Papers

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

Accepted

• 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. To appear in Mathematische Annalen.

• Property (NL) for group actions on hyperbolic spaces, joint with Sahana Balasubramanya and Anthony Genevois, with Appendix by Alessandro Sisto, 48 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. To apper in Groups, Geometry and Dynamics.

• 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 fixed point-free actions on the line are proximal (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. To appear in Ergodic Theory and Dynamical Systems.

• Aut-invariant quasimorphisms on groups, joint with Ric Wade, 20 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. To appear in Transactions of the American Mathematical Society.

• No quasi-isometric rigidity for proper actions on CAT(0) cube complexes, joint with Anthony Genevois, 13 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. To appear in Proceedings of the American Mathematical Society.

• Braided Thompson groups with and without quasimorphisms, joint with Yash Lodha and Matt Zaremsky, 22 pages. We studied second bounded cohomology and quasimorphisms of braided Thompson groups such as $bV, bF$, or their ribbon cousins such as $rV$. These exhibit some interesting bounded cohomological behaviours. To appear in Algebraic & Geometric Topology.

• Second bounded cohomology of groups acting on $1$-manifolds and applications to spectrum problems, joint with Yash Lodha, 37 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. To appear in Advances in Mathematics.

• Bounded cohomology and binate groups, joint with Clara Löh and Marco Moraschini, 33 pages. We proved that binate groups are boundedly acyclic, i.e. their bounded cohomology vanishes in every positive degree. This essentially contains all previously known non-amenable examples (at the time of posting) and includes many groups of homeomorphisms. We also computed the bounded cohomology of Thompson's group $T$, assuming a conjecture about the bounded cohomology of Thompson's group $F$, which is now a theorem. To appear in Journal of the Australian Mathematical Society.

• Bounded cohomology of finitely presented groups: Vanishing, non-vanishing and computability, joint with Clara Löh and Marco Moraschini, 30 pages. We provided the first examples of non-amenable finitely generated and finitely presented groups for which it is possible to compute bounded cohomology in all degrees: these include boundedly acyclic groups (with vanishing in every degree) and groups with large bounded cohomology (with strong non-vanishing in every degree). Moreover, we proved that vanishing of bounded cohomology is not algorithmically decidable. To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.

• Normed amenability and bounded cohomology over non-Archimedean fields, 92 pages. I studied natural notions of amenability and bounded cohomology over non-Archimedean fields (with particular attention to the field $\mathbb{Q}_p$ of $p$-adic numbers), and the way they interact. This is all done for totally disconnected locally compact groups, with the last (independent) section on bounded cohomology of topological spaces. To appear in Memoirs of the American Mathematical Society.

Preprints

• Local Hilbert--Schmidt stability, joint with Maria Gerasimova and Pieter Spaas, 29 pages. Following the recent introduction of local permutation stability, we set up a general framework for local stability, and initiate the study of local Hilbert--Schmidt (HS) stability. We prove a version of the Hadwin--Shulman character criterion for amenable groups, provide several examples, and prove that property (T) is an obstruction to local stability.

• 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.

• 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.

• 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.

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).

Theses

• 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.

• Comments on "Discrete Groups, Expanding Graphs and Invariant Measures", by Alexander Lubotzky, 74 pages. This is a semester paper that I wrote during the first semester of my Masters at ETH. The goal was to fill in the details of the first four chapters of this wonderful book, and add a couple new things. It was supervised by Alessandra Iozzi and Konstantin Golubev.

Editorial work

• Bounded Cohomology and Simplicial Volume, edited jointly with Caterina Campagnolo, Nicolaus Heuer and Marco Moraschini, 170 pages. These are proceedings from the "What is?" style seminar that was held online during the Fall Semester of 2020. It includes 12 chapters that should serve as a gentle introduction to young researchers in the field to topics of current research interest. Published in the LMS Lecture notes series.

