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 the theory of enhanced ind-sheaves and the Riemann–Hilbert correspondence for holonomic D-modules by D’Agnolo–Kashiwara, new topological methods for their study have come up. In my doctoral thesis, I used this approach to compute the Fourier–Laplace transform of Stokes data for certain meromorphic connections.
It is an overall aim of my research to make use of these new methods and their underlying ideas to tackle previously more difficult problems.
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 aspects 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 o-minimal geometry.
Publications and preprints
Kashiwara conjugation and the enhanced Riemann-Hilbert correspondence, Preprint (2023), pdf.
Unusual functorialities for weakly constructible sheaves (with Pierre Schapira), Preprint (2023), arXiv:2303.11189.
Moderate Growth and Rapid Decay Nearby Cycles via Enhanced Ind-Sheaves (with Brian Hepler), Preprint (2022), arXiv:2206.06095.
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, rnac095 (2022), https://doi.org/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
Field extensions and Galois descent for sheaves of vector spaces, Preprint (2023), arXiv:2302.14837, pdf.
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).