Research

This is my research home page.

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

Works in progress§

  • Self-dual Donaldson–Thomas theory. I. Invariants.

  • Self-dual Donaldson–Thomas theory. II. Wall-crossing formulae.

  • Intrinsic Donaldson–Thomas theory. I. Component lattices of stacks.
    With Daniel Halpern-Leistner, Andrés Ibáñez Núñez, and Tasuki Kinjo.

  • Intrinsic Donaldson–Thomas theory. II. Stability measures and invariants.
    With Andrés Ibáñez Núñez and Tasuki Kinjo.

  • Intrinsic Donaldson–Thomas theory. III. Wall-crossing and applications.
    With Andrés Ibáñez Núñez and Tasuki Kinjo.

  • Cohomology of symmetric stacks.
    With Ben Davison, Andrés Ibáñez Núñez, Tasuki Kinjo, and Tudor Pădurariu.

Preprints§

  • A motivic integral identity for $(-1)$-shifted symplectic stacks.
    Preprint v2, 45 pp. (arXiv)

  • Enumerative invariants in self-dual categories. II. Homological invariants.
    Preprint v2, 122 pp. (arXiv)

  • Enumerative invariants in self-dual categories. I. Motivic invariants.
    Preprint v3, 147 pp. (arXiv)

Publications§

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

Slides§

See also the full list of talks.

  • 顶点代数与同调 [Vertex algebras and homology].
    22 July 2024, Tsinghua University. (pdf)

  • A theory of type B/C/D enumerative invariants.
    20 November 2023, University of Oxford. (pdf)

  • Counting sheaves on curves.
    7 November 2022, University of Oxford. (pdf)

Other writings§

Introductory notes§

Notes written for reading groups that I organized as an undergraduate.

  • Homotopical algebra and homological algebra.
    Notes on $\infty$-categories, 89 pp., 2019. (pdf)

  • 示性类 [Characteristic classes].
    2019. (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)