I am researching arithmetic analogues of topological quantum field theories. The prevailing example is arithmetic Chern-Simons theory, invented in 2015 by Minhyong Kim. The theory is based on similiarities between the cohomology of a 3-manifold and the etale cohomology of the ring of integers of a number field. In special cases it is well understood, e.g. for totally imaginary number fields that contain the n-th roots of unity, the action of arithmetic Chern-Simons theory modulo 2 coincides with the Legendre symbol.
Master thesis: Irreducible polynomials over finite fields as factors of sparse polynomials
Bachelor thesis: Dedekind-Weber-Aequivalenz und der Vergleich von glatten mit regulaeren Schemata
Seminar "Function fields" SoSe22
Teaching Assistant Algebraic number theory III SoSe22
Teaching Assistant Algebraic number theory II WiSe21
Teaching Assistant Algebraic number theory I SoSe21
Teaching Assistant Linear algebra I SoSe20