Research

Current research interests:

• D-modules, irregular singularities and Stokes phenomena
• Riemann–Hilbert correspondences
• integral transforms
• moduli spaces of connections
• subanalytic geometry
• logarithmic geometry

My research is centred around topics from Algebraic Analysis, the algebraic study of differential equations.

The study of irregular singularities is an active field of research. With modern frameworks for irregular Riemann–Hilbert correspondences, new topological methods for their study have come up. It is an overall aim of my research to combine traditional and recent methods and their underlying ideas in order to tackle problems in different directions, from the computation of Fourier transforms through number-theoretic questions to the study of invariants for singular loci.

The theory of D-modules has touching points and applications in various areas of mathematics such as algebraic geometry, symplectic topology, mirror symmetry and mathematical physics, as well as representation theory, and I am studying different facets of these fascinating interactions.

Moreover, I am broadly interested in analytic and algebraic geometry, in particular in the construction of moduli spaces, homological algebra and logarithmic geometry.

Publications and preprints

Combinatorics of the Fourier transform: Stokes data, Gale duality and frieze patterns (with Jean Douçot), Preprint (2026), arXiv:2608.17992.

Stokes phenomenon of Kloosterman and Airy connections (with Konstantin Jakob), Preprint (2026), arXiv:2404.09582v2.

A topological algorithm for the Fourier transform of Stokes data at infinity (with Jean Douçot), Journal of the London Mathematical Society 112, no. 2, e70253 (2025), doi:10.1112/jlms.70253. — arXiv

Kashiwara conjugation and the enhanced Riemann–Hilbert correspondence, Portugaliae Mathematica 81, no. 3/4, 347–387 (2024), doi:10.4171/PM/2122. — arXiv

Unusual functorialities for weakly constructible sheaves (with Pierre Schapira), Pacific Journal of Mathematics 334, no. 1, 153–166 (2025), doi:10.2140/pjm.2025.334.153. — arXiv

An introduction to field extensions and Galois descent for sheaves of vector spaces, Rendiconti del Seminario Matematico della Università di Padova Online First (2025), doi:10.4171/RSMUP/189. — arXiv

Moderate Growth and Rapid Decay Nearby Cycles via Enhanced Ind-Sheaves (with Brian Hepler), Publications of the Research Institute for Mathematical Sciences 61, no. 1, 1–51 (2025), doi:10.4171/prims/61-1-1. — arXiv

Stokes matrices for Airy equations (with Konstantin Jakob), Tohoku Mathematical Journal (second series) 74, no. 4, 501–520 (2022), doi:10.2748/tmj.20210506. — arXiv

Betti Structures of Hypergeometric Equations (with Davide Barco, Marco Hien and Christian Sevenheck), International Mathematics Research Notices 2023, no. 12, 10641–10701 (2023), doi:10.1093/imrn/rnac095. — arXiv

D-modules of pure Gaussian type and enhanced ind-sheaves, Manuscripta Mathematica 167, 435–467 (2022), doi:10.1007/s00229-021-01281-y. — arXiv

Theses

D-Modules of Pure Gaussian Type from the Viewpoint of Enhanced Ind-Sheaves, Dissertation, Universität Augsburg (2020).

Enhanced Solutions of Exponential D-Modules, Master’s thesis, Technische Universität München (2016).

Sheaves on the subanalytic site and tempered solutions of D-modules on curves, Bachelor’s thesis, Universität Augsburg (2014).