Research

Last updated

I work in algebraic geometry, with primary interests in the theory of algebraic stacks, enumerative invariants such as Donaldson–Thomas invariants and their categorification, and related aspects of geometric representation theory and derived algebraic geometry.

See also a list of my talks.

Contents

Publications§

  • C. Bu. Modules and generalizations of Joyce vertex algebras.
    To appear in Forum of Mathematics, Sigma.
    (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. Proper moduli spaces of orthosymplectic complexes.
    9 pp., 2025. (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 article§

  • 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)

Works in progress§

  • C. Bu, T. Pădurariu, Y. Toda.
    Semiorthogonal decompositions for stacks.

  • C. Bu, A. Ibáñez Núñez, T. Kinjo.
    Intrinsic Donaldson–Thomas theory. III. Wall-crossing and applications.

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 that some have found helpful.)
    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)