I am now a tenure-track associate professor at the Department of Mathematics, Sun Yat-sen University, Guangzhou, China.
I got my PhD in mathematics at the Department of Mathematics, Indiana University Bloomington.
I was working under the supervision of Professor Valery Lunts. Before that, I received my master's degree in Mathematics at Kansas State University, Manhattan, KS, USA, where I worked with Professor Alexander Rosenberg; I was a postdoctoral research associate at The University of Edinburgh under an ERC grant. My mentor was Professor Arend Bayer. I was also a postdoc fellow at the Max-Plank Institute for Mathematics, and my mentor was Professor Daniel Huybrechts. Then I was a CIMI postdoc at the institute of Mathematics at Toulouse under the supervision of Laurent Manivel and Marcello Bernardara. From Sep. to Dec. 2023, I was a guest researcher in the Junior Trimester Program at Hausdorff Research Institute for Mathematics on derived categories, Hodge theory, and Chow groups. Then, I was a postdoc fellow at SLM/MSRI@Berkeley on the Noncommutative Algebraic Geometry program in Spring 2024 and my mentor is Alexander Perry. From Oct 2024 to Aug 2025, I was a senior researcher at IBS-CGP in Pohang, South Korea.
My email address is zhangshzh28@mail.sysu.edu.cn and shizhuozhang@msri.org
Research
I am interested in Algebraic Geometry, in particular, Birational geometry from the point of view of derived category and interaction with moduli problem. I am now working on Bridgeland stability conditions on Fano threefolds/fourfolds and wall-crossing techniques with application to HyperKahler geometry. Recently, I have been working on categorical Torelli theorems.
1.Cyclic strong exceptional collection of line bundles(with Alexey Elagin and Junyan Xu), European Journal of Mathematics. 7, 69-115 (2021)
2.Note on applications of Toric systems on surfaces. Journal of Pure and Applied Algebra 223(2019), no.3, 1139-1160.
3.Brill-Noether and existence of semistable sheaves for del Pezzo surfaces.(with Daniel Levine), Annales de l'institut Fourier，Tome 74, no3 (2024), p. 1189-1227
4.Infinitesimal categorical Torelli theorems for Fano threefolds.(with Augustinas Jacovskis, Zhiyu Liu and Xun Lin), Journal of Pure and Applied Algebra. 227(2023), no.12
5.A note on Bridgeland moduli spaces and moduli spaces of sheaves on Y_3 and X14(with Zhiyu Liu), Mathematische Zeitschrift (2022): v.302, 803-837.
6.Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces(with Hanfei Guo and Zhiyu Liu), Mathematical Research Letters, Volume 31, Number 4, 1059–1104, 2024.
7.Categorical Torelli Theorems for Gushel-Mukai threefolds. (with Augustinas Jacovskis, Zhiyu Liu and Xun Lin), Journal of London Mathematical Society, Volume109, Issue3
8.Serre algebra, matrix factorization and categorical Torelli theorem for hypersurface.(with Xun Lin), Mathematische Annalen, Volume 391, pages 163–177, (2025)
9.New perspectives on categorical Torelli theorems for del Pezzo threefolds (with Soheyla Feyzbakhsh and Zhiyu Liu), published in Journal de Mathématiques Pures et Appliquées, Volume 191, November 2024, 103627
10.Kuznetsov Fano threefold conjecture via Hochschild-Serre algebra(with Xun Lin), Mathematische Zeitschrift，Volume 308, article number 26, (2024)
11. Lagrangian families of Bridgeland moduli spaces from Gushel-Mukai fourfolds. (joint with Soheyla Feyzbakhsh, Hanfei Guo, and Zhiyu Liu), to appear in Compositio Mathematica.
12. Double EPW cubes from twisted cubics on Gushel-Mukai fourfolds. (joint with Soheyla Feyzbakhsh, Hanfei Guo, and Zhiyu Liu), submitted.
