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.