Alexis Marchand

Alexis Marchand

IM PAN / Universität Regensburg

amarchand@impan.pl

arXivORCIDzbMATHMathSciNet

About me

I am a mathematician, employed as an Adiunkt (Assistant Professor) at IM PAN, Warsaw, in the NCN Maestro Project Analysis on Groups of Piotr Nowak, and (for the summers of 2026 and 2027) as a Humboldt Fellow at Universität Regensburg, in the group of Clara Löh.

Before that, I was a JSPS postdoctoral fellow at Kyōto University, working with Kōji Fujiwara. I completed my PhD at the University of Cambridge in 2024, under the supervision of Henry Wilton. My research is in geometric group theory, a field concerned with understanding groups — algebraic structures encoding the symmetries of mathematical objects — by studying their actions on geometric spaces. I am generally interested in understanding connections between group-theoretical structure and non-positive curvature. Here is a poster explaining my research on stable commutator length.

Together with Piotr Nowak, Mark Pengitore, and Arturo Espinosa Baro, I am organising the Analytic and geometric group theory seminar at IM PAN. Please feel free to send me an email if you would like to give a talk!

数学者です。 2025年からポーランドの国立数学研究所で特任助教としてPiotr Nowak先生と働いています。 2026、2027年の夏、レーゲンスブルク大学Humboldt FellowとしてClara Löh先生と研究滞在します。 2025年まで、京都大学で一年間研究員として働きました。藤原 耕二先生にお世話になりました。ケンブリッジ大学では、Henry Wilton先生の指導のもと2024年に博士課程を卒業しました。専門分野は幾何学的群論です。ぜひ、日本語で話しかけてください!

Keywords: stable commutator length, bounded cohomology, quasimorphisms, topology of surfaces, hyperbolicity, CAT(0) cube complexes, group rings, free group automorphisms.

CV: in English日本語で

Statement on large language models


Considering the role of large language models in aggravating the climate crisis, considering the harm they can produce in mathematics and human thought, and considering our responsibility as mathematicians, my personal choice is the following.

I will not (knowingly) use any large language model in my work and private life.

I will refuse to review papers making (significant) use of large language models, I will refuse to collaborate on projects using large language models, and I will not consent to any of my writing being fed to large language models. I will keep to this stance as long as large language models are based on the Earth- and human-damaging philosophy which is currently at their core.

My views on large language models are developed in the text Mathematicians, machines, and the Earth.
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Papers

Publications (peer-reviewed)

  1. From letter-quasimorphisms to angle structures and spectral gaps for scl, Israel J. Math. (online first) • arXiv
  2. Bavard duality for the relative Gromov seminorm, Enseign. Math., 2026 • arXiv
  3. Isometric embeddings of surfaces for scl, Groups Geom. Dyn., 2025 • arXiv
  4. (with Rémi Coulon) Growth and co-growth in negatively curved groups, in Dahmani, Erschler, Horbez, Wise (eds.), Groups acting on fractals, hyperbolicity and auto-similarity, Panoramas et Synthèses 63, 2025
  5. Free representations of outer automorphism groups of free products via characteristic abelian coverings, J. Group Theory, 2023 • arXiv

Expository articles

  1. Makers of patterns: from Escher to Coxeter, Eureka 66, 2020
  2. Géométrie des groupes et courbure négative, Journal de Mathématiques des Élèves de l'ENS de Lyon IV, 2020

Theses and dissertations

  1. Computations and lower bounds for scl and the relative Gromov seminorm, PhD thesis, University of Cambridge, 2024
  2. Automorphismes extérieurs de produits libres : revêtements abéliens caractéristiques et représentations libres, Master's thesis, Université Grenoble Alpes, 2021
  3. Rigidity theorems for hyperbolic groups, Part III essay, University of Cambridge, 2020
  4. Topology of complex affine varieties, Master's research internship report, IMPA (Rio de Janeiro), 2019
  5. Geometry of Coxeter groups, Bachelor's research internship report, KIT (Karlsruhe), 2018
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Miscellaneous notes

Notes on topics related to group theory

Lecture notes

During my Bachelor's and Master's studies, I typed lecture notes for the courses I attended. I am making them available here in the hope that they will be useful to others. Please note that they may not reflect the contents of the courses, as I have made some modifications. In particular, all the responsibility for mistakes is mine. Back to top

Talk recordings

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Teaching resources

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