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AUTHOR = {Elekes, Gy\"orgy and Szab\'o, Endre},
TITLE = {How to find groups? (and how to use them in {E}rd\"os
geometry?)},
JOURNAL = {Combinatorica},
FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
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YEAR = {2012},
NUMBER = {5},
PAGES = {537--571},
ISSN = {0209-9683},
MRCLASS = {05A16 (14N10)},
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DOI = {10.1007/s00493-012-2505-6},
URL = {http://dx.doi.org/10.1007/s00493-012-2505-6},
}
@article {pach-sharir,
AUTHOR = {Pach, J\'anos and Sharir, Micha},
TITLE = {On the number of incidences between points and curves},
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YEAR = {1998},
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}
@book {TaoVu,
AUTHOR = {Tao, Terence and Vu, Van},
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SERIES = {Cambridge Studies in Advanced Mathematics},
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MRNUMBER = {2289012},
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DOI = {10.1017/CBO9780511755149},
URL = {https://doi.org/10.1017/CBO9780511755149},
}
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}
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AUTHOR = {Hrushovski, Ehud},
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}
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}
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AUTHOR = {Evans, David M. and Hrushovski, Ehud},
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AUTHOR = {Faure, Claude-Alain},
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@book {TentZiegler,
AUTHOR = {Tent, Katrin and Ziegler, Martin},
TITLE = {A course in model theory},
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VOLUME = {40},
PUBLISHER = {Association for Symbolic Logic, La Jolla, CA; Cambridge
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YEAR = {2012},
PAGES = {x+248},
ISBN = {978-0-521-76324-0},
MRCLASS = {03C35 (03-01 03C45)},
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@book {Sheffer-incidence,
AUTHOR = {Sheffer, Adam},
TITLE = {Polynomial Methods and Incidence Theory},
NOTE = {Unfinished draft, 22.08.2019},
YEAR = {2019},
URL = {http://faculty.baruch.cuny.edu/ASheffer/000book.pdf}
}
@article{BHM-CCMA,
AUTHOR = {Bays, Martin and Hils, Martin and Moosa, Rahim},
TITLE = {Model theory of compact complex manifolds with an
automorphism},
JOURNAL = {Trans. Amer. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical Society},
VOLUME = {369},
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NUMBER = {6},
PAGES = {4485--4516},
ISSN = {0002-9947},
MRCLASS = {03C60 (03C45 03C65 32J99)},
MRNUMBER = {3624418},
DOI = {10.1090/tran/6941},
URL = {http://dx.doi.org/10.1090/tran/6941},
}
@article {HrUnimod,
AUTHOR = {Hrushovski, Ehud},
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JOURNAL = {J. London Math. Soc. (2)},
FJOURNAL = {Journal of the London Mathematical Society. Second Series},
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YEAR = {1992},
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DOI = {10.1112/jlms/s2-46.3.385},
URL = {http://dx.doi.org/10.1112/jlms/s2-46.3.385},
}
@book{Pillay-GST,
AUTHOR = {Pillay, Anand},
TITLE = {Geometric stability theory},
SERIES = {Oxford Logic Guides},
VOLUME = {32},
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ADDRESS = {New York},
YEAR = {1996},
PAGES = {x+361},
ISBN = {0-19-853437-X},
MRCLASS = {03C45 (03-02 20A15)},
MRNUMBER = {MR1429864 (98a:03049)},
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@article{Scanlon-MLUniformity,
AUTHOR = {Scanlon, Tom},
TITLE = {Uniformity in the Mordell-Lang Conjecture},
YEAR = {2001},
NOTE = {arXiv:math/0105238 [math.LO]},
}
@incollection{Pillay-ACF,
AUTHOR = {Pillay, Anand},
TITLE = {Model theory of algebraically closed fields},
BOOKTITLE = {Model theory and algebraic geometry},
SERIES = {Lecture Notes in Math.},
VOLUME = {1696},
PAGES = {61--84},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1998},
MRCLASS = {12L12 (03C60 14A99)},
MRNUMBER = {MR1678602 (2000f:12008)},
MRREVIEWER = {M. Yasuhara},
}
@article{Ziegler-noteGeneric,
author = {Ziegler, Martin},
