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Graph regularity and incidence phenomena in distal structures
Post-edited
Authors : Chernikov, Artem (Author of the conference)
CIRM (Publisher )
03C45 - Classification theory, stability and related concepts [See also 03C48]
03C60 - Model-theoretic algebra
03C64 - Model theory of ordered structures; o-minimality
CIRM (Publisher )
Abstract :
In recent papers by Alon et al. and Fox et al. it is demonstrated that families of graphs with a semialgebraic edge relation of bounded complexity have strong regularity properties and can be decomposed into very homogeneous semialgebraic pieces up to a small error (typical example is the incidence relation between points and lines on a real plane, or higher dimensional analogues). We show that in fact the theory can be developed for families of graphs definable in a structure satisfying a certain model theoretic property called distality, with respect to a large class of measures (this applies in particular to graphs definable in arbitrary o-minimal theories and in p-adics). (Joint work with Sergei Starchenko.)
MSC Codes : 03C45 - Classification theory, stability and related concepts [See also 03C48]
03C60 - Model-theoretic algebra
03C64 - Model theory of ordered structures; o-minimality
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 22/04/15 Conference Date : 07/04/15 Subseries : Research talks arXiv category : Logic ; Combinatorics Mathematical Area(s) : Logic and Foundations Format : QuickTime (.mov) Video Time : 00:49:25 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-04-07_Chernikov.mp4 
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Information on the Event
Event Title : Model Theory, Difference/Differential Equations and Applications / Théorie des modèles, équations différentielles et aux différences et applicationsEvent Organizers : Beyarslan, Özlem ; Hils, Martin ; Martin-Pizarro, Amador Dates : 07/04/15 - 10/04/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1194.html
Citation Data
DOI : 10.24350/CIRM.V.18745203Cite this video as: Chernikov, Artem (2015). Graph regularity and incidence phenomena in distal structures. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18745203 URI : http://dx.doi.org/10.24350/CIRM.V.18745203 |
Bibliography
- Alon, N., Pach, J., Pinchasi, R., Radoicic, R., & Sharir, M. (2005). Crossing patterns of semi-algebraic sets. Journal of Combinatorial Theory. Series A, 111(2), 310-326 - http://dx.doi.org/10.1016/j.jcta.2004.12.008
- Basu, S. (2010). Combinatorial complexity in o-minimal geometry. Proceedings of the London Mathematical Society. Third Series, 100(2), 405-428 - http://dx.doi.org/10.1112/plms/pdp031
- Chernikov, A., & Starchenko, S. Regularity lemma for distal graphs. Preprint -
- Chernikov, A., & Simon, P. (2012). Externally definable sets and dependent pairs II. < arXiv:1202.2650> - http://arxiv.org/abs/1202.2650
- Fox, J., Pach, J., & Suk, A. (2015). A polynomial regularity lemma for semi-algebraic hypergraphs and its applications in geometry and property testing.
- Fox, J., Gromov, M., Lafforgue, V., Naor, A., & Pach, J. (2012). Overlap properties of geometric expanders. Journal für die Reine und Angewandte Mathematik, 671, 49-83 - http://dx.doi.org/10.1515/CRELLE.2011.157
- Hrushovski, E., Pillay, A., & Simon, P. (2013). Generically stable and smooth measures in NIP theories. Transactions of the American Mathematical Society, 365(5), 2341-2366 - http://dx.doi.org/10.1090/S0002-9947-2012-05626-1
- Simon, P. (2013). Distal and non-distal NIP theories. Annals of Pure and Applied Logic, 164(3), 294-318 - http://dx.doi.org/10.1016/j.apal.2012.10.015
