Stony Brook  University   Mathematics Department

Research

My research interests are in complex algebraic and differential geometry. Currently, I am studying several theories related to secondary geometric invariants of manifolds including Harvey-Lawson spark theory, Cheeger-Simons differential characters and Deligne cohomology. Using the presentation of Deligne cohomology  in terms of forms and currents via spark theory, I give an explicit product formula for Deligne cohomology.  Moreover, I define Massey products in differential characters which descend to Massey products in Deligne cohomology.

Publications and Preprints

4)Massey products in differential characters and Deligne cohomology, to appear soon;

3)D-bar spark theory and Deligne cohomology, arXiv: 0808.1741;

2)On the ring structure of spark characters, arXiv: 0808.0724;

1)Higher cohomology of the pluricanonical bundle is not deformation invariant, joint with Li Li, arXiv: math/0612006.