title = {A note on generic types},
year = {2006},
note = {arXiv:0608433v1 [math.LO]},
}
@article {RSZ-ESR,
AUTHOR = {Raz, Orit and Sharir, Micha and De Zeeuw, Frank},
TITLE = {Polynomials vanishing on {C}artesian products: the
{E}lekes-{S}zab\'o theorem revisited},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {165},
YEAR = {2016},
NUMBER = {18},
PAGES = {3517--3566},
ISSN = {0012-7094},
MRCLASS = {52C10 (05D99)},
MRNUMBER = {3577370},
DOI = {10.1215/00127094-3674103},
URL = {https://doi.org/10.1215/00127094-3674103},
}
@article {RSZ-ES4,
AUTHOR = {Raz, Orit and Sharir, Micha and de Zeeuw, Frank},
TITLE = {The {E}lekes-{S}zab\'{o} theorem in four dimensions},
JOURNAL = {Israel J. Math.},
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VOLUME = {227},
YEAR = {2018},
NUMBER = {2},
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ISSN = {0021-2172},
MRCLASS = {52C10 (11B30 14R05)},
MRNUMBER = {3846338},
MRREVIEWER = {Esen Aksoy Yazici},
DOI = {10.1007/s11856-018-1728-7},
URL = {https://doi.org/10.1007/s11856-018-1728-7},
}
@article {BMP-beauxGroupes,
AUTHOR = {Blossier, Thomas and Martin-Pizarro, Amador},
TITLE = {De beaux groups},
JOURNAL = {Confluentes Math.},
FJOURNAL = {Confluentes Mathematici},
VOLUME = {6},
YEAR = {2014},
NUMBER = {1},
PAGES = {29--39},
ISSN = {1793-7434},
MRCLASS = {03C45},
MRNUMBER = {3266883},
MRREVIEWER = {Martin Bays},
URL = {https://doi.org/10.5802/cml.11},
}
@book {Artin-geometricAlgebra,
AUTHOR = {Artin, Emil},
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YEAR = {1957},
PAGES = {x+214},
MRCLASS = {15.0X},
MRNUMBER = {0082463},
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@article {BGT-approxLinear,
AUTHOR = {Breuillard, Emmanuel and Green, Ben and Tao, Terence},
TITLE = {Approximate subgroups of linear groups},
JOURNAL = {Geom. Funct. Anal.},
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@book {Cameron-pps,
AUTHOR = {Cameron, Peter J.},
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URL = {https://doi.org/10.1007/BF02579367},
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@book{Marker-MT,
AUTHOR = {Marker, David},
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@book {Jacobson-PIAlgs,
AUTHOR = {Jacobson, Nathan},
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theorem},
NOTE = {arXiv:1801.09301 [math.LO]},
}
@article{Wang-gap,
AUTHOR = {Wang, Hong},
TITLE = {An application of algebraic geometry to combinatorics, a refinement
of the {E}lekes-{S}zab\'o theorem},
YEAR = 2014,
NOTE = {Masters thesis, Universit\'e Paris-Sud, Orsay},
}
@article {shparlinski-sumProdElliptic,
AUTHOR = {Shparlinski, Igor},
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VOLUME = {14},
YEAR = {2008},
NUMBER = {3},
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ISSN = {1071-5797},
MRCLASS = {11B75 (11G20)},
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MRREVIEWER = {Moubariz Z. Garaev},
DOI = {10.1016/j.ffa.2007.12.002},
URL = {https://doi.org/10.1016/j.ffa.2007.12.002},
}
@article {bgt,
AUTHOR = {Breuillard, Emmanuel and Green, Ben and Tao, Terence},
TITLE = {Approximate subgroups of linear groups},
JOURNAL = {Geom. Funct. Anal.},
FJOURNAL = {Geometric and Functional Analysis},
VOLUME = {21},
YEAR = {2011},
NUMBER = {4},
PAGES = {774--819},
ISSN = {1016-443X},
MRCLASS = {20H30 (20G40)},
MRNUMBER = {2827010},
MRREVIEWER = {Herbert Abels},
DOI = {10.1007/s00039-011-0122-y},
URL = {https://doi.org/10.1007/s00039-011-0122-y},
}
@article{breuillard-wang,
AUTHOR = {Breuillard, Emmanuel and Wang, Hong},
TITLE = {{Erd\H{o}s} geometry and the group configuration},
YEAR = 2016,
NOTE = {Oberwolfach report, Model Theory Workshop},
}
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DOI = {10.1090/S0894-0347-2011-00708-X},
URL = {https://doi.org/10.1090/S0894-0347-2011-00708-X},
}
@article {szemeredi-trotter,
AUTHOR = {Szemer\'edi, Endre and Trotter, Jr., William T.},
TITLE = {Extremal problems in discrete geometry},
JOURNAL = {Combinatorica},
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@incollection {hrushovski-wagner,
AUTHOR = {Hrushovski, Ehud and Wagner, Frank},
TITLE = {Counting and dimensions},
BOOKTITLE = {Model theory with applications to algebra and analysis. {V}ol.
