Email: xlzhao@math.ucsb.edu

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

Several seminars that I help organizing:

Derived Seminar: Tuesday 8am-9am PT. This is an international seminar, centered loosely around derived categories in algebraic geometry.

UCSB Seminar on Geometry and Arithmetic: Friday 3pm-4pm PT.

Learning Seminar on Algebraic Geometry: Monday 1pm-2pm PT.

Research:

  1. Moduli spaces of stable objects in Enriques categories (joint with Perry, Pertusi), in preparation.

  2. Derived categories of quartic double fivefolds (joint with Chen, Cheng, Feng, Perry), in preparation.

  3. On the Picard groups of moduli spaces of sheaves on algebraic surfaces (joint with Jun Li, Lin, Nuer), in preparation.

  4. Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fiberations (joint with Li, Pertusi), arXiv: 2007.14108, submitted.

  5. Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties (joint with Perry, Pertusi), arXiv: 1912.06935, submitted.

  6. A refined derived Torelli theorem for Enriques surfaces (joint with Li, Nuer, Stellari), to appear in Math. Ann. (pdf)

  7. Period integrals and Hodge modules (joint with Flapan, Walters), arXiv: 1910.00035.

  8. Twisted cubics on cubic fourfolds and stability conditions (joint with Li, Pertusi), arXiv: 1802.01134, submitted.

  9. On the group of zero-cycles of holomorphic symplectic varieties (joint with Marian), Épijournal de Géométrie Algébrique 4 (2020), Article Nr.3. (pdf)

  10. Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties (joint with Shen, Yin), Compositio Math. 156 (2020), 179-197. (pdf)

  11. The Torelli Theorem for cubic fourfolds (joint with Bayer, Lahoz, Macrì, Stellari) - appendix to Stability conditions on Kuznetsov components by Bayer, Lahoz, Macrì, Stellari, arXiv: 1703.10839, submitted.

  12. Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces (joint with Li), Math. Z. 291 (2019), 437-447.(pdf)

  13. Bridgeland stability conditions on Fano threefolds (joint with Bernardara, Macrì, Schmidt), Épijournal de Géométrie Algébrique 1 (2017), Article Nr. 2. (pdf)

  14. Birational models of moduli spaces of coherent sheaves on the projective plane (joint with Li), Geometry & Topology 23-1 (2019), 347-426. (pdf)

  15. 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)

  16. Topological Abel-Jacobi mapping and Jacobi inversion, University of Michigan thesis. (pdf)

  17. 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)