Research

Last updated

I work in algebraic geometry and geometric representation theory, with primary interests in the theory of algebraic stacks, their geometric invariants such as cohomology and categories of sheaves, and algebraic structures and enumerative invariants constructed from them.

See also a list of my talks.

Contents

Publications§

  • C. Bu (2026). Proper moduli spaces of orthosymplectic complexes.
    Bulletin of the London Mathematical Society 58 (7), e70447, 9 pp.
    (doi) (zbMATH) (arXiv)

  • C. Bu (2026). Modules and generalizations of Joyce vertex algebras.
    Forum of Mathematics, Sigma 14, e82, 41 pp.
    (doi) (zbMATH) (arXiv)

  • C. Bu (2025). A motivic integral identity for $(-1)$-shifted symplectic stacks.
    Moduli 2, e16, 38 pp.
    (doi) (zbMATH) (arXiv)

  • C. Bu (2023). Counting sheaves on curves.
    Advances in Mathematics 434, 109334, 87 pp.
    (doi) (zbMATH) (arXiv)

Preprints§

  • C. Bu, T. Pădurariu, Y. Toda.
    Semiorthogonal decompositions for stacks.
    64 pp., 2026. (arXiv)

  • C. Bu, Y.-H. Kiem.
    Generalized intersection pairings on moduli spaces of vector bundles over a curve.
    43 pp., 2025. (arXiv)

  • C. Bu. Orthosymplectic Donaldson–Thomas theory.
    55 pp., 2025. (arXiv)

  • C. Bu, A. Ibáñez Núñez, T. Kinjo.
    Intrinsic Donaldson–Thomas theory. II. Stability measures and invariants.
    61 pp., 2025. (arXiv)

  • C. Bu, D. Halpern-Leistner, A. Ibáñez Núñez, T. Kinjo.
    Intrinsic Donaldson–Thomas theory. I. Component lattices of stacks.
    68 pp., 2025. (arXiv)

  • C. Bu, B. Davison, A. Ibáñez Núñez, T. Kinjo, T. Pădurariu.
    Cohomology of symmetric stacks.
    131 pp., 2025. (arXiv)

Survey articles§

  • C. Bu. What is a vertex algebra?
    10 pp., 2026. (pdf)

  • C. Bu. Stacks and combinatorics in enumerative geometry.
    17 pp., 2026. (pdf)

Deprecated works§

  • C. Bu. Enumerative invariants in self-dual categories. II. Homological invariants.
    122 pp., 2023. (arXiv)

  • C. Bu. Enumerative invariants in self-dual categories. I. Motivic invariants.
    147 pp., 2023. (arXiv)

Thesis§

  • C. Bu. Orthosymplectic enumerative geometry.
    PhD thesis, 2025. (pdf)

Other writings§

Introductory notes§

  • Homotopical algebra and homological algebra.
    (A gentle introduction to $\infty$-categories.)
    89 pp., 2019. (pdf) (web, in Chinese)

  • 示性类 [Characteristic classes].
    120 pp., 2019. (pdf) (web)

Course projects§

Little pieces of research done during my undergraduate years.

  • Homology of configuration spaces.
    22 pp., 2020. (pdf)

  • Stable irrationality of varieties.
    48 pp., 2020. (pdf)

  • A generalized handle theory.
    23 pp., 2019. (pdf)