Ziyu Zhang
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Research

My primary research interest is algebraic geometry, focusing on the interaction between moduli spaces of sheaves and holomorphic symplectic manifolds, more specifically including

  • moduli spaces of sheaves and complexes on Calabi-Yau manifolds

  • holomorphic symplectic manifolds and their degenerations

  • derived categories, stability conditions and wall-crossing

Preprints

My preprints can be found on arXiv.

Publications

My publications can be found on MathSciNet and zbMATH.

  • Halle, Lars H.; Hulek, Klaus; Zhang, Ziyu. Relative VGIT and an application to degenerations of Hilbert schemes. Michigan Math. J. 73 (2023), no. 1, 67–96.
    [DOI][MathSciNet][PDF]

  • Reede, Fabian; Zhang, Ziyu. Stable vector bundles on generalized Kummer varieties. Forum Math. 34 (2022), no. 4, 1015–1031.
    [DOI][MathSciNet][PDF]

  • Reede, Fabian; Zhang, Ziyu. Stability of some vector bundles on Hilbert schemes of points on K3 surfaces. Math. Z. 301 (2022), no. 1, 315–341.
    [DOI][MathSciNet][zbMATH][PDF]

  • Reede, Fabian; Zhang, Ziyu. Examples of smooth components of moduli spaces of stable sheaves. Manuscripta Math. 165 (2021), no. 3-4, 605–621.
    [DOI][MathSciNet][zbMATH][PDF]

  • Floccari, Salvatore; Fu, Lie; Zhang, Ziyu. On the motive of O'Grady's ten-dimensional hyper-Kähler varieties. Commun. Contemp. Math. 23 (2021), no. 4, Paper No. 2050034, 50 pp.
    [DOI][MathSciNet][zbMATH][PDF]

  • Gulbrandsen, Martin G.; Halle, Lars H.; Hulek, Klaus; Zhang, Ziyu. The geometry of degenerations of Hilbert schemes of points. J. Algebraic Geom. 30 (2021), no. 1, 1–56.
    [DOI][MathSciNet][zbMATH][PDF]

  • Shinder, Evgeny; Zhang, Ziyu. L-equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces. Bull. Lond. Math. Soc. 52 (2020), no. 2, 395–409.
    [DOI][MathSciNet][zbMATH][PDF]

  • Budur, Nero; Zhang, Ziyu. Formality conjecture for K3 surfaces. Compos. Math. 155 (2019), no. 5, 902–911.
    [DOI][MathSciNet][zbMATH][PDF]

  • Lo, Jason; Zhang, Ziyu. Preservation of semistability under Fourier-Mukai transforms. Geom. Dedicata 193 (2018), 89–119.
    [DOI][MathSciNet][zbMATH][PDF]

  • Lo, Jason; Zhang, Ziyu. Duality spectral sequences for Weierstrass fibrations and applications. J. Geom. Phys. 123 (2018), 362–371.
    [DOI][MathSciNet][zbMATH][PDF]

  • Zhang, Ziyu. Moduli spaces of sheaves on K3 surfaces and symplectic stacks. Comm. Anal. Geom. 25 (2017), no. 5, 1063–1106.
    [DOI][MathSciNet][zbMATH][PDF]

  • Bayer, Arend; Craw, Alastair; Zhang, Ziyu. Nef divisors for moduli spaces of complexes with compact support. Selecta Math. (N.S.) 23 (2017), no. 2, 1507–1561.
    [DOI][MathSciNet][zbMATH][PDF]

  • Meachan, Ciaran; Zhang, Ziyu. Birational geometry of singular moduli spaces of O'Grady type. Adv. Math. 296 (2016), 210–267.
    [DOI][MathSciNet][zbMATH][PDF]

  • Zhang, Ziyu. A note on singular moduli spaces of sheaves on K3 surfaces. Geom. Dedicata 173 (2014), 347–363.
    [DOI][MathSciNet][zbMATH][PDF]

  • Lo, Jason; Zhang, Ziyu. Representing stable complexes on projective spaces. J. Algebra 400 (2014), 185–218.
    [DOI][MathSciNet][zbMATH][PDF]

  • Zhang, Ziyu. A note on formality and singularities of moduli spaces. Mosc. Math. J. 12 (2012), no. 4, 863–879, 885.
    [DOI][MathSciNet][zbMATH][PDF]

  • Zhang, Ziyu. On singular moduli spaces of sheaves on K3 surfaces. Thesis (Ph.D.)–Stanford University. 2009. 73 pp. ISBN: 978-1109-44707-1, ProQuest LLC
    [MathSciNet]

Invited Talks

  • Type II degenerations of Hilbert schemes and variations of GIT , Geometry of Hyperkähler varieties, Banff International Research Station & Institute for Advanced Study in Mathematics, Hangzhou, September 2023

  • Lecture series on moduli spaces of semistable sheaves, International Summer School on Algebraic Geometry, Shanghai Center for Mathematical Sciences, Fudan University, July 2023.

  • Semi-continuity in variation of GIT, Conference on Algebraic Geometry and Related Topics, Nanjing University, May 2023.

  • Semi-continuity in variation of GIT, Algebraic Geometry Conference in Shanghai, ECNU, Shanghai, December 2022.

  • Degenerations of Hilbert schemes of points on K3 surfaces, USTC Algebraic Geometry Workshop, Hefei, January 2022.

