A reduction algorithm for Hilbert modular groups (2022)
Journal Article
Strömberg, F. (2022). A reduction algorithm for Hilbert modular groups. Journal of Number Theory, 241, 581-602. https://doi.org/10.1016/j.jnt.2022.02.011

The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [20]. The exposition is self-contained and suff... Read More about A reduction algorithm for Hilbert modular groups.

Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class (2020)
Journal Article
Langley, J. (2020). Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class. Journal d'Analyse Mathématique, 141(1), 225-246. https://doi.org/10.1007/s11854-020-0115-6

The Bank-Laine conjecture concerning the oscillation of solutions of second order homogeneous linear differential equations has recently been disproved by Bergweiler and Ere-menko. It is shown here, however, that the conjecture is true if the set of... Read More about Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class.

Asphericity and finiteness for certain group presentations (2019)
Journal Article
Edjvet, M., & Eljamel, N. (2019). Asphericity and finiteness for certain group presentations. Journal of Algebra, 536, 39-81. https://doi.org/10.1016/j.jalgebra.2019.06.028

We study diagrammatic reducibility for the relative group presentations Rn(k, l, ε) = H, x | t 3 x k t 2 x ε(k+l) where H = t | t n , n ≥ 7, k ≥ 1, l ≥ 0 and ε = ±1. We apply our results to classify finiteness for the group Gn(k, l, ε) defined by Rn(... Read More about Asphericity and finiteness for certain group presentations.

Solvable crossed product algebras revisited (2019)
Journal Article
Brown, C., & Pumpluen, S. (2019). Solvable crossed product algebras revisited. Glasgow Mathematical Journal, 1-21. https://doi.org/10.1017/S0017089519000089

For any central simple algebra over a field F which contains a maximal subfield M with non-trivial automorphism group G = AutF (M), G is solvable if and only if the algebra contains a finite chain of subalgebras which are generalized cyclic algebras... Read More about Solvable crossed product algebras revisited.

The effect of forest dislocations on the evolution of a phase-field model for plastic slip (2018)
Journal Article
Dondl, P., Kurzke, M., & Wojtowytsch, S. (2019). The effect of forest dislocations on the evolution of a phase-field model for plastic slip. Archive for Rational Mechanics and Analysis, 232(1), 65–119. https://doi.org/10.1007/s00205-018-1317-2

We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model is based on a Peierls-Nabarro type energy penalizing non-integer slip and elastic stress... Read More about The effect of forest dislocations on the evolution of a phase-field model for plastic slip.