Research

Quasi-BPS categories for K3 surfaces

With Yukinobu Toda

Forum of Mathematics, Pi 14 (2026), e11, 1–69.

The categorical DT/PT correspondence and quasi-BPS categories for local surfaces

With Yukinobu Toda

Moduli 3 (2026), e1, 1–44.

Topological K-theory of quasi-BPS categories for Higgs bundles

With Yukinobu Toda

Journal of Topology 18 (2025), no. 4, e70049.

Quasi-BPS categories for symmetric quivers with potential

With Yukinobu Toda

Compositio Mathematica 161 (2025), no. 8, 1799–1854.

The local categorical DT/PT correspondence

With Yukinobu Toda

Advances in Mathematics 442 (2024), 109590.

Categorical and K-theoretic Donaldson–Thomas theory of C³ (part I)

With Yukinobu Toda

Duke Mathematical Journal 173 (2024), no. 10, 1973–2038.

Generators for K-theoretic Hall algebras of quivers with potential

Selecta Mathematica 30 (2024), no. 1, Article 4.

Groups of order p³ are mixed Tate

Rendiconti del Seminario Matematico della Università di Padova 152 (2024), 59–81.

Categorical and K-theoretic Donaldson–Thomas theory of C³ (part II)

With Yukinobu Toda

Forum of Mathematics, Sigma 11 (2023), e108, 1–47.

Relative stable pairs and a non-Calabi–Yau wall crossing

International Mathematics Research Notices 2023, no. 24, 21109–21166.

Categorical and K-theoretic Hall algebras for quivers with potential

Journal of the Institute of Mathematics of Jussieu 22 (2023), no. 6, 2717–2747.

Generators for Hall algebras of surfaces

Mathematische Zeitschrift 303 (2023), no. 2, Article 40.

K-theoretic Hall algebras of quivers with potential as Hopf algebras

International Mathematics Research Notices 2023, no. 7, 5781–5815.

Deformed dimensional reduction

With Ben Davison

Geometry & Topology 26 (2022), no. 2, 721–776.

Semiorthogonal decompositions for stacks

With Chenjing Bu and Yukinobu Toda

Preprint, arXiv:2605.25976 (2026).

The Dolbeault geometric Langlands conjecture via limit categories

With Yukinobu Toda

Preprint, arXiv:2508.19624 (2025).

Cohomology of symmetric stacks

With Chenjing Bu, Ben Davison, Andrés Ibáñez Núñez, and Tasuki Kinjo

Preprint, arXiv:2502.04253 (2025).

Quasi-BPS categories for Higgs bundles

With Yukinobu Toda

Preprint, arXiv:2408.02168 (2024).

Topological K-theory of quasi-BPS categories of symmetric quivers with potential

With Yukinobu Toda

Preprint, arXiv:2309.08432 (2023).

Intersection K-theory

Preprint, arXiv:2103.06223 (2021).

Noncommutative resolutions and intersection cohomology for quotient singularities

Preprint, arXiv:2103.06215 (2021).

K-theoretic Hall algebras for quivers with potential

PhD thesis, Massachusetts Institute of Technology, 2020.

The articles “Generators for K-theoretic Hall algebras of quivers with potential” and “Categorical and K-theoretic Hall algebras for quivers with potential” are revised and corrected versions of material discussed in it.