Model Theory, Difference/Differential Equations and Applications / Théorie des modèles, équations différentielles et aux différences et applications

Collection Model Theory, Difference/Differential Equations and Applications / Théorie des modèles, équations différentielles et aux différences et applications

Organizer(s) Beyarslan, Özlem ; Hils, Martin ; Martin-Pizarro, Amador

Date(s) 07/04/2015 - 10/04/2015

linked URL http://conferences.cirm-math.fr/1194.html

00:00:00 / 00:00:00

3 4

Chapters

Graph regularity and incidence phenomena in distal structures

By Artem Chernikov

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.)

Information about the video

Date of recording 07/04/2015
Date of publication 22/04/2015
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18745203
Cite this video Chernikov, Artem (07/04/2015). Graph regularity and incidence phenomena in distal structures. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18745203
URL https://dx.doi.org/10.24350/CIRM.V.18745203

Domain(s)

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. <arXiv:1502.01730> - http://arxiv.org/abs/1502.01730
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

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