# Papers

You can find my papers on Researchgate, or on arXiv.

## Preprints

• Ulam stability of lamplighters and Thompson groups, joint with Bharatram Rangarajan, 27 pages. We prove Ulam stability of lamplighters of the form $\Gamma \wr \Lambda$, where $\Lambda$ is infinite and amenable, as well as several groups of dynamical origin such as Thompson's groups $F, F', T$ and $V$. The proof uses a new cohomology theory called asymptotic cohomology, introduced in this paper, and along the way we prove several new results about asymptotic cohomology. We also tackle metric approximation questions for such groups, with respect to unitary and symmetric groups.

• Property (NL) for group actions on hyperbolic spaces, joint with Sahana Balasubramanya and Anthony Genevois, with Appendix by Alessandro Sisto, 44 pages. We introduce and study property (NL), standing for "no loxodromics": a group $G$ is said to have property (NL) if it admits as few actions on hyperbolic spaces as possible (i.e. only elliptic and parabolic). We produce many examples of groups with property (NL), mainly Thompson-like groups, and prove that property (NL) is stable under several natural group constructions. Alessandro Sisto's appendix describes a method to associate to an action of $G$ on a hyperbolic space, another action that is moreover cobounded, and keeps several useful properties from the original action.

• Finitely presented left orderable monsters, joint with Yash Lodha and Matt Zaremsky, 12 pages. A left orderable monster is a finitely generated group acting faithfully on the real line, all of whose actions on the line are globally contracting (i.e. as complicated as possible). The first examples emerged in the last few years, and are all infinitely presented and quite complicated to construct. We provide an elementary construction that moreover produces the first finitely presented (and even type $F_\infty$) examples.

• Hopfian wreath products and the stable finiteness conjecture, joint with Henry Bradford, 28 pages. We study the problem of when a wreath product $\Delta \wr \Gamma$ is Hopfian, for finitely generated Hopfian groups $\Delta$ and $\Gamma$. Our main result establishes a strong connection between the case in which $\Delta$ is abelian, and the direct and stable finiteness conjectures of Kaplansky in group rings. Namely the latter hold true if and only if $\Delta \wr \Gamma$ is Hopfian whenever $\Delta$ is finitely generated and abelian and $\Gamma$ is finitely generated and Hopfian.

• Aut-invariant quasimorphisms on groups, joint with Ric Wade, 17 pages. We proved that for $G$ in a large class of groups that includes non-elementary hyperbolic groups and non-virtually abelian RAAGs and RACGs, there is an infinite-dimensional space of homogeneous quasimorphisms on $G$ that are invariant under the action of the automorphism group. The case of the free group of rank at least $3$ settles a question of Miklós Abert.

• Median quasimorphisms on CAT(0) cube complexes and their cup products, joint with Benjamin Brück and Clara Löh, 34 pages. We extended vanishing results on cup products of Brooks quasimorphisms of free groups to cup products of median quasimorphisms, i.e., Brooks-type quasimorphisms of group actions on CAT(0) cube complexes. Special attention is paid to groups acting on trees and right-angled Artin groups.

• No quasi-isometric rigidity for proper actions on CAT(0) cube complexes, joint with Anthony Genevois, 12 pages. We exhibited groups acting properly and cocompactly on CAT(0) cube complexes, with quasi-isometric groups that do not admit any proper actions on a CAT(0) cube complex, settling a question of Niblo, Sageev and Wise.

• Finitely generated simple left orderable groups with vanishing second bounded cohomology, joint with Yash Lodha, 18 pages. We proved that the finitely generated simple left orderable groups constructed by Yash and James Hyde in this paper have vanishing second bounded cohomology, settling a question from Navas's 2018 ICM problem list.

• Second bounded cohomology of groups acting on $1$-manifolds and applications to spectrum problems, joint with Yash Lodha, 28 pages. We provided a simple dynamical criterion for second bounded cohomology vanishing, and applied it to settling several questions about the bounded cohomology of left-orderable groups, the spectrum of stable commutator length, and the spectrum of simplicial volume. We had previously only looked at stable commutator length, and that result is presented in a self-contained way in the preprint Algebraic irrational stable commutator length in finitely presented groups.

• Ultrametric analogues of Ulam stability of groups, 87 pages. I studied stability of metric approximations of groups, when the approximating groups are endowed with bi-invariant ultrametrics. The main case study is a $p$-adic analogue of Ulam stability, where unitary matrices are replaced by integral $p$-adic ones.

• Infinite sums of Brooks quasimorphisms and cup products in bounded cohomology, 66 pages. This is my Master Thesis, in which I studied infinite sums of Brooks quasimorphisms with combinatorial methods, and provided new classes of quasimorphisms of the free group which have trivial cup product in bounded cohomology. It was supervised by Alessandra Iozzi and Konstantin Golubev.

## Chapter in book

• In: Bounded Cohomology and Simplicial Volume - see "Editorial work" below. I wrote Chapter 9: "Extension of quasicocycles from hyperbolically embedded subgroups", 15 pages. The text is an exposition of this paper, thought for people who are interested in bounded cohomology but are not necessarily familiar with the notions from geometric group theory that are involved. It is a more detailed version of a "What is?" talk that I gave (see below).