Alexis Marchand
アレクシ・マルシャン

Kyoto University । 京都大学

E-mail । メール : marchand.alexis.85h@st.kyoto-u.ac.jp

arXiv • ORCID • zbMATH • MathSciNet

About me

Since September 2024, I am a JSPS postdoctoral fellow in mathematics at Kyoto University, working with Koji 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 the research of my PhD around stable commutator length.

2024年9月から京都大学数学専攻学振の特別研究員です。ケンブリッジ大学で2024年に博士課程を修了しました。専門分野は幾何学的群論です。日本語を少し話せます。日本語で話しかけてもらっても大丈夫です！

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

L²-Betti numbers. In Spring 2025, I am organising a reading seminar on L²-Betti numbers at Kyoto University. The schedule can be found here, and notes from the first two talks are here.

Picture by Macarena Arenas.

Papers

Research articles (published / accepted in peer-reviewed journals)

From letter-quasimorphisms to angle structures and spectral gaps for scl, Israel J. Math. (to appear) • arXiv
Isometric embeddings of surfaces for scl, Groups Geom. Dyn. (online first) • arXiv
Bavard duality for the relative Gromov seminorm, Enseign. Math. (online first) • arXiv
Free representations of outer automorphism groups of free products via characteristic abelian coverings, J. Group Theory, 2023 • arXiv

Expository articles

(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, 2025
Makers of patterns: from Escher to Coxeter, Eureka, Issue 66, 2020
Géométrie des groupes et courbure négative, Journal de Mathématiques des Élèves de l'ENS de Lyon, Vol. IV, 2020

Theses and dissertations

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

Teaching

2021-24 • Undergraduate supervisions (Trinity College & Peterhouse College, Cambridge)
2018-19 • Colles (Lycée Aux Lazaristes, Lyon)
2017-21 • French as a foreign language (ItinérENS, Lyon)

Miscellany

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.

Lycée Louis-le-Grand - MPSI/MP* • Mathématiques (première année) • Mathématiques (deuxième année) • Physique (première année) • Chimie (première année)
ENS Lyon - L3 - First term • Algèbre 1 • Analyse Complexe • Topologie et Calcul Différentiel • Intégration et Mesure
ENS Lyon - L3 - Second term • Algèbre 2 • Équations aux Dérivées Partielles • Calcul Différentiel 2 • Intégration et Probabilités • Groupe Fondamental et Revêtements • Nombres p-adiques
ENS Lyon - M1 - First term • Advanced Algebra • Advanced Analysis • Advanced Geometry • Advanced Probability
ENS Lyon - M1 - Second term • Algebraic Geometry • Géométrie Différentielle • Number Theory • Riemann Surfaces
University of Cambridge - Part III - Michaelmas • Algebraic Topology • Category Theory • Mapping Class Groups • Percolation and Related Topics
University of Cambridge - Part III - Lent • Metric Embeddings • Profinite Groups • Approximate Group Actions and Ulam Stability • Geometric Group Theory
Université Grenoble Alpes - M2 • Algorithmic Topology and Groups • Hyperbolic Geometry and Discrete Groups • Hyperbolicities in Discrete Groups

Various notes

Generalisations of hyperbolicity • These are notes from a reading group that I organised in Cambridge, whose goal was to learn about relative, hierarchical, and acylindrical hyperbolicity.
The Loop & Sphere Theorems • Notes from a talk for a reading group on 3-manifolds, organised by Will Cohen.
The Stallings–Swan Theorem • Notes from a talk for a reading group on ends of groups, organised by Julian Wykowski.
The Higman Embedding Theorem • Notes from a talk for a reading group on the Boone–Higman Conjecture, organised by Francesco Fournier-Facio.