Talks

Recorded

• July 2023, at ESI (Vienna) for GAGTA 2023 on Ulam stability in general, and Ulam stability of Thompson groups in particular, after my paper with Bharatram Rangarajan on this topic. The recording is available here.

• November 2022, Fields Institute Toronto, for the Simons Distinguished Visitor Seminar, also on Ulam stability of lamplighter and Thompson groups, this time with a friendly introduction to Thompson groups. The recording is available here.

• March 2021, for the Stability and Testability Seminar at IAS Princeton on ultrametric stability problems, with special attention to a $p$-adic analogue of Ulam stability, after my paper on this topic. The recording is available here.

• January 2021, for the International "What is?" seminar on bounded cohomology and simplicial volume about this really cool paper, which explains how to extend an alternating quasicocycle from a hyperbolically embedded family of subgroups. The recording is available on the website. More details can be found in the Proceedings of the seminar (see above).

• October 2020, for the Geometry Graduate Colloquium of ETH about bounded cohomology and some of the things that one can do with it. The recording is available upon request.

• April 2020, for the International young seminar on bounded cohomology and simplicial volume on Brooks quasimorphisms and the more combinatorial aspects of my Master Thesis. The recording is available upon request.

Other

• June 2023, at ICMAT (Madrid) for the Workshop on Orderings and Groups: "Finitely presented left orderable monsters".

• April 2023, for the Group theory seminar at ICMAT: "Hopfian wreath products and the stable finiteness conjecture".

• March 2023 at the conference Manifolds and groups in Bologna at Università di Bologna: "Groups not acting on hyperbolic spaces".

• February 2023 for the Geometric group theory seminar at University of Oxford: "Computing bounded cohomology of discrete groups".

• January 2023 at the 8th KTGU workshop for young researchers at Kyoto University. "Aut-invariant quasimorphisms on groups".

• November 2022, for the Geometry and geometric analysis seminar at Purdue: "Aut-invariant quasimorphisms on groups".

• November 2022, for the Algebra/Topology seminar at University at Albany (SUNY): "Hopfian wreath products and the stable finiteness conjecture".

• October 2022, Colloquium Talk at the University of Hawai'i at Manoa: "Unveiling the spectrum of stable commutator length".

• September 2022, at the conference Recent advances in bounded cohomology at Universität Regensburg: "Bounded cohomology over non-Archimedean fields".

• September 2022, for the Groupe de travail: Actions! at ENS Lyon: "One-dimensional actions and bounded cohomology".

• June 2022, for the Geometry Group Theory Seminar at Cambdridge University: "Computing bounded cohomology of discrete groups".

• January 2022, for the Topology Seminar at UT Austin: "New values in the spectra of stable commutator length and simplicial volume".

• January 2022, for the Groups and Dynamics Seminar at Texas A&M: "On the second bounded cohomology of some left orderable groups".

• December 2021, for the Ergodic and Geometric Group Theory Seminar at EPFL: "Groups acting on $1$-manifolds and their bounded cohomology".

• November 2021, for the SFB Seminar at Universität Regensburg: "A dynamical approach to bounded cohomology vanishing".

• November 2021, for the Baby Geometri Seminar at Università di Pisa: "La stable commutator length e i suoi valori".

• October 2021, for the Geometry and Analysis on Groups Research Seminar at Universität Wien: "Stable commutator length and its values".

• September 2021, contributed talk for the Young Topologists and Geometers section of DMV-ÖMG-Jahrestagung 2021: "New examples in the bounded cohomology of finitely generated groups".

• April 2021, for the Zurich Graduate Colloquium of ETH and UZH: "What is... group stability?".

• February 2021, for the Topological Groups seminar of the University of Hawai'i: "Normed $p$-adic amenability and bounded cohomology".

• June 2020, for the LKS seminar of the Universität Regensburg: "Normed $p$-adic amenability".

• December 2019, for the Geometry groups and topology seminar of the Karlsruher Institut für Technologie (KIT): "Decompositions of the free group and cup products in bounded cohomology".