Research

I work in algebraic geometry and number theory. Currently, I am using tools from the transcendental aspect of algebraic geometry (mixed Hodge modules) and ideas from geometric representation theory of real groups (see this paper) to approach questions in singularities of hypersurfaces and more generally local complete intersection varietes.

In particular, I am interested in the Strong Monodromy Conjecture, which predicts a mysterious relationship between the arithmetic invariants of the singularity (poles of the p-adic zeta function) with the geometric/analytic counterparts (roots of the Bernstein-Sato polynomial).

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.