Email: xlzhao at math dot ucsb dot edu
I am an assistant professor at University of California, Santa Barbara. During 2015-2018, 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.
CV (updated on September 15, 2023)
Focused Research Group: Derived Categories, Moduli Spaces, and Classical Algebraic Geometry
Upcoming events:
Workshop at UCSB, May 1-4, 2024: Derived Categories and Moduli Spaces
Past events:
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
Conference at Imperial College London, July 3-7, 2023: Derived Categories, Moduli Spaces, and Counting Invariants
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 4pm-6pm PT.
Research:
Higher dimensional moduli spaces on Kuznetsov components of Fano threefolds (joint with Chunyi Li, Yinbang Lin, Pertusi)
in preparation.
Non-commutative abelian surfaces and generalized Kummer varieties (joint with Bayer, Perry, Pertusi)
in preparation.
Stability conditions on hyper-Kähler manifolds and deformations (joint with Chunyi Li, Macrì, Stellari)
in preparation.
Derived categories of quartic double fivefolds (joint with Raymond Cheng, Perry)
Fully faithful functors, skyscraper sheaves, and birational equivalence (joint with Chunyi Li, Xun Lin)
Some remarks about deformation theory and formality conjecture (joint with Huachen Chen, Pertusi)
to appear in Annali dell'Università di Ferrara, special volume Edge Days: 2018-2022 (pdf)
Moduli spaces of stable objects in Enriques categories (joint with Perry, Pertusi)
arXiv: 2305.10702, submitted.
Finiteness of the Tate-Shafarevich group for some elliptic curves of analytic rank>1 (joint with Hamacher, Ziquan Yang)
arXiv: 2207.11904, submitted.
Derived categories of hearts on Kuznetsov components (joint with Chunyi Li, Pertusi)
J. London Math. Soc. 108(2) (2023), 2146–2174 (pdf)
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)
Stability manifolds of varieties with finite Albanese morphisms (joint with Lie Fu, Chunyi Li)
Tran. Amer. Math. Soc. 375(8) (2022), 5669-5690 (pdf)
Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations (joint with Chunyi Li, Pertusi)
Adv. Math. 408 (2022) (pdf)
Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties (joint with Perry, Pertusi)
Geometry & Topology 26-7 (2022), 3055-3121 (pdf)
A refined derived Torelli theorem for Enriques surfaces (joint with Chunyi Li, Nuer, Stellari)
Math. Ann. 379 (2021), 1475-1505 (pdf)
Twisted cubics on cubic fourfolds and stability conditions (joint with Chunyi Li, Pertusi)
Algebraic Geometry 10 (5) (2023), 620-642 (pdf)
On the group of zero-cycles of holomorphic symplectic varieties (joint with Marian)
Épijournal de Géométrie Algébrique 4 (2020), Article Nr.3 (pdf)
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)
The Torelli Theorem for cubic fourfolds (joint with Bayer, Lahoz, Macrì, Stellari) - appendix to Stability conditions on Kuznetsov components by Bayer, Lahoz, Macrì, Stellari
Ann. Sci. ENS 56 (2023), 517-570 (pdf)
Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces (joint with Chunyi Li)
Math. Z. 291 (2019), 437-447 (pdf)
Bridgeland stability conditions on Fano threefolds (joint with Bernardara, Macrì, Schmidt)
Épijournal de Géométrie Algébrique 1 (2017), Article Nr. 2 (pdf)
Birational models of moduli spaces of coherent sheaves on the projective plane (joint with Chunyi Li)
Geometry & Topology 23-1 (2019), 347-426 (pdf)
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)
Topological Abel-Jacobi mapping and Jacobi inversion
University of Michigan thesis (pdf)
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:
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)
Period integrals and Hodge modules (joint with Flapan, Walters), arXiv: 1910.00035.