@article {34894,
	title = {Approximating rational points on surfaces},
	journal = {arXiv preprint arXiv:2403.02480},
	year = {2024},
	abstract = {<p class="MsoPlainText">
	Let X\&nbsp;be a smooth projective algebraic variety over a number field k\&nbsp;and P\&nbsp;in X(k). In 2007, the second author conjectured that, in a precise sense, if rational points on X\&nbsp;are dense enough, then the best rational approximations to P\&nbsp;must lie on a curve. We present a strategy for deducing a slightly weaker conjecture from Vojta{\textquoteright}s conjecture, and execute this strategy for the full conjecture for split surfaces.
</p>
},
	url = {http://arxiv.org/abs/2403.02480},
	author = {Brian Lehmann and David McKinnon and Matthew Satriano}
}
@article {mckinnonerratum,
	title = {ERRATUM FOR APPROXIMATING RATIONAL POINTS ON TORIC VARIETIES},
	year = {2023},
	author = {McKinnon, David and Satriano, Matthew}
}
@article {mckinnon2023rational,
	title = {Rational approximation on cubic hypersurfaces},
	journal = {Algebraic Geometry (to appear)},
	year = {2023},
	url = {arXiv preprint arXiv:2310.01640},
	author = {McKinnon, David}
}
@article {mckinnon2020codimension,
	title = {Codimension two integral points on some rationally connected threefolds are potentially dense},
	journal = {J. Algebraic Geometry},
	volume = {31},
	year = {2022},
	pages = {345-386},
	author = {McKinnon, David and Roth, Mike}
}
@article {mckinnon2021approximating,
	title = {Approximating rational points on toric varieties},
	journal = {Transactions of the American Mathematical Society},
	volume = {374},
	number = {5},
	year = {2021},
	pages = {3557{\textendash}3577},
	author = {McKinnon, David and Satriano, Matthew}
}
@article {mckinnon2021curves,
	title = {On curves with high multiplicity on P (a, b, c) for min (a, b, c)},
	journal = {NEW YORK JOURNAL OF MATHEMATICS},
	volume = {27},
	year = {2021},
	pages = {1060{\textendash}1084},
	publisher = {ELECTRONIC JOURNALS PROJECT UNIV ALBANY, DEPT MATHEMATICS \& SCIENCE, ALBANY {\textellipsis}},
	author = {McKinnon, David and Razafy, Rindra and Satriano, Matthew and Sun, Yuxuan}
}
@article {huang2021fraction,
	title = {What fraction of an Sn-orbit can lie on a hyperplane?},
	journal = {Linear Algebra and its Applications},
	volume = {613},
	year = {2021},
	pages = {1{\textendash}23},
	publisher = {North-Holland},
	author = {Huang, Jiahui and McKinnon, David and Satriano, Matthew}
}
@unpublished {mckinnoncounting,
	title = {Counting rational points on ruled varieties over function fields},
	year = {2019},
	author = {McKinnon, David}
}
@article {mckinnon2018arithmetic,
	title = {The arithmetic puncturing problem and integral points},
	journal = {arXiv preprint arXiv:1806.03180},
	year = {2018},
	author = {McKinnon, David and Zhu, Yi}
}
@article {mckinnon2016analogue,
	title = {An analogue of Liouville\&rsquo;s theorem and an application to cubic surfaces},
	journal = {European Journal of Mathematics},
	volume = {2},
	number = {4},
	year = {2016},
	pages = {929{\textendash}959},
	publisher = {Springer International Publishing Cham},
	author = {McKinnon, David and Roth, Mike}
}
@database {34094,
	title = {PDF file containing tables of generators of various cones in the N{\'e}ron-Severi group of a smooth cubic surface},
	year = {2016},
	url = {https://www.math.uwaterloo.ca/~dmckinno/Papers/cubictable.pdf},
	author = {David McKinnon}
}
@article {forest2015exact,
	title = {Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets},
	journal = {Journal of Mathematical Physics},
	volume = {56},
	number = {8},
	year = {2015},
	publisher = {AIP Publishing},
	author = {Forest, Simon and Gosset, David and Kliuchnikov, Vadym and McKinnon, David}
}
@article {mckinnon2015seshadri,
	title = {Seshadri constants, diophantine approximation, and Roth\&rsquo;s theorem for arbitrary varieties},
	journal = {Inventiones mathematicae},
	volume = {200},
	number = {2},
	year = {2015},
	pages = {513{\textendash}583},
	publisher = {Springer Berlin Heidelberg},
	author = {McKinnon, David and Roth, Mike}
}
@article {levin2012ideals,
	title = {Ideals of degree one contribute most of the height},
	journal = {Algebra \& Number Theory},
	volume = {6},
	number = {6},
	year = {2012},
	pages = {1223{\textendash}1238},
	publisher = {Mathematical Sciences Publishers},
	author = {Levin, Aaron and McKinnon, David}
}
@article {mckinnon2011vojta,
	title = {Vojta\&$\#$39;s conjecture implies the Batyrev\&ndash;Manin conjecture for K 3 surfaces},
	journal = {Bulletin of the London Mathematical Society},
