Submitted to a journal.

Abstract: We show that any partial ascending HNN extension of a free group embeds in an actual ascending HNN extension of a free group.  Moreover, we can ensure that it embeds as the parabolic subgroup of a relatively hyperbolic group.

Link to arXiv: https://arxiv.org/abs/2408.00453.

Published in Glasgow Mathematical Journal, 65(3), 569-572 (2023)

Abstract: We study a family of finitely generated residually finite small-cancellation groups. These groups are quotients of $F_2$ depending on a subset $S$ of positive integers. Varying $S$ yields continuously many groups up to quasi-isometry.

Link to published paper: https://www.cambridge.org/core/journals/...

Link to arXiv: https://arxiv.org/abs/2207.00354

Published in Journal of Group Theory, 25(2), 207-216 (2021)

Abstract: We study a family of finitely generated residually finite groups. These groups are doubles $F_2 ∗_H F_2$ of a rank-2 free group $F_2$ along an infinitely generated subgroup $H$. Varying $H$ yields uncountably many groups up to isomorphism.

Link to published paper: https://www.degruyter.com/document/doi/10.1515/jgth-2021-0094/html 

Link to arXiv: https://arxiv.org/abs/2207.00410 

The associated thesis is linked here.  Some of the proofs are simplified and generalised in the submitted paper on the journal.