in algebraic geometry and (2) degenerat families of Calabi-Yau mainfolds, special Lagrangian torus fibrations and mirror symmetry. I'm also interested in applications of geometric ideas to signal processing. My research often utilizes connections between geometry and partial differential equationsy. At the heart of my research lies the real and complex Monge-Ampère equations, which have connections to geometry, optics, meteorology and machine learning.
Research interests: Real and complex Monge-Ampère equations, canonical Kähler metrics, K-stability, Calabi-Yau manifolds, optimal transport, affine geometry, tropical manifolds.
I teach mathematics at undergradaute and graduate level. Some courses I've recently taught are Calculus II (series and intergrals) for math and engineering majors, Discrete Mathematics for Life Sciences and Optimal Transport and Geometry for graduate students in mathematcs.