Research
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 geometric representation theory and derived algebraic geometry.
Contents
Publications§
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§
Proper moduli spaces of orthosymplectic complexes.
9 pp., 2025. (arXiv)Generalized intersection pairings on moduli spaces of vector bundles over a curve.
With Y.-H. Kiem.
43 pp., 2025. (arXiv)Modules and generalizations of Joyce vertex algebras.
48 pp., 2025. (arXiv)Orthosymplectic Donaldson–Thomas theory.
55 pp., 2025. (arXiv)Intrinsic Donaldson–Thomas theory. II. Stability measures and invariants.
With A. Ibáñez Núñez and T. Kinjo.
61 pp., 2025. (arXiv)Intrinsic Donaldson–Thomas theory. I. Component lattices of stacks.
With D. Halpern-Leistner, A. Ibáñez Núñez, and T. Kinjo.
68 pp., 2025. (arXiv)Cohomology of symmetric stacks.
With B. Davison, A. Ibáñez Núñez, T. Kinjo, and T. Pădurariu.
131 pp., 2025. (arXiv)Enumerative invariants in self-dual categories. II. Homological invariants.
122 pp., 2023. (arXiv)Enumerative invariants in self-dual categories. I. Motivic invariants.
147 pp., 2023. Superseded by a new work. (arXiv)
Works in progress§
Semiorthogonal decompositions for stacks.
With T. Pădurariu and Y. Toda.Intrinsic Donaldson–Thomas theory. III. Wall-crossing and applications.
With A. Ibáñez Núñez and T. Kinjo.
Thesis§
- Orthosymplectic enumerative geometry.
PhD thesis, 2025. (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) (web, in Chinese)
Course projects§
Little pieces of research done during my undergraduate years.