Publications

• On a coarse invertibility spectrum for coarse groups
  with Federico Vigolo
  Mathematische Zeitschrift 310 (2025), arXiv:2404.08536

  Abstract

  We introduce a coarse algebraic invariant for coarse groups and use it to differentiate various coarsifications of the group of integers. This lets us answer two questions posed by Leitner and Vigolo. The invariant is obtained by considering the set of exponents n such that taking n-th powers defines a coarse equivalence of the coarse group.

• On everywhere locally soluble varieties in families over toric bases
  with Vladi Mitankin, Damaris Schindler and Florian Wilsch
  arXiv:2609.01825

  Abstract

  We determine the density of locally soluble fibres in certain families of varieties over a toric base. For this we develop a new form of the hyperbola method for toric bases which allows for counting functions with a growth behaviour of the form $B^a (\log B)^{−\Delta}$.

PhD Thesis

• Sums with hyperbolic conditions
  Georg-August-Universität Göttingen (e-diss)

  Abstract

  We develop a generalization of the hyperbola method, a technique used to obtain asymptotic estimates for summations involving a product of variables as a constraint, given that similar sums over rectangular regions can be evaluated. Compared to previous variations, our approach widens the range of admissible main terms and requires milder assumptions on the error terms. We then make use of the hyperbola method to work on a specific counting problem. Using the Hardy-Littlewood circle method, we compute an asymptotic formula where our previous results are used to evaluate or bound the exponential sums that arise