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.
Contents
Publications§
C. Bu (2025). A motivic integral identity for -shifted symplectic stacks.
Moduli, to appear.
(arXiv)C. Bu (2023). Counting sheaves on curves.
Advances in Mathematics 434, 109334, 87 pp.
(doi) (zbMATH) (arXiv)
Preprints§
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.
64 pp., 2025. (arXiv)Cohomology of symmetric stacks.
With B. Davison, A. Ibáñez Núñez, T. Kinjo, and T. Pădurariu.
119 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 Superseded by a new work.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§
Intrinsic Donaldson–Thomas theory. III. Wall-crossing and applications.
With A. Ibáñez Núñez and T. Kinjo.Orthosymplectic enumerative geometry.
PhD thesis.
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 -categories, 89 pp., 2019. (pdf)示性类 [Characteristic classes].
2019. (web)
Course projects§
Little pieces of research done during my undergraduate years.