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
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.