Email: xlzhao at math dot ucsb dot edu

I am an assistant professor at University of California, Santa Barbara. I was a Zelevinsky Research Instructor at Northeastern University, working with Emanuele Macri. I obtained my Ph.D. from University of Michigan in 2015, under the supervision of Herb Clemens and Karen Smith.

Research:

  1. Twisted cubics on cubic fourfolds and stability conditions (joint with Li, Pertusi), arXiv: 1802.01134, submitted.
  2. On the group of zero-cycles of holomorphic symplectic varieties (joint with Marian), arXiv: 1711.10045.
  3. Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties (joint with Shen, Yin), arXiv: 1705.06953, submitted.
  4. The Torelli Theorem for cubic fourfolds (joint with Bayer, Lahoz, Macri, Stellari) - appendix to Stability conditions on Kuznetsov components by Bayer, Lahoz, Macri, Stellari, arXiv: 1703.10839.
  5. Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces (joint with Li), to appear in Math. Z. (pdf)
  6. Bridgeland stability conditions on Fano threefolds (joint with Bernardara, Macri, Schmidt), Épijournal de Géométrie Algébrique 1 (2017), Article Nr. 2. (pdf)
  7. Birational models of moduli spaces of coherent sheaves on the projective plane (joint with Li), to appear in Geometry & Topology. (pdf)
  8. Nef cones of Hilbert schemes of points on surfaces (joint with Bolognese, Huizenga, Lin, Riedl, Schmidt, Woolf), Algebra & Number Theory 10-4 (2016), 907--930. (pdf)
  9. Topological Abel-Jacobi mapping and Jacobi inversion, University of Michigan thesis. (pdf)
  10. The MMP for deformations of Hilbert schemes of points on the projective plane (joint with Li), Algebraic Geometry 5 (3) (2018) 1-35. (pdf)

Notes:

Holomorphic height pairing and Poincare bundle. This gives a different construction of Clemens' holomorphic height pairing, more close to Hain's approach to the classic height pairing. (pdf)