Welcome to Xun Lin's Homepage

林汛

  • 2014/09 -- 2018/06, Undergraduate student. Southern University of Science and Technology, Shenzhen. Mathematics.
  • 2018/09 -- 2023/06, Ph.D. Yau Mathematical Sciences Center, Tsinghua University, Beijing. Mathematics.
  • 2023/09 -- 2025/09, Max Planck Institute for Mathematics, Bonn. My mentor is Professor Daniel Huybrechts.
  • 2025/09 -- 2026/09, Postdoc in Mathematics, Hong Kong University of Science and Technology.
  • 2026/09 -- , Assistant professor in Mathematics, The Chinese Unviersity of Hong Kong(Shenzhen).

    Office: IAS for study, Hong Kong university of Science and Technology. Room 2204. Hong Kong, China.
    Email:linx@ust.hk; lin-x18@tsinghua.org.cn

    My supervisor of doctoral thesis is Professor William Donovan. My Curriculum Vitae .

    Research

    My research is in algebraic geometry. I am interested in geometry of derived categories and GLSM models, Serre-Hochschild algebra of smooth proper dg categories, Hodge theory of algebraic varieties, and Hitchin fibration.

    Currently I am working at categorical Torelli problems, categorical Hitchin fibration, and the Torelli problem for hypersurfaces in projective space.

  • Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives.(with Shizhuo Zhang and Zheng Zhang.)
  • Higgs objects over noncommutative varieties. (with Shizhuo Zhang) In progress.
  • Fully faithful functors, skyscraper sheaves, and birational equivalence. (with Chunyi Li, and Xiaolei Zhao).
  • IVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces. (with Jørgen Vold Rennemo, and Shizhuo Zhang).
  • Categorical Torelli theorem for Verra threefolds and fourfolds. (with Zhiyu Liu, and Shizhuo Zhang) In preparation.
  • Singular category: Hodge theory and (birational) categorical Torelli theorem for nodal Fano threefolds. (with Fei Xie, Daniele Faenzi, and Shizhuo Zhang) In preparation.
  • Three approaches to categorical Torelli theorem for cubic threefold of non-Eckardt type via equivariant Kuznetsov components. (with Xianyu Hu, Sebastian Casalaina-Martin, Shizhuo Zhang, Zheng Zhang).
  • Kuznetsov's Fano threefold conjecture via Hochschild-Serre algebra . (with Shizhuo Zhang) To appear in Math.Z.
  • Serre Algebra, Matrix factorization and categorical Torelli theorem for hypersurfaces . (with Shizhuo Zhang)To appear in Math.Ann.(2024).
  • Infinitesimal categorical Torelli theorems for Fano threefolds.(with Augustinas Jacovskis, Zhiyu Liu, Shizhuo Zhang) Journal of Pure and Applied Algebra, Volume 227, Issue 12, 2023, 107418.
  • Indecomposability of the bounded derived categories of Brill-Noether varieties (with Chenglong Yu). Proc. Amer. Math. Soc. 152 (2024), 1457-1465.
  • On nonexistence of semi-orthogonal decompositions in algebraic geometry. International Mathematics Research Notices, Volume 2026, Issue 2, January 2026.
  • Categorical Torelli theorems for Gushel--Mukai threefolds(with Augustinas Jacovskis, Zhiyu Liu, Shizhuo Zhang), Categorical Torelli theorems for Gushel–Mukai threefolds. J. London Math. Soc., 109: e12878.
  • Noncommutative Hodge conjecture. J. Noncommut. Geom. 17 (2023), 1367–1389.

    • Notes

  • Some remarks of Hochschild homology and semi-orthogonal decompositions.

    • Teaching

    Fundation of Mathematics, Instructor. Hong Kong university of Science and Technology. The note of the course.

    General Topology, TA. Tsinghua University

    Mathematical Analysis 2, TA. Tsinghua University

    Functional Analysis 1, TA. Tsinghua University

    Calculus A, TA. Tsinghua University

    Algebraic geometry 1, TA. Tsinghua University

    Talks

    [October, 2025] Infinitesimal Torelli for special Gushel-Mukai three folds. Algebraic geometry seminar in Sun Yat-Sen University, Guang Zhou, China.

    [November 28, 2024] IVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces. SAG seminar in University of Bonn, Germany.