13.Bridgeland moduli spaces for Gushel-Mukai threefolds and Kuznetsov Fano threefold conjecture. submitted.
14.Brill-Noether theory for Kuznetsov components and refined categorical Torelli theorems for index one Fano threefolds(with Augustinas Jacovskis and Zhiyu Liu), submitted.
15.A moduli theoretic approach to Lagrangian subvarieties of hyperkähler varieties: Examples(with Hanfei Guo and Zhiyu Liu), submitted.
16.Linear subspaces of the intersection of two quadrics via Kuznetsov component(with Yanjie Lie), submitted.
17.Three approaches to categorical Torelli theorem for cubic threefold of non-Eckardt type via equivariant Kuznetsov components (with Xianyu Hu, Xun Lin, Zheng Zhang, Sebastian Casalaina-Martin), submitted.
18 IVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces(with Jørgen Vold Rennemo and Xun Lin).
19.Moduli of quiver representations for exceptional collections on surfaces I (with Xuqiang Qin), submitted.
20. Categorical Torelli theorems for nodal Fano threefolds and parametrization via Bridgeland moduli spaces . (with Xun Lin and Daniele Faenzi), in preparation, draft available.
21. Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives (with Xun Lin and Zheng Zhang).
22. Categorical resolution of Kuznetsov components of nodal Gushel-Mukai threefolds and fourfolds with application to categorical Torelli problem (with Kacper Grzelakowski and Marco Rampazzo), in preparation.
23. Periods of special Gushel--Mukai threefolds via moduli spaces of semistable objects(with Ziqi Liu), in preparation.
Categorical Torelli theorem of index one prime Fano threefolds of lower degree as double covers. (with Xun Lin). In preparation.
Hilbert scheme of low degree rational curves and Gieseker moduli spaces (with Yanjie Li and Zhiyu Liu), in preparation.
Kuznetsov's conjecture on Geometric correspondence of Fano threefolds. (with Soheyla Feyzbakhsh, Zhiyu Liu and Daniele Faenzi), in preparation.
Categorical Torelli theorem for Verra threefolds and fourfolds(with Zhiyu Liu, Xun Lin) , In preparation.
Higgs objects over noncommutative varieties--semi-orthogonal components of cubic hypersurfaces. (with Xun Lin). In progress.
Invited talks
Instanton sheaves, fiber of (categorical)period map and Bridgeland moduli space. 2024 ECNU Algebraic Geometry workshop, East Central Normal University, Shanghai, China. Dec 2024.
Instanton sheaves, fiber of (categorical)period map and Bridgeland moduli space. The 3rd Beijing Algebraic Geometry Day, Capital Normal University, Beijing, China, Dec 2024.
1-nodal maximally non-factorial prime Fano threefolds parametrized by Bridgeland moduli spaces. MCM, Chinese Academy of Science, Beijing, China, Oct 2024.
1-nodal prime Fano threefolds parametrized by Bridgeland stable objects in Kuznetsov component of del Pezzo threefolds. BIMSA-YMSC Geometry and Dynamics Seminar(online), Sep 2024.
Auto-equivalences of Kuznetsov components and categorical Torelli problems for Fano threefolds. Zhejiang University, Hangzhou, China, July 2024
Recent advances on categorical Torelli theorems for Fano varieties, Department of Mathematics, Shanghai Jiaotong University, Shanghai, China, July 2024
Recent advances on categorical Torelli theorems for Fano varieties, Geometry and Moduli spaces, Zhejiang, China, July 2024.
Recent advances on categorical Torelli theorems for Fano varieties, Yau Mathematical Science Center, Tsinghua University, Beijing, China, June 2024
Recent advances on categorical Torelli theorems for Fano varieties, Institute of Mathematics, Shanghai Tech University Shanghai, China, May 2024
Categorical Torelli theorems for Fano varieties, Southern East Algebraic Geometry workshop}, Dong Guan, China, Nov. 2023
New Perspectives on categorical Torelli problems for del Pezzo threefolds. Indiana University Algebra Seminar, Bloomington, US, April 2023
Auto-equivalences of Kuznetsov components and categorical Torelli problems for Fano theefolds. Purdue Algebraic Geometry Seminar, West Lafayette, US, April 2023.
