Neko

Gabriel Pallier


Université de Lille
Faculté des sciences et technologies
Laboratoire Paul Painlevé, UMR 8524



Office: M2 302

E-mail: name.surname A univ-lille.fr


Français

Presentation

Since September 2023, I am an assistant professor (maître de conférences) in the mathematics department of the university of Lille. Here is an academic family picture.
AI statement (August 18, 2026): I support the Leiden declaration. In addition,
  1. I do not use generative AI in my work, and from now on I will avoid being exposed to AI-produced content as much as I can in all aspects of daily life.
  2. My writings have always been meant to be read by humans. I encourage any human reader willing to understand any aspect of my work to reach out to me (or a co-author or colleague) instead of using generative AI. This applies to all my students regarding the coursework.
These are grounded in ethical principles, but also more basically on an imperative of self-preservation. I have no certainty on the ethical principles, they remain to be built in part, and I do not pretend to be perfect, but the self-preservation comes first. I refer to the texts of Vladimir Lazić, Alexis Marchand, and Max Weinreich where a solid argument for my commitment can be found.

Research

Interests: I work in geometric group theory, using tools coming from geometric analysis in the broad sense (i.e., on metric spaces). The main objects that I study are Lie groups and their lattices. Here is a short version of an old research statement.

Preprints

Published, accepted or to appear

  1. [PDF (27p), arXiv, DOI] with Ido Grayevsky, Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups,
    J. Lond. Math. Soc. 113, No. 4, 31 p. (2026)
  2. [PDF (56p), arXiv, ancillary file] with Jerónimo García-Mejía and Claudio Llosa Isenrich, On the Dehn functions of central products of nilpotent groups (2023).
    Trans. Amer. Math. Soc.
  3. [PDF (24p), arXiv, DOI, BibTex] with Yulan Qing, Sublinear bilipschitz equivalence and sublinearly Morse boundaries,
    J. Lond. Math. Soc. 110, No. 2, 26 p. (2024)
  4. [PDF (31p), arXiv, DOI, BibTex] with Enrico Le Donne and Xiangdong Xie, Rough similarity of left-invariant Riemannian metrics on some Lie groups,
    Groups Geom. Dyn. 19 (2025), 227–263
  5. [PDF (51p), arXiv, DOI, BibTex] On the logarithmic coarse structures of Lie groups and hyperbolic spaces,
    Geom. Dedicata 216, 56 (2022).
  6. [PDF (64p), arXiv, DOI, BibTex] with Claudio Llosa Isenrich and Romain Tessera, Cone-equivalent nilpotent groups with different Dehn functions,
    Proc. Lond. Math. Soc. (3) 126 (2), 704-789 (2023).
  7. [PDF (33p), arXiv, DOI, BibTex] Sublinear quasiconformality and the large-scale geometry of Heintze groups,
    Conform. Geom. Dyn. 24, 131-163 (2020).
  8. [PDF (42p), arXiv, DOI, BibTex] Large-scale sublinearly Lipschitz geometry of hyperbolic spaces,
    J. Inst. Math. Jussieu 19 (6), 1831-1876 (2020).

Theses

Some selected presentations and posters

  • [slides] Quasi-isometries and rough isometries of solvable Lie groups (Heidelberg, Geometry day, 2023)
  • [slides] Sublinear coarse structures and Lie groups (YGGT Lightning talk, 2021)
  • [notes, Slides] Dehn functions of nilpotent groups
  • [slides (long)] Géométrie à grande échelle des groupes de Lie de courbure négative (Marseille, 2019).
  • [slides (short)] Sublinearly quasisymmetric homeomorphisms (Jyväskylä, 2019).
  • [poster] Large-scale sublinearly Lipschitz geometry of hyperbolic spaces (Rennes 2017)
  • [poster] Invariants for sublinear bilipschitz equivalence (Oxford 2019).

Some presentations of my research to a general mathematical audience

Lecture notes of minicourse the lecture notes of Aussois's minicourse on nilpotent Lie groups and SBE in the ANR PLAGE ``Coarse geometry of groups'' meeting.



Translation and notes on P. Pansu's Carnot-Carathéodory metrics and quasiisometries of rank one symmetric spaces.

Teaching

Almost all the teaching material I produced is available only in French and can be found on the French version of this webpage.

Other mathematical writings

Includes some writings in French.

Gallery

Geodesic flow on a homogeneous space

Uniform polyhedra and polytopes

Nilpotent Lie algebras of small dimension