    [July 2024] Algebraic geometry seminar in Southern University of Science and Technology. Cagtegorical Torelli for smooth hypersurfaces.

    [Feb 2024] Obserseminar in MPIM. Infinitesimal categorical Torelli: an application to Kuznetsov' Fano 3-folds conjecture.

    [Sept 2023] 5 minutes talk in JTP program of Hausdorff center, Bonn. A genralized theorem of Bondal Orlov reconstruction for fully faithful embedding.

    [April 2023] Seminar of Advance Topics in Algebra and Geometry, Tsinghua university. A new proof of Torelli for cubic 4-folds.

    [March 2023] Geometric representation theory seminar, Tsinghua university. Infinitesimal categorical Torelli.

    [Nov 2022] Tsinghua preprint seminar. Hodge theory of combinatorics: an introduction.

    [Oct 2022] Tsinghua preprint seminar. Categorical Torelli.

    [July 2022] University of Warwick, online poster session of VBAC seminar. Indecomposibility of the bounded derived categories of Brill-Noether varieties.

    [April 2022] Stony Brook university, algebraic geometry seminar. Nonexistence of semi-orthogonal decompositions and sections of para-canonical systems.

    [March 2022] Cornell university, algebraic geometry seminar. Nonexistence of semi-orthogonal decompositions and sections of para-canonical systems.

    [Jan 2022] Southern University of Science and Technology, Shenzhen, Geometry and Topology seminar. Nonexistence of semi-orthogonal decompositions and sections of para-canonical systems.

    [Fall 2021] Tsinghua University, student seminar, VGIT and derived categories.

    [Sept 2021] Tata Institute of Fundamental Research, India. Nonexistence of semi-orthogonal decompositions and the base locus of para-canonical systems.

    [June 2021] Edinburgh University, Internal seminar. Derived categories of symmetric product of curves.

    [May 2021] Tsinghua University, Geometry representation seminar. Noncommutative Hodge conjecture.

    [March 2021] Southern University of Science and Technology, Shenzhen. Noncommutative Hodge conjecture.

    [March 2021] Shanghaitech University, Shanghai. Noncommetative Hodge conjecture.

    [Fall 2019] Tsinghua University, student algebraic geometry seminar. Examples of Shimura varieties.

    [Spring 2019] Tsinghua University, student algebraic geometry seminar. Derived Torelli of K3 surfaces.

    [Spring 2019] Tsinghua University, student algebraic geometry seminar. Nonexistence of semi-orthogonal decompositions and sections of canonical bundle.

    [Fall 2018] Tsinghua University, student algebraic geometry seminar. Geometry of moduli space of sheaves on surfaces.

    Visiting and seminars

    [April 20 - April 25, 2026] Workshop on Moduli spaces in various flavors of geometry, Kyoto Univerisity, Kyoto, Japan.

    [December 10 - December 15, 2025] Workshop on derived category. Yonsei University, Seoul, Korea.

    [July 15 - July 22, 2024] Southern University of Science and Technology, China.

    [June 27 - Sept 30, 2024] Morningside Center of Mathematics, Chinese Academy of Sciences, China.

    [June 26 - July 24, 2024] Yau Mathematical Sciences Center, Tsinghua university, China.

    [June 4 - June 22, 2024] Shanghai center for mathematical sciences, Fudan University, China

    [May 26 - May 31, 2024] Stockholm University, Sweden.

    [Jan 22, 2024 - Jan 26, 2024] University of Genova, Italy.

    [Dec 15, 2023 -Dec 20, 2023] University of Oslo, Norway.

    [Sept 2023 - Dec 2023] Hausdorff Center for Mathematics, Bonn. JTP program, Germany

    [July 26, 2023 - August 10, 2023] Sichuan University, China.

    [July 10, 2023 - July 21, 2023] Tsinghua University, China.

    [March 2022 - June 2022] Cornell University, USA.

    [March, 2021] Shanghai Technology University, China

    [Sept 2019] Geometry of derived categories, Liverpool University, UK.

    [May 2019] Derived categories seminar in Sun Yat-Sen University, China

    [May 2019] Algebraic geometry for Young scholars in USTC, China

    Links

    Students seminar in Tsinghua University, Fall, 2022. preprint seminar.