2},
SERIES = {London Math. Soc. Lecture Note Ser.},
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YEAR = {2008},
MRCLASS = {03C45 (14G05)},
MRNUMBER = {2436141},
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@article {zhal-szabo-sheffer,
AUTHOR = {Sheffer, Adam and Szab\'o, Endre and Zahl, Joshua},
TITLE = {Point-{C}urve {I}ncidences in the {C}omplex {P}lane},
JOURNAL = {Combinatorica},
FJOURNAL = {Combinatorica. An International Journal on Combinatorics and
the Theory of Computing},
VOLUME = {38},
YEAR = {2018},
NUMBER = {2},
PAGES = {487--499},
ISSN = {0209-9683},
MRCLASS = {52C10},
}
@article {HZ,
AUTHOR = {Hrushovski, Ehud and Zilber, Boris},
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YEAR = {1996},
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MRNUMBER = {1311822},
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@article {Tao-expanding,
AUTHOR = {Tao, Terence},
TITLE = {Expanding polynomials over finite fields of large
characteristic, and a regularity lemma for definable sets},
JOURNAL = {Contrib. Discrete Math.},
FJOURNAL = {Contributions to Discrete Mathematics},
VOLUME = {10},
YEAR = {2015},
NUMBER = {1},
PAGES = {22--98},
ISSN = {1715-0868},
MRCLASS = {11T06 (05C75)},
MRNUMBER = {3386249},
MRREVIEWER = {Tom Sanders},
}
@article {pach-midpoints,
AUTHOR = {Pach, J\'anos},
TITLE = {Midpoints of segments induced by a point set},
JOURNAL = {Geombinatorics},
FJOURNAL = {Geombinatorics},
VOLUME = {13},
YEAR = {2003},
NUMBER = {2},
PAGES = {98--105},
ISSN = {1065-7371},
MRCLASS = {11B75 (11P99)},
MRNUMBER = {2007498},
}
@article {scanlon-automaticUniformity,
AUTHOR = {Scanlon, Thomas},
TITLE = {Automatic uniformity},
JOURNAL = {Int. Math. Res. Not.},
FJOURNAL = {International Mathematics Research Notices},
YEAR = {2004},
NUMBER = {62},
PAGES = {3317--3326},
ISSN = {1073-7928},
MRCLASS = {14D99 (03C60 11G10 11U09)},
MRNUMBER = {2097105},
MRREVIEWER = {Thiruvalloor E. Venkata Balaji},
DOI = {10.1155/S1073792804140816},
URL = {https://doi.org/10.1155/S1073792804140816},
}
@incollection {deZeeuw-surveyER,
AUTHOR = {de Zeeuw, Frank},
TITLE = {A survey of {E}lekes-{R}\'{o}nyai-type problems},
BOOKTITLE = {New trends in intuitive geometry},
SERIES = {Bolyai Soc. Math. Stud.},
VOLUME = {27},
PAGES = {95--124},
PUBLISHER = {J\'{a}nos Bolyai Math. Soc., Budapest},
YEAR = {2018},
MRCLASS = {11B13 (52C10)},
MRNUMBER = {3889258},
}
@article{coversfRM,
AUTHOR = {Bays, Martin and Hart, Bradd and Pillay, Anand},
TITLE = {Universal covers of commutative finite Morley rank groups},
NOTE = {arXiv:1403.4883 [math.LO]; to appear in J. Inst. Math. Jussieu},
%JOURNAL = {J. Inst. Math. Jussieu},
%YEAR = {2018},
%URL = {http://dx.doi.org/10.1017/S1474748018000191},
}