Algebraic geometry. I am currently trying to understand the geometric, topolgical and arithmetic properties of algebraic varieties by studying the rational curves on them. I am also interested in birational geometry and moduli spaces and their applications to other geometric problems.
All the papers can be found on Arxiv, which might be different from (but equivalent to) the published version.
2. Symplectic geometry and rationally connected 4-folds. to appear in J. Reine. Angew. Math. (Crelle’s Journal) arxiv 1208.4343
1. Weak approximation for cubic hypersurfaces, submitted arxiv 1303.7273.
2. Towards the symplectic Grabber-Harris-Starr theorems. submitted arxiv 1208.4340
3. (with Zhiyuan Li) Moduli of complete intersection K3 surfaces. arxiv1304.3219.
4 (with Hong R. Zong) Weak approximation for isotrivial families, submitted. arxiv 1003.3502
5. R-equivalence on del Pezzo surfaces of degree 4 and cubic surfaces, arxiv 1307.1801
6. Separable rational connectedness and stability, submitted arxiv1312.4238.
7. (with Francois Greer and Zhiyuan Li) Picard groups on moduli of K3 surfaces with Mukai models, submitted, arxiv 1402.2330
Ma 130c Algebraic geometry
Ma 132 Topics in algebraic geometry: derived categories
Topics in algebraic geometry: Hodge theory
Ma 157b Riemannian geometry II (complex and algebraic geometry)