Auto-equivalences of Kuznetsov components and categorical Torelli problems for Fano theefolds. NW Algebraic Geometry Seminar, Evanston, US, April 2023.
Auto-equivalences of Kuznetsov components and categorical Torelli problem for Fano threefolds, MCM Algebraic Geometry Seminar, Beijing, China, Feb 2023.
Kuznetsov components for Gushel-Mukai threefolds and fourfolds, Complex Geometry Seminar, Toulouse, France, Jan 2023.
Categorical Torelli theorems for Fano varieties, ANR FanoHK workshop Fano varieties, hyper-Kähler varieties, and algebraic cycles, Strasbourg, France, Jan 2023
Categorical Torelli theorems for Fano varieties. Seminar of Algebraic Geometry, MPIM, Bonn, Germany, Dec 2022.
Conics on Gushel-Mukai varieties, Bridgeland moduli spaces and Lagrangian covering family. ANR FanoHK Thematic workshop in Toulouse, France, May 2022.
Bridgeland moduli spaces and Kuznetsov's Fano threefold conjecture. Algebraic Geometry Seminars, KIAS, Seoul, Korea, May 2021.
Bridgeland moduli spaces and Kuznetsov's Fano threefold conjecture. Algebraic Geometry Seminars, YMSC, Beijing, China, March 2021
Categorical Torelli Theorems for Gushel-Mukai threefolds. Algebraic Geometry Seminars, Sichuan University, Chengdu,Sichuan, China, March 2021
Bridgeland moduli spaces and Kuznetsov's Fano threefold conjecture. Algebraic geometry Seminar, SCMS, Shanghai, China, Jan 2021.
Exceptional collection of line bundles and Brill-Noether problem, EDGE geometry Seminar, the University of Edinburgh. Edinbugrh, UK, Feb 2020.
Research Visit
SCMS, Fudan University. 06/04/2024-06/26/2024.
Institute of Mathematics, Shanghai Tech University. 05/27/2024-05/31/2024.
Northwestern University, Evanston. 04/19/2023-04/22/2023.
Indiana University, Bloomington. 04/09/2023-04/18/2023.
Yau Mathematical Science Center, Tsinghua University, 02/26/2023-03/05/2023.
Morningside Center of Mathematics, China Academy of Science, 02/26/2023-03/05/2023
Sichuan University, Chengdu, 02/13/2023-02/23/2023.
Sun-Yat sen University, Zhuhai, 11/05/2022-11/10/2022.
Institute of Advanced Studies in Mathematics, Zhejiang University, 10/27/2022-11/04/2022.
Sichuan University, 10/20/2021-11/20/2021
Sichuan University, 3/20/2021-3/25/2021.
Chongqing University of Technology, MSRC 1/23/2021-1/28/2021.
Sun-Yat sen University, 1/10/2021-1/15/2021.
Notes and Slides
Here are some notes and slides I have written.
Bridgeland moduli spaces and refined categorical Torelli theorems for prime Fano threefolds
Bridgeland moduli spaces and Kuznetsov's Fano threefold conjecture
OUTREARCH
Mentor for undergraduate Research Project: Linear subspaces of the intersection of two quadrics via Kuznetsov component(joint with Yanjie Li), preprint, submitted.
Mentor for undergraduate Research Project: A note on Bridgeland moduli spaces and moduli spaces of sheaves on X14 and Y3 (joint with Zhiyu Liu). slides and preprint, to appear in Math Z.
Mentor for PCP-Highschool student Research program: On exceptional collection of line bundles on rational surfaces(joint with Ziheng Shan, Yingge Sun, Yujun Wu, Shijian Xi). Research Proposal and preprint (submitted).