	volume = {43},
	number = {6},
	year = {2011},
	pages = {1111{\textendash}1118},
	publisher = {Oxford University Press},
	author = {McKinnon, David}
}
@article {logan2010density,
	title = {Density of rational points on diagonal quartic surfaces},
	journal = {Algebra \& Number Theory},
	volume = {4},
	number = {1},
	year = {2010},
	pages = {1{\textendash}20},
	publisher = {Mathematical Sciences Publishers},
	author = {Logan, Adam and McKinnon, David and van Luijk, Ronald}
}
@article {baragar2010k3,
	title = {K3 surfaces, rational curves, and rational points},
	journal = {Journal of Number Theory},
	volume = {130},
	number = {7},
	year = {2010},
	pages = {1470{\textendash}1479},
	publisher = {Academic Press},
	author = {Baragar, Arthur and McKinnon, David}
}
@article {hare2009patterns,
	title = {Patterns and periodicity in a family of resultants},
	journal = {Journal de th{\'e}orie des nombres de Bordeaux},
	volume = {21},
	number = {1},
	year = {2009},
	pages = {215{\textendash}234},
	author = {Hare, Kevin G and McKinnon, David and Sinclair, Christopher D}
}
@article {levin2008error,
	title = {On the error terms and exceptional sets in conjectural second main theorems},
	journal = {The Quarterly Journal of Mathematics},
	volume = {59},
	number = {4},
	year = {2008},
	pages = {487{\textendash}498},
	publisher = {Oxford University Press},
	author = {Levin, Aaron and McKinnon, David and Winkelmann, J{\"o}rg}
}
@article {geelen2008straight,
	title = {Straight line embeddings of cubic planar graphs with integer edge lengths},
	journal = {Journal of Graph Theory},
	volume = {58},
	number = {3},
	year = {2008},
	pages = {270{\textendash}274},
	publisher = {Wiley Subscription Services, Inc., A Wiley Company Hoboken},
	author = {Geelen, Jim and Guo, Anjie and McKinnon, David}
}
@article {34093,
	title = {A conjecture on rational approximations to rational points},
	journal = {Journal of Algebraic Geometry},
	volume = {16},
	year = {2007},
	pages = {257-303},
	author = {David McKinnon}
}
@article {mckinnon2007curves,
	title = {Curves arising from endomorphism rings of Kronecker modules},
	journal = {The Rocky Mountain Journal of Mathematics},
	year = {2007},
	pages = {879{\textendash}892},
	publisher = {The Rocky Mountain Mathematics Consortium},
	author = {McKinnon, David and Roth, Mike}
}
@article {magidin2005gauss,
	title = {Gauss\&$\#$39;s lemma for number fields},
	journal = {The American Mathematical Monthly},
	volume = {112},
	number = {5},
	year = {2005},
	pages = {385{\textendash}416},
	publisher = {Taylor \& Francis},
	author = {Magidin, Arturo and McKinnon, David}
}
@article {etgu2005lagrangian,
	title = {Lagrangian tori in homotopy elliptic surfaces},
	journal = {Transactions of the American Mathematical Society},
	volume = {357},
	number = {9},
	year = {2005},
	pages = {3757{\textendash}3774},
	author = {Etg{\"u}, Tolga and McKinnon, David and Park, B}
}
@article {mckinnon2004counting,
	title = {Counting rational points on ruled varieties},
	journal = {Canadian Mathematical Bulletin},
	volume = {47},
	number = {2},
	year = {2004},
	pages = {264{\textendash}270},
	publisher = {Cambridge University Press},
	author = {McKinnon, David}
}
@article {mckinnon2004reduction,
	title = {A reduction of the Batyrev-Manin conjecture for Kummer surfaces},
	journal = {Canadian Mathematical Bulletin},
	volume = {47},
	number = {3},
	year = {2004},
	pages = {398{\textendash}406},
	publisher = {Cambridge University Press},
	author = {McKinnon, David}
}
@article {mckinnon2003vojta,
	title = {Vojta\&rsquo;s main conjecture for blowup surfaces},
	journal = {Proceedings of the American Mathematical Society},
	volume = {131},
	number = {1},
	year = {2003},
	pages = {1{\textendash}12},
	author = {McKinnon, David}
}
@article {mckinnon2001arithmetic,
	title = {An arithmetic analogue of Bezout\&$\#$39;s theorem},
	journal = {Compositio Mathematica},
	volume = {126},
	number = {2},
	year = {2001},
	pages = {147{\textendash}155},
	publisher = {London Mathematical Society},
	author = {McKinnon, David}
}
@article {mckinnon2000counting,
	title = {Counting rational points on K3 surfaces},
	journal = {Journal of Number Theory},
	volume = {84},
	number = {1},
	year = {2000},
	pages = {49{\textendash}62},
	publisher = {Academic Press},
	author = {McKinnon, David}
}
@mastersthesis {mckinnon1999counting,
	title = {Counting rational points of bounded height on algebraic varieties},
	year = {1999},
	school = {University of California, Berkeley},
	type = {PhD thesis},
	author = {McKinnon, David Kerr}
}