### Contact Information

- Email
`zhangziyu at shanghaitech dot edu dot cn`

- Due to the complication of the mail service on campus, if you would like to send me anything by post, please kindly contact me in advance to request a shipping label.

### About Me

I recently joined the Institute of Mathematical Sciences at ShanghaiTech University as an Associate Professor. Previously I held research positions at Hannover, Bath, Bonn and Mainz, mentored by Prof. Dr. Klaus Hulek, Dr. Alastair Craw, Prof. Dr. Daniel Huybrechts and Prof. Dr. Manfred Lehn respectively. I received my Ph.D. in Mathematics from Stanford University under the supervision of Prof. Jun Li.

### Research

My research focuses on several aspects in algebraic geometry, including

- moduli spaces of sheaves and complexes on K3 surfaces;
- holomorphic symplectic manifolds and their degenerations;
- derived categories, stability conditions and wall-crossing.

### Publications

My publications and preprints can be found on zbMATH, MathSciNet and arXiv.

- On the motive of O’Grady’s ten-dimensional hyper-Kähler varieties

(with Salvatore Floccari and Lie Fu)

to appear in*Commun. Contemp. Math.*, arXiv:1911.06572. - Relative VGIT and an application to degenerations of Hilbert schemes

(with Lars H. Halle and Klaus Hulek)

*submitted*, arXiv:1909.03780. - Examples of smooth components of moduli spaces of stable sheaves

(with Fabian Reede)

to appear in*Manuscripta Math.*, arXiv:1908.00368. - The geometry of degenerations of Hilbert schemes of points

(with Martin G. Gulbrandsen, Lars H. Halle and Klaus Hulek)

to appear in*J. Algebraic Geom.*, arXiv:1802.00622. - L-equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces

(with Evgeny Shinder)

*Bull. London Math. Soc.*, 52(2):395-409, 2020. - Formality conjecture for K3 surfaces

(with Nero Budur)

*Compos. Math.*, 155(5):902-911, 2019. - Duality spectral sequences for Weierstrass fibrations and applications

(with Jason Lo)

*J. Geometry Phys.*, 123:362-371, 2018. - Preservation of semistability under Fourier-Mukai transforms

(with Jason Lo)

*Geom. Dedicata*, 193(1):89-119, 2018. - Moduli spaces of sheaves on K3 surfaces and symplectic stacks

*Comm. Anal. Geom.*, 25(5):1063-1106, 2017. - Nef divisors for moduli spaces of complexes with compact support

(with Arend Bayer and Alastair Craw)

*Selecta Math. (N.S.)*, 23(2):1507-1561, 2017. - Birational geometry of singular moduli spaces of O’Grady type

(with Ciaran Meachan)

*Adv. Math.*, 296:210-267, 2016. - Representing stable complexes on projective spaces

(with Jason Lo)

*J. Algebra*, 400:185-218, 2014. - A note on singular moduli spaces of sheaves on K3 surfaces

*Geom. Dedicata*, 173(1):347-363, 2014. - A note on formality and singularities of moduli spaces

*Mosc. Math. J.*, 12(4):1-17, 2012. - On singular moduli spaces of sheaves on K3 surfaces

*Ph.D. thesis*, Stanford University, 2009.

### Teaching

ShanghaiTech University:

- 2019/20: Mathematical Analysis I & II.

Leibniz University Hannover:

- 2018/19: Übung zu Mathematik für Ingenieure I & II.
- 2017/18: Übung zu Mathematik für Ingenieure I & II.

University of Bath:

- 2015/16: Algebraic Curves.
- 2014/15: Number Theory.
- 2013/14: Discrete Mathematics and Programming (tutorials).

University of Bonn:

- 2012/13: Algebraic Geometry II (tutorials).

Stanford University:

- 2008/09: Calculus I.
- 2005/06 - 2008/09: Calculus I & II (tutorials).

### Invited Talks

- 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,

Fudan University, Shanghai, 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.

### Seminar

- Reading seminar on cubic hypersurfaces (co-organised with Víctor González-Alonso)

Leibniz University Hannover, Winter Semester 2016-17.