Abstract of my Thesis:

We study the solvability of a Diophantine equation with mixed real exponents for sufficiently large natural numbers. The connection to a condition on the sum over the reciprocals of the exponents was first shown by Freĭman and Scourfield and recently made effective by Brüdern and Wooley. We prove an effective statement for the case of real exponents, which involves flooring in the equation. To this end, we apply the theory of the Hardy-Littlewood circle method adapted to Diophantine inequalities. In the fourth chapter, we show a mean value estimate utilising diminishing ranges and prove a novel Weyl-type estimate for exponential sums with a non-integer exponent. The calculations on the arcs in the fifth chapter lead to conditions that are translated into the effective result in the last chapter. 

Before the PhD:

Previously, I gained a broad mathematical background during my Master, studying Functional Analysis, as well as Complex Analysis and Number Theory. The title of my Master's thesis is "Stability of the squeezing function on a sequence of bounded domains", describing the behaviour of a biholomorphic invariant with respect to a certain limit process applied to the domains.

Generally I am interested in a lot of topics in the field of Complex Analysis, Number Theory and Functional Analysis, especially the more analytic part.