Adrien Kassel Researcher at CNRS – mathematical sciences institute; based at ENS de Lyon, France         Unité de Mathématiques Pures et Appliquées [contact details] [Brief academic vita] Research topics: probability, combinatorics, mathematical physics

My research lies at the intersection of probability, graph theory, and matroid theory, inspired by ideas from geometry, statistical physics, gauge theory, and computational complexity.
I am interested in how random processes reflect the geometry of the spaces they inhabit and what this tells us about the interplay between discrete and continuous structures.

Publications

• Géométries combinatoires et aléatoires – quelques exemples. (Combinatorial and random geometries – a few examples.)
  Habilitation à diriger des recherches, École Normale Supérieure de Lyon, Université de Lyon, 2023.
  [HAL]
• Determinantal random subgraphs, with Thierry Lévy.
  Combinatorial Theory, to appear (2025).
  [arXiv] [HAL] [journal]
• On the mean projection theorem for determinantal point processes, with Thierry Lévy.
  ALEA, Lat. Am. J. Probab. Math. Stat. 20, 497–504 (2023).
  [arXiv] [HAL] [journal] [view]
• Graph coverings and twisted operators, with David Cimasoni.
  Algebraic Combinatorics, Volume 6 (2023) no. 1, pp. 75–94.
  [arXiv] [HAL] [journal]
• Determinantal probability measures on Grassmannians, with Thierry Lévy.
  Ann. Inst. Henri Poincaré Comb. Phys. Interact. 9 (2022), no. 4, pp. 659–732.
  [arXiv] [HAL] [journal]
• A colourful path to matrix-tree theorems, with Thierry Lévy.
  Algebraic Combinatorics, Volume 3 (2020) no. 2, pp. 471–482.
  [arXiv] [HAL] [journal]
• Covariant Symanzik identities, with Thierry Lévy.
  Probability and Mathematical Physics 2-3 (2021), 419–475.
  [arXiv] [HAL] [journal]
• Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for κ > 8, with Ewain Gwynne, Jason P. Miller, and David B. Wilson.
  Comm. Math. Phys. 2018, Vol. 358, Issue 3, 1065–1115.
  [arXiv] [journal] [view]
• Active spanning trees and Schramm–Loewner evolution, with David B. Wilson.
  Phys. Rev. E 93, 062121 (2016).
  [arXiv] [journal]
• Revisiting the combinatorics of the 2D Ising model, with Dmitry Chelkak and David Cimasoni.
  Ann. Inst. Henri Poincaré Comb. Phys. Interact. 4 (2017), no. 3, pp. 309–385.
  [arXiv] [journal]
• Learning about critical phenomena from scribbles and sandpiles.
  ESAIM: Proc., 51 (2015) 60–73.
  [journal]
• The looping rate and sandpile density of planar graphs, with David B. Wilson.
  Amer. Math. Monthly 123(1):19–39, 2016.
  [arXiv] [journal]
• Transfer current and pattern fields in spanning trees, with Wei Wu.
  Probab. Theory Related Fields 163 (2015), no. 1-2, 89–121.
  [arXiv] [journal]
• Random curves on surfaces induced from the Laplacian determinant, with Richard Kenyon.
  Ann. Probab. 2017, Vol. 45, No. 2, 932–964.
  [arXiv] [journal]
• Random two-component spanning forests, with Richard Kenyon and Wei Wu.
  Ann. Inst. Henri Poincaré Probab. Stat. 51 (2015), no. 4, 1457–1464.
  [arXiv] [journal]

Coauthors: Dmitry Chelkak, David Cimasoni, Ewain Gwynne, Richard Kenyon, Thierry Lévy, Jason P. Miller, David B. Wilson, Wei Wu.

PhD student and postdoc

• Isao Sauzedde, MILYON post-doctoral researcher at ENS de Lyon, since September 2025;
• Héloïse Constantin (PhD student 2020–2023);
  She successfully defended her PhD thesis entitled Forêts couvrantes et transition de phase (Spanning forests and phase transition) on 28.06.2023 at ENS de Lyon.

Teaching

• Théorie des Probabilités (dans le cadre de la préparation à l'agrégation au Département de mathématiques de l'ENS de Lyon);
  Avec Corentin Faipeur et Théo Lenoir, 2025–2026.
• Determinantal processes (2nd year of Master course at the Mathematics Department of ENS de Lyon).
  Syllabus: [2020–2021] [2021–2022]
• Intégration et Probabilités (cours de L3 au Département de mathématiques de l'ENS de Lyon).
  Page du cours : [2017–2018] [2018–2019] [2019–2020]

Popularization

• Responsible for the Activité de diffusion (outreach activity) in the 1st year of Master at the Mathematics Department of ENS de Lyon, since 2018.
• MathαLyon monthly travelling exhibition for middle and high schools in the greater Lyon area (coordinator at ENS de Lyon from 2017 to 2022, working jointly with
  the coordinators at Université Lyon 1: Régis Goiffon, Charles–Edouard Bréhier, and Oriane Blondel); here is a presentation of the exhibit by MMI.
• Le modèle de dimères (short article in French about the dimer model). Images des Mathématiques, CNRS, 2016.
  This expository piece was translated to English here by Olga Kravchenko in 2025 (for amathr.org).
• ETH Studienwoche (Zürich, June 6–10, 2016). Responsible for a group of highschool students on the topic of large random networks;
  Description in German: Grosse zufällige Netzwerke.
• Other projects and outreach activities I had the chance to participate in:
  MATh.en.JEANS, Animath, Berkeley Math Circle, MSRI math night at Playground Theater, Marin Math Circle, MMI.
• Report on the Búzios Clay Mathematics Institute Summer School and XIV Brazilian School of Probability, written with Ivan Corwin and Marcelo Hilário;
  Published in the 2010 Clay Mathematics Institute Annual Report (pages 26–29).

Events co-organized

• ICJ–UMPA joint probability seminar, Thursdays at 2pm, 2017–2022, Lyon
• Spring meeting of the ANR Project DIMERS, March 29–30 2022, Lyon
• Random maps and matrices from a geometric perspective, May 20–24th 2019, Lyon
• SISSA meets ENSL, September 27–28th 2018, Trieste, Italy; notices by ENS de Lyon and SISSA.
• Random matrices, maps, and gauge theories, June 25–29th 2018, Lyon
• ENS de Lyon meets SISSA, December 5–6th 2017, Lyon; notice by SISSA.

Images

• [ENTER GALLERY]