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.

    Office: 223, Max Planck Institute for Mathematics, Bonn.
    Email:xlin@mpim-bonn.mpg.de; 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 of complete intersection, categorical Hitchin fibration, and the Hodge conjecture for complete intersection.

  • 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 Veronese double cones. (with Jørgen Vold Rennemo, and Shizhuo Zhang) In preparation.
  • 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) In preparation.
  • Kuznetsov's Fano threefold conjecture via Hochschild-Serre algebra . (with Shizhuo Zhang) Submitted.
  • Serre Algebra, Matrix factorization and categorical Torelli theorem for hypersurfaces . (with Shizhuo Zhang) Submitted.
  • 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.
  • Some remarks of Hochschild homology and semi-orthogonal decompositions. Submitted.
  • 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. Submitted
  • 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.

    • Teaching

    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

    [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

    [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.

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

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

    [March 2022 - June 2022] Cornell University.

    [March, 2021] Shanghai Technology University.

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

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

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

    Links

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