Research
I use Hodge theory to approach questions in complex algebraic geometry, especially singularity and topology of algebraic maps.
More specifically, I am interested in several invariants of singularities: Bernstein-Sato polynomial, Kashiwara-Malgrange V-filtration, (higher) multiplier ideals and Archimedean/p-adic/motivic zeta functions.
Preprints
14. Filtrations of D-modules along semi-invariant functions [arxiv]
with András Lőrincz.
13. On the Hodge and V-filtrations of mixed Hodge modules [arxiv]
with Dougal Davis.
12. Archimedean zeta functions, singularities and Hodge theory [arxiv]
with Dougal Davis and András Lőrincz.
11. Higher multiplier ideals [arxiv]
with Christian Schnell.
10. L^2 minimal extensions over Hermitian symmetric domains [arxiv]
Published and accepted papers
9. Homological criterion for higher Du Bois and higher rational singularities [arxiv]
with Laurentiu G.Maxim, to appear in Advanced Studies in Pure Mathematics, 2025.
8. A log resolution for the theta divisor of a hyperelliptic curve [arxiv]
with Christian Schnell, to appear in Algebraic Geometry (2026).
7. Hirzebruch-Milnor classes of hypersurfaces with nontrivial normal bundles and applications to higher du Bois and rational singularities [arxiv]
with Laurentiu G.Maxim and Morihiko Saito, International Mathematics Research Notices Volume 24, Issue 16, Pages 11977-11988, August 2024.
6. Cohomology of semisimple local systems and the Decomposition theorem [arxiv]
with Chuanhao Wei, Selecta Mathematica Volume 30, article number 5, (2024).
5. Zeros of one-forms and homologically trivial fibrations [arxiv]
with Stefan Schreieder, Michigan Math. J. 1-10 (2023).
4. Hodge modules and singular Hermitian metrics [arxiv]
with Christian Schnell, Mathematische Zeitschrift 303, 28 (2023).
3. Nodal elliptic curves on K3 surfaces [arxiv]
with Nathan Chen and François Greer, Mathematische Annalen, Volume 386, pages 2349–2370, (2023).
2. On irrationalities of hypersurfaces in P^{n+1} [arxiv]
Proceedings of the American Mathematical Society, 147(3):971–976, 2019.
1. Nef cones of nested Hilbert schemes of points on surfaces [arxiv]
with Tim Ryan, International Mathematics Research Notices, 2020(11):3260–3294.