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.

My research is partially supported by NSF grants DMS-2101789 and FRG-2052665.

Focused Research Group: Derived Categories, Moduli Spaces, and Classical Algebraic Geometry

Two upcoming events in 2022!

Workshop at Cornell University, April 29-May 1, 2022: Derived Categories and Moduli Spaces

Conference and minischool at the University of Michigan, July 30-August 5, 2022: Derived Categories, Moduli Spaces, and Hyperkähler Varieties

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: Thursday 4:30pm-6pm PT.

Learning Seminar on Algebraic Geometry: Friday 4:30pm-6pm PT.

Research:

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

in progress

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

in preparation

  1. Derived categories of hearts on Kuznetsov components (joint with Chunyi Li, Pertusi)

arXiv: 2203.13864, submitted.

  1. A refined derived Torelli theorem for Enriques surfaces II: the non-generic case (joint with Chunyi Li, Stellari)

Math. Z. 300 (2022), 3527-3550, special volume in honor of Olivier Debarre (pdf)

  1. Stability manifolds of varieties with finite Albanese morphisms (joint with Lie Fu, Chunyi Li)

arXiv: 2103.07728, to appear in Tran. Amer. Math. Soc.

  1. Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations (joint with Chunyi Li, Pertusi)

arXiv: 2007.14108, submitted

  1. Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties (joint with Perry, Pertusi)

arXiv: 1912.06935, to appear in Geometry & Topology

  1. A refined derived Torelli theorem for Enriques surfaces (joint with Chunyi Li, Nuer, Stellari)

Math. Ann. 379 (2021), 1475-1505 (pdf)

  1. Twisted cubics on cubic fourfolds and stability conditions (joint with Chunyi Li, Pertusi)

arXiv: 1802.01134, submitted

  1. On the group of zero-cycles of holomorphic symplectic varieties (joint with Marian)

Épijournal de Géométrie Algébrique 4 (2020), Article Nr.3 (pdf)

  1. Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties (joint with Junliang Shen, Qizheng Yin)

Compositio Math. 156 (2020), 179-197 (pdf)

  1. 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, to appear in Ann. Sci. ENS

  1. Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces (joint with Chunyi Li)

Math. Z. 291 (2019), 437-447 (pdf)

  1. Bridgeland stability conditions on Fano threefolds (joint with Bernardara, Macrì, Schmidt)

Épijournal de Géométrie Algébrique 1 (2017), Article Nr. 2 (pdf)

  1. Birational models of moduli spaces of coherent sheaves on the projective plane (joint with Chunyi Li)

Geometry & Topology 23-1 (2019), 347-426 (pdf)

  1. Nef cones of Hilbert schemes of points on surfaces (joint with Bolognese, Huizenga, Yinbang Lin, Riedl, Schmidt, Woolf)

Algebra & Number Theory 10-4 (2016), 907--930 (pdf)

  1. Topological Abel-Jacobi mapping and Jacobi inversion

University of Michigan thesis (pdf)

  1. The MMP for deformations of Hilbert schemes of points on the projective plane (joint with Chunyi Li)

Algebraic Geometry 5 (3) (2018) 328-358 (pdf)

Notes:

  1. 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)

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

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