Gabriel Pallier's homepage

Gabriel Pallier

KIT
Fakultät für Mathematik
Institut für Algebra und Geometrie

Office: 1.015

E-mail: name.surname A kit.edu

Presentation

I am currently a postdoc in mathematics at the Karlsruher Institut für Technologie, in the group led by JProf. Claudio Llosa Isenrich, and associated to the Research Training Group 2229 Asymptotic Invariants and Limits of Groups and Spaces based in Heidelberg and Karlsruhe. Previously I was in Sorbonne université in Paris, and before that in Fribourg and Pisa, in the ERC Geomeg. I achieved my PhD under the supervision of Prof. Pierre Pansu in the Université Paris-Saclay in 2019. It was motivated by the work and questions of Yves Cornulier.

Here is a cv, and an academic family picture.

New: Online reading seminar on the works of Kleiner, Müller and Xie (February- April 2023), co-organized with Francesca Tripaldi.

Research

Interests Geometric group theory, and especially the large-scale geometry of connected Lie groups and their lattices. I have local interests in Riemannian geometry, and in dynamics on homogeneous spaces as well. short version.

Publications and preprints

[PDF (5p), arXiv] On the finitely generated groups quasiisometric to bifiliform-by-cyclic groups, appendix to Geometric rigidity of quasi-isometries in horospherical products by Tom Ferragut, submitted (2022).
[PDF (24p), arXiv] with Yulan Qing, Sublinear bilipschitz equivalence and sublinearly Morse boundaries, submitted (2022).
[PDF (31p), arXiv] with Enrico Le Donne and Xiangdong Xie, Rough similarity of left-invariant Riemannian metrics on some Lie groups, submitted (2022).
[PDF (51p), arXiv, journal, BibTex] On the logarithmic coarse structures of Lie groups and hyperbolic spaces, Geometriae Dedicata 216, 56 (2022).
[PDF (64p), arXiv, journal, BibTex] with Claudio Llosa Isenrich and Romain Tessera, Cone-equivalent nilpotent groups with different Dehn functions. Proceedings of the London Mathematical Society 126 (2), 704-789 (2023).
[PDF (33p), arXiv, journal, BibTex] Sublinear quasiconformality and the large-scale geometry of Heintze groups, Conformal Geometry and Dynamics 24, 131-163 (2020).
[PDF (42p), arXiv, journal, BibTex] Large-scale sublinearly Lipschitz geometry of hyperbolic spaces, Journal of the Institute of Mathematics of Jussieu 19 (6), 1831-1876 (2020).

Theses

[PDF (168p), TEL, slides] Sublinear asymptotic geometry, PhD thesis. Erratum (pdf). The earliest two publications above are extracted from this manuscript.
[PDF (99p), slides] Isopérimétrie des métriques périodiques, Master thesis (in French). Defended in Orsay on August 31, 2016.

Some selected presentations and posters

[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

[slides] Looking at Lie groups through Gromov's telescope (Bern, 2022)
[slides] Géométrie hyperbolique à grande échelle (Lyon, 2018; in French).
[slides] Géométrie hyperbolique sous-linéairement lipschitzienne à grande échelle (Rennes, 2017; in French).

Reviews for Zentralblatt and Mathematical Reviews (the latter requires access to MathSciNet).

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.

2020: List of subjects for the Séminaire Libre - Freies Seminar. Tips: Wie halte ich einen Seminarvortrag? by Prof. Dr. Manfred Lehn.

Other mathematical writings

Includes some writings in French.

PDF (20p) SET ou la pêche à la ligne [The card game SET, or: Finding a haystack without a needle], Quadrature 106 (2017), 25-34.
PDF (5p), Une géométrie pour les graphes d'amitié [A geometry for friendship graphs], Quadrature 99 (2016), 16-19. An addendum (PDF) (not published).
slides Comment jouer (et gagner) au morpions sur les surfaces ?
2017: slides of the presentation Johannes Kepler's mathematical stars. Star polyhedra and Riemann surfaces.
2016: notes (38p) of the Master course ``Introduction à la théorie mesurée des groupes'' given by Romain Tessera in Orsay (in French). Mostly, exercises with or without correction. With an appendix presenting an elementary proof of the quartic growth of the first Heisenberg group.
2014: lecture notes (11p), Transfert et groupes finis [On the transfer homomorphism and finite groups]: lecture notes of a student's seminar enumerating the groups of order 2014 or 2015.

Gallery

Geodesic flow on a homogeneous space

Uniform polyhedra and polytopes

Nilpotent Lie algebras of small dimension (better on a large screen)

Société mathématique de France.
Revue de presse d'Image des maths (mensuelle).
Femmes et maths.
MATh.en.JEANS.

Last update: May 2023.