  • Examples of stable bundles on hyperkähler manifolds of higher dimensions, Algebraic Geometry Conference, Tongji University, Shanghai, November 2021.

  • Degenerations of Hilbert schemes of points on K3 surfaces, Pacific Rim Complex & Symplectic Geometry Conference, IBS-CGP, Korea, July 2021.

  • Degenerations of Hilbert schemes of points on K3 surfaces, Shanghai Center for Mathematical Sciences, Fudan University, September 2020.

  • Formality conjecture for K3 surfaces, Workshop on Teichmüller dynamics and the moduli space of curves, Xiamen University, January 2020.

  • Smooth components of moduli spaces, ShanghaiTech-Yonsei Mathematics Conference, ShanghaiTech University, November 2019.

  • Irreducible holomorphic symplectic manifolds – Fantastic beasts and where to find them, ShanghaiTech University, February 2019.

  • Formality conjecture for K3 surfaces, Université libre de Bruxelles, January 2019.

  • Formality conjecture and moduli spaces of sheaves on K3 surfaces, North German Algebraic Geometry Seminar, Max Planck Institute for Mathematics in the Sciences, Leipzig, November 2018.

  • Formality conjecture and moduli spaces of sheaves on K3 surfaces, University of Lyon 1, October 2018.

  • Formality conjecture for K3 surfaces, Shanghai Center for Mathematical Sciences, Fudan University, September 2018.

  • Formality conjecture and moduli spaces of sheaves on K3 surfaces, University of Science and Technology of China, Hefei, September 2018.

  • Formality conjecture and moduli spaces of sheaves on K3 surfaces, King's College London & University College London, June 2018.

  • Formality conjecture on K3 surfaces, University of Mainz, June 2018.

  • Formality conjecture and moduli spaces of sheaves on K3 surfaces, Leibniz University Hannover, April 2018.

  • Formality and singularities of some moduli spaces of sheaves on K3 surfaces, School on Deformation Theory, University of Turin, July 2017.

  • Singularities of moduli spaces of sheaves on K3 surfaces and formality, Leibniz University Hannover, June 2017.

  • Degenerations of Hilbert schemes of points on K3 surfaces, University of Sheffield, May 2017.

  • Degenerations of Hilbert schemes of points on K3 surfaces, KU Leuven, April 2017.

  • Birational geometry of moduli spaces of sheaves on K3 surfaces via stability conditions, University of Chemnitz, March 2017.

  • Holomorphic symplectic manifolds among Bridgeland moduli spaces, Workshop on Fano varieties and Calabi-Yau varieties, Kobe University, January 2017.

  • Moduli spaces of sheaves on K3 surfaces and Bridgeland stability conditions, University of Copenhagen, December 2016.

  • Moduli spaces of sheaves on K3 surfaces and Bridgeland stability conditions, Tsinghua University, Beijing, September 2016.

  • Holomorphic symplectic manifolds among Bridgeland moduli spaces, Leibniz University Hannover, June 2016.

  • Wall-crossing and birational geometry of moduli spaces, University of Science and Technology of China, April 2016.

  • Introduction to Bridgeland stability conditions, University of Science and Technology of China, April 2016.

  • Local structures of moduli spaces of sheaves on K3 surfaces and formality, GLEN seminar, University of Glasgow, March 2016.

  • Formality and singularities of moduli spaces of sheaves on K3 surfaces, KU Leuven, April 2015.

  • Holomorphic symplectic manifolds among Bridgeland moduli spaces, University of Warwick, February 2015.

  • Birational geometry of singular moduli spaces of O'Grady type, University of Sheffield, November 2014.

  • The Bayer-Macrì map and birational geometry of moduli spaces, University of Bath, October 2014.

  • Birational geometry of singular moduli spaces of O'Grady type, University of Edinburgh, May 2014.

  • The Bayer-Macrì map and birational geometry of moduli spaces, COW Seminar, Imperial College London, April 2014.

  • Singular moduli spaces of sheaves on K3 surfaces and their cotangent complexes, University of Bath, May 2013.

  • Singular moduli spaces of sheaves on K3 surfaces and their cotangent complexes, University of Freiburg, July 2012.

  • Singular moduli spaces of sheaves on K3 surfaces, Max Planck Institute for Mathematics, Bonn, February 2012.

  • Cotangent complexes of moduli of sheaves and symplectic stacks, SFB-TR/45 Seminar, University of Bonn, January 2012.

  • Singular moduli spaces of sheaves on K3 surfaces and their cotangent complexes, University of Bielefeld, December 2011.

  • On singular moduli spaces of sheaves on K3 surfaces, University of Science and Technology of China, July 2011.

  • Cotangent complexes of moduli of sheaves and symplectic stacks, University of Missouri, June 2011.

  • DG algebras and formality, University of Mainz, November 2009.

  • Quadratic singularities of moduli spaces of sheaves on K3 surfaces, Ohio State University, February 2009.

  • Quadratic singularities of moduli spaces of sheaves on K3 surfaces, Chinese University of Hong Kong, December 2008.

  • Birationality and deformation equivalence of holomorphic symplectic manifolds, Area Exam Talk, Stanford University, May 2008.

  • Holomorphic symplectic manifolds, Student Algebraic Geometry Seminar, Stanford University, October 2007.