LAMFA, Université UPJV Amiens

Yann Palu

Research interests

My main interests lie in:

• Cluster algebras and cluster categories;
• Representation theory of quivers and finite dimensional algebras;
• Triangulated categories (and the like);
• Model categories (and the like);
• Some combinatorics: triangulations, non-kissing complex...
• Higher homological algebra;
• I am also secretly interested in higher category theory.

Publications and preprints:

• With Xin Fang, Mikhail Gorsky, Pierre-Guy Plamondon and Matthew Pressland: Extriangulated ideal quotients, with applications to cluster theory and gentle algebras [math.RT].
• A survey from a talk given at the 2022 Abel Symposium: Some applications of extriangulated categories [math.RT].
• With Mikhail Gorsky and Hiroyuki Nakaoka: Hereditary extriangulated categories: Silting objects, mutation, negative extensions [math.RT].
• With Jenny August, Johanne Haugland, Karin M. Jacobsen, Sondre Kvamme, and Hipolito Treffinger: A characterisation of higher torsion classes [math.RT].
• With Benjamin Dequêne, Mélodie Lapointe, Pierre-Guy Plamondon, Christophe Reutenauer and Hugh Thomas: A generalization of perfectly clustering words and band bricks for certain gentle algebras [math.CO].
• With Mikhail Gorsky and Hiroyuki Nakaoka: Positive and negative extensions in extriangulated categories [math.CT].
• With Hiroyuki Nakaoka: External triangulation of the homotopy category of an exact quasi-category [math.CT].
• With Arnau Padrol, Vincent Pilaud and Pierre-Guy Plamondon: Associahedra for finite type cluster algebras and minimal relations between g-vectors Proc. London Math. Soc. 127 (3) 2023, pp 513-588 (open access).
• With Vincent Pilaud and Pierre-Guy Plamondon: Non-kissing and non-crossing complexes for locally gentle algebras Journal of Combinatorial Algebra Vol. 3 No. 4 (2019), 401-438.
• With Osamu Iyama and Hiroyuki Nakaoka: Auslander--Reiten theory in extriangulated categories, arXiv:1805.03776 [math.CT], accepted for publication in Trans. AMS, series B.
• With Vincent Pilaud and Pierre-Guy Plamondon : Non-kissing complexes and tau-tilting for gentle algebras, Mem. Amer. Math. Soc. 274 (2021), no. 1343, vii+110 pp.
• With Hiroyuki Nakaoka: Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories, arXiv:1605.05607 [math.CT]. Published under the new name: Extriangulated categories, Hovey twin cotorsion pairs and model structures in Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume LX-2 (2019).
• With Aslak Buan and Idun Reiten: Algebras of finite representation type arising from maximal rigid objects. Journal of Algebra 446 (2016) - Open Access.
• From triangulated categories to module categories via homotopical algebra., arXiv:1412.7289 [math.RT] (not submitted).
• With Bethany Marsh: Nearly Morita equivalences and rigid objects, Nagoya Math. J. Volume 225 (2017) , pp. 64-99
• With Bethany Marsh: Coloured quivers for rigid objects and partial triangulations: The unpunctured case. Proc. London Math. Soc. Vol 108, Number 2 (2014), 411-440
• With Peter Jorgensen: A Caldero-Chapoton map for infinite clusters Trans. Amer. Math. Soc. 365 (2013), 1125-1147
• Cluster characters II: A multiplication formula Proc. London Math. Soc. Vol 104, Number 1 (2012), 57-78(22)
• Grothendieck group and generalized mutation rule for 2-Calabi--Yau triangulated categories J. Pure Appl. Algebra 213 (2009) 1438-1449.
• Cluster characters for 2-Calabi--Yau triangulated categories Annales de l'institut Fourier, 58 no. 6 (2008), 2221-2248

Supervision:

• Lucie Jacquet-Malo (2014-2017) co-supervised, with Alexander Zimmermann, PhD thesis "Objets rigides : de la combinatoire des catégories amassées supérieures à l'algèbre homotopique". She defended on 29th Septebmer, 2017.
• Michaël Schoonheere, since September 2022.
• Jules Besson, since September 2023, co-supervised with Bernhard Keller.

PhD Thesis:

Here is a copy of my PhD thesis (mostly in English): "Des categories triangulees aux algebres amassees", under the supervision of Bernhard Keller, defended June 8, 2009.

Some talks:

• July 2023, Extriangulated categories and mutations, Homological algebra and representation theory, Karlovasi (Samos, Greece).
• July 2023, Flips of accordions and mutation of rigid objects via gentle algebras, Session "Representation Theory and Combinatorics" at the Nordic Congress of Mathematicians, Aalborg (Denmark).
• June 2022, Some applications of extriangulated categories, Triangulated categories in representation theory and beyond, Abel symposium 2022, Ålesund (Norway).
• February 2020, Complexe platonique, algèbres aimables et catégories extriangulées Colloque tournant du GDR TLAG, Paris.
• January 2020, Complexe platonique et catégories extriangulées Séminaire Itinérant de Catégories, Amiens.
• July 2019, Poster Non-kissing vs non-crossing FPSAC'19, Ljubljana (Slovenia).
• June 2018, Non-kissing complex and tau-tilting over gentle algebras, Bielefeld (Germany).
• April 2018, Complexe platonique des algèbres aimables, Séminaire d'algèbre de l'IHP (France).
• February-March 2018, three talks on Higher-dimensional cluster combinatorics and representation theory by S. Oppermann and H. Thomas, working group on Higher representation theory, Paris 7 (France).
• September 2017, Complexe des embrassades et algèbres aimables, Amiens (France).
• September 2017, Non-kissing complex and tau-tilting over gentle algebras, CIRM, Luminy (France).
• May 2017, Non-kissing complex and tau-tilting over gentle algebras, Leicester (U.K.).
• May 2017, Cotorsion pairs and model category structures, Leeds (U.K.).
• May 2017, An introduction to quasi-categories, Newcastle (U.K.).
• April 2017, Non-kissing complex and tau-tilting over gentle algebras, Nagoya (Japan).
• March 2017, Paires de cotorsion et structures de modèles (d'après Hovey, Gillespie), Séminaire Groupes, Représentations et Géométrie, Paris 7.
• May 2006, Algèbres amassées et représentations de carquois, LIX, Polytechnique (France).
• June 2014, NTNU Trondheim, From triangulated categories to module categories via model categories.
• March 2014, Bandung University, An introduction to Caldero-Chapoton maps.
• March 2014, Bandung University, Graduate mini-course: An introduction to cluster categories.
• August 2013, Nagoya University, Iyama-Yoshino reductions of cluster categories from surfaces.
• October 2012, Séminaire Chevalley, Introduction à la catégorification d'algèbres amassées.

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