I am now a postdoc fellow at SLM/MSRI@Berkeley on the program Noncommutative Algebraic Geometry .
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 degree in Mathematics at Kansas State University, Manhattan, KS, USA where I was working with professor Alexander Rosenberg, I was a postdoctoral research associate at The university of Edinburgh under ERC grant. My mentor was professor Arend Bayer. I was also a postdoc fellow at Max-Plank institute for Mathematics and my mentor was professor Daniel Huybrechts. Then I worked as a CIMI postdoc at Institute of Mathematics at Toulouse, France, my mentor were professor Laurent Manivel and Marcello Bernardara. During Sep. to Dec. 2023, I was a guest researcher at Junior Trimester Program at Hausdorff Research Institute for Mathematics on derived categories, Hodge theory and Chow groups.
My email address is shizhuozhang@mpim-bonn.mpg.de. If this email is no longer working, please send email to 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, wall-crossing techniques with application to HyperKahler geometry. Recently, I am working on categorical Torelli theorems.
Cyclic strong exceptional collection of line bundles(with Alexey Elagin and Junyan Xu), European Journal of Mathematics. 7, 69-115 (2021)
Note on applications of Toric systems on surfaces. Journal of Pure and Applied Algebra 223(2019), no.3, 1139-1160.
Brill-Noether and existence of semistable sheaves for del Pezzo surfaces.(with Daniel Levine), to appear in Annales de l'institut Fourier
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
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.
Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces(with Hanfei Guo and Zhiyu Liu), to appear in Mathematical Research Letters.
Categorical Torelli Theorems for Gushel-Mukai threefolds. (with Augustinas Jacovskis, Zhiyu Liu and Xun Lin), Journal of London Mathematical Society, Volume109, Issue3
Bridgeland moduli spaces for Gushel-Mukai threefolds and Kuznetsov Fano threefold conjecture. submitted.
Brill-Noether theory for Kuznetsov components and refined categorical Torelli theorems for index one Fano threefolds(with Augustinas Jacovskis and Zhiyu Liu), submitted.
A moduli theoretic approach to Lagrangian subvarieties of hyperkähler varieties: Examples(with Hanfei Guo and Zhiyu Liu).
New perspectives on categorical Torelli theorems for del Pezzo threefolds (with Soheyla Feyzbakhsh and Zhiyu Liu), submitted.
Kuznetsov Fano threefold conjecture via Hochschild-Serre algebra(with Xun Lin), submitted.
Linear subspaces of the intersection of two quadrics via Kuznetsov component(with Yanjie Lie), submitted.
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).
Serre algebra, matrix factorization and categorical Torelli theorem for hypersurface.(with Xun Lin), submitted.
IVHS via Kuznetsov components and categorical Torelli theorems for Veronese double cones. (with Jørgen Vold Rennemo and Xun Lin).
Moduli of quiver representations for exceptional collections on surfaces I (with Xuqiang Qin), submitted.
Lagrangian families of Bridgeland moduli spaces from Gushel-Mukai fourfolds and double EPW cubes. (with Soheyla Feyzbakhsh, Hanfei Guo and Zhiyu Liu).
Singular category: Hodge theory and (birational) categorical Torelli theorem for nodal Fano threefolds. (with Xun Lin, Fei Xie and Daniele Faenzi). In preparation, available very soon.
Hilbert scheme of low degree rational curves and Gieseker moduli spaces (with Yanjie Li and Zhiyu Liu), in preparation.
Moduli space of sheaves on intersection of three quadrics in projective spaces(with Fei Xie), in progress.
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--semiorthogonal components of cubic hypersurfaces. (with Xun Lin). In progress.
Invited talks
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
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).