Overview

My research is in algebraic geometry, especially Hodge theory and singularity theory. I am interested in how the rich structures arising from Hodge theory and D-modules (modules over differential operators) can reveal information that first appears in very different forms—in analysis, number theory,  topology, birational geometry, and representation theory. I also borrow ideas from geometry representation theory.

Much of my recent work concerns invariants of singularities and the unexpected relationships among them,  for example the Strong Monodromy Conjecture. I also work on applications of Hodge theory to birational geometry and theta divisors, and, on interactions between D-modules and representation theory.

Singularities and Hodge theory

Multivariate V-filtrations and the Strong Monodromy Conjecture for hyperplane arrangements [arxiv], with Dougal Davis.

Filtrations of D-modules and multiplicities of roots of Bernstein-Sato polynomials [arxiv], with András Lőrincz.

Archimedean zeta functions, singularities and Hodge theory [arxiv], with Dougal Davis and András Lőrincz, to appear in Compositio Mathematica.

On the Hodge and V-filtrations of mixed Hodge modules [arxiv], with Dougal Davis, Selecta Mathematica, Volume 32, article number 48, (2026). Here is a self-contained version.

Birational geometry and abelian varieties

Higher multiplier ideals [arxiv], with Christian Schnell, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 2026, no. 832, 2026, pp. 153-197. 

A log resolution for the theta divisor of a hyperelliptic curve [arxiv], with Christian Schnell, Algebraic Geometry, 13 (4) (2026) 462–503.

D-modules, representation theory and topology

Filtrations of D-modules along semi-invariant functions [arxiv], with András Lőrincz, Advances in Mathematics, 499:111037, 2026.

Homological criterion for higher Du Bois and higher rational singularities [arxiv], with Laurentiu G.Maxim, Advanced Studies in Pure Mathematics, 89 (2025), pp. 375-402.

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.

Analytic aspects of Hodge theory

Hodge modules and singular Hermitian metrics [arxiv], with Christian Schnell, Mathematische Zeitschrift 303, 28 (2023).

L^2 minimal extensions over Hermitian symmetric domains [arxiv]

Cohomology of semisimple local systems and the Decomposition theorem [arxiv], with Chuanhao Wei, Selecta Mathematica Volume 30, article number 5, (2024).

Classical algebraic geometry

Zeros of one-forms and homologically trivial fibrations [arxiv], with Stefan Schreieder, Michigan Math. J.  75(5): 917-926 (November 2025).

Nodal elliptic curves on K3 surfaces [arxiv], with Nathan Chen and François Greer,  Mathematische Annalen, Volume 386, pages 2349–2370, (2023).

On irrationalities of hypersurfaces in P^{n+1} [arxiv], Proceedings of the American Mathematical Society, 147(3):971–976, 2019.

Nef cones of nested Hilbert schemes of points on surfaces [arxiv], with Tim Ryan, International Mathematics Research Notices, 2020(11):3260–3294.