How the intrinsic geometry of a variety is related to the geometry of curves it contains,
How the geometry of parameter spaces of rational curves on a variety are related to extrinsic geometry, e.g., producing sections, weak approximation, etc.
Understanding how varieties are or are close to being rational.
Papers:
Complete Families of Linearly Non-Degenerate Curves: Arxiv Link.
Relatively Very Free Curves and Rational Simple Connectedness: Arxiv Link.
Studying Rational Curves on Hypersurfaces without using Bend and Break. In Preparation.
Globally F-regular varieties and Rational Curves. In Preparation.