I am a PostDoc at the Institue of Mathematics in Mainz.
My research project Differential Galois theory and linear algebraic grops over algebraic function fields is
funded by the DFG.
- Differential Galois theory
- Algebraic groups and generalizations (proalgebraic groups, difference algebraic groups)
- Division algebras and local-global principles over semiglobal fields
- Algebraic groups as difference Galois groups of linear differential equations. Joint with Michael Wibmer. Preprint.
- Torsors for Difference Algebraic Groups. Joint with Michael Wibmer. Preprint.
- Frobenius Difference Equations with Classical Groups as Galois groups. Preprint.
- The differential Galois group of the rational function field. Joint with David Harbater, Julia Hartmann and Michael Wibmer. Advances in Mathematics (to appear). Preprint.
- Free differential Galois groups. Joint with David Harbater, Julia Hartmann and Michael Wibmer. Transactions of the American Mathematical Society (to appear). Preprint.
- Large Fields in Differential Galois Theory. Joint with David Harbater, Julia Hartmann and Florian Pop. Journal of the Institute of Mathematics of Jussieu (to appear). Link.
- Differential Embedding Problems over Laurent series fields. Joint with David Harbater and Julia Hartmann. Journal of Algebra 513, 99-112, 2018. Link.
- Differential Embedding Problems over Complex Function Fields. Joint with David Harbater, Julia Hartmann and Michael Wibmer. Documenta Mathematica 23, 241-291,2018. Link.
- New classes of parameterized differential Galois groups. Mathematische Zeitschrift 288, 361-381, 2018. Link.
- Differential Galois Groups over Laurent Series Fields. Joint with David Harbater and Julia Hartmann. Proceedings of the London Mathematical Society 112 (3): 455-476, 2016. Link.
- On the parameterized differential inverse Galois problem over k((t))(x). Journal of Algebra 428, 43-53, 2015. Link.
- Embedding problems of division algebras. Communications in Algebra 43(4), 1472-1486, 2015. Link.
- A Difference Version of Nori's Theorem. Mathematische Annalen 359(3), 759-784, 2014. Link.
- Additive Polynomials for ﬁnite groups of Lie type. Joint with Maximilian Albert. Israel J. Math. 186(1), 125-195, 2011. Link.
Difference equations with semisimple Galois groups in positive characteristic. Dissertation. Link.