English
Quasirandomness of definable subsets of definable groups in finite fields
Multi angle
Auteurs : Pillay, Anand (Auteur de la Conférence)
CIRM (Editeur )
03C45 - Classification theory, stability and related concepts [See also 03C48]
05C75 - Structural characterization of types of graphs
11B30 - Arithmetic combinatorics; higher degree uniformity
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3112/Slides/Anand-Pillay.pdf
CIRM (Editeur )
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Résumé :
We give an arithmetic version of Tao's algebraic regularity lemma (which was itself an improved Szemerédi regularity lemma for graphs uniformly definable in finite fields). In the arithmetic regime the objects of study are pairs $(G, D)$ where $G$ is a group and $D$ an arbitrary subset, all uniformly definable in finite fields. We obtain optimal results, namely that the algebraic regularity lemma holds for the associated bipartite graph $(G, G, E)$ where $E(x, y)$ is $x y^{-1} \in D$, witnessed by a the decomposition of $G$ into cosets of a uniformly definable small index normal subgroup $H$ of $G$.
Keywords : Arithmetic regularity; finite fields
Codes MSC : Keywords : Arithmetic regularity; finite fields
03C45 - Classification theory, stability and related concepts [See also 03C48]
05C75 - Structural characterization of types of graphs
11B30 - Arithmetic combinatorics; higher degree uniformity
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3112/Slides/Anand-Pillay.pdf
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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de publication : 28/10/2024 Date de captation : 03/10/2024 Sous collection : Research talks arXiv category : Algebraic Geometry ; Logic Domaine : Algebra ; Algebraic & Complex Geometry ; Logic and Foundations Format : MP4 (.mp4) - HD Durée : 00:53:59 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-10-03_Pillay.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Model Theory and Applications to Groups and Combinatorics / Théorie des modèles et applications en théorie des groupes et en combinatoireOrganisateurs de la rencontre : Ben Yaacov, Itaï ; Hempel, Nadja ; Hils, Martin ; Zou, Tingxiang Dates : 30/09/2024 - 04/10/2024 Année de la rencontre : 2024 URL Congrès : https://conferences.cirm-math.fr/3112.html
Données de citation
DOI : 10.24350/CIRM.V.20252803Citer cette vidéo: Pillay, Anand (2024). Quasirandomness of definable subsets of definable groups in finite fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20252803 URI : http://dx.doi.org/10.24350/CIRM.V.20252803 |
Voir aussi
- [Multi angle] Pseudofinite omega-categorical groups / Auteur de la Conférence Tent, Katrin.
- [Multi angle] A Borovik-Cherlin bound for primitive pseudo-finite permutation groups / Auteur de la Conférence Ramsey, Nicholas.
- [Multi angle] Almost periodicity from a model-theoretic perspective / Auteur de la Conférence Martin-Pizarro, Amador.
- [Multi angle] Finite-dimensional pseudofinite groups of small dimension, without CFSG / Auteur de la Conférence Karhumäki, Ulla.
Bibliographie
- TAO, Terence. Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets. arXiv preprint arXiv:1211.2894, 2012. - https://arxiv.org/abs/1211.2894
- GOWERS, W. T. Quasirandom groups, eprint. arXiv, 2007, vol. 710. - https://arxiv.org/abs/0710.3877
- GREEN, Ben. A Szemerédi-type regularity lemma in abelian groups, with applications. Geometric & Functional Analysis GAFA, 2005, vol. 15, no 2, p. 340-376.
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