GdT : Stabilité homologique via les E_k-algèbres cellulaires

List of talks

• Talk 0 (01/10/2024): Présentation. | Ricardo Campos. Notes par Ricardo
• Talk 1 (15/10/2024): Filtered, cellular and CW algebras; skeletal filtration and the associated graded [C; §5, §6 (thm 6.14)]. Model structures on operads and algebras [C; §9]. | Mario Fuentes. Notes par Mario, Ricardo.
• Talk 2 (05/11/2024): Continuation. Notes par Ricardo.
• Talk 3 (12/11/2024): Ek-algebras in sSet, (derived ) indecomposables [L; §2]. | Joost Nuiten. Notes par Mario, Joan.
• Talk 4 (26/11/2024): The homology of free Ek-algebras [L; §4]. | Joan Millès. Notes par Ricardo
• Talk 5 (21/01/2025): More indecomposables, connectivity, Hurewicz and Whitehead theorems, CW approximation [L; §5], see also [C; §11] | Jiaqi Fu. Notes par Joan, Mario, Ricardo.
• Talk 6 (28/01/2025): Continuation. Notes par Mario
• Talk 7 (11/02/2025): Classical facts about mapping class groups [L;3, 6]. [MCG] isn't yet too pertinent but worth looking at. | Mario Fuentes. Notes par Mario.
• Talk 8 (04/03/2025): Iterated bar constructions and derived indecomposables [L; §7]. | Ricardo Campos
• Talk 9 (25/03/2025): Applications to computation of E_k homology of configurations of points with limited multiplicity. [L; §8]. | Ricardo Campos.
• Talk 10 (08/04/2025??): Generic homological stability – E_2-algebras from braided monoidal groupoids [L; §9]. | Mario Fuentes.
• Talk 11: The Generic Homological Stability result [L; §10]. | Joost Nuiten. Notes par Mario, Joan.
• Talk 12: Homological stability for mapping class groups over Q (and also secondary stability) [L; §11].
• Optional additional talk: Other applications such as homology of the E_\infty algebra \sqcap_n BGL_n(Fp) [Fp].
• Optional additional talk: Homological stability of mapping class groups over Z [L; §13].

References

• [L] Lecture notes: Lecture notes on Cellular Ek-algebras
• [C] All the theory: Cellular Ek-algebras
• [MCG] Applications to mapping class groups: E2-cells and mapping class groups
• [Fp] Applications to GLn(Fp): E∞-cells and general linear groups of finite fields