On numbers, germs, and transseries
(with L. van
den Dries and J. van
der Hoeven), submitted. |
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Maximal immediate extensions of valued
differential fields (with L. van
den Dries and J. van
der Hoeven), submitted. |
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Dimension in the realm of transseries
(with L. van
den Dries and J. van
der Hoeven), In: F. Broglia et al. (eds.): Ordered Algebraic
Structures and Related Topics, pp. 23-39, Contemp.
Math. 697, Amer. Math. Soc.,
Providence, RI, 2017. |
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The surreal numbers as a universal
H-field (with L. van
den Dries and J. van
der Hoeven)J. Eur. Math. Soc. (JEMS), to appear. |
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Asymptotic
Differential Algebra and Model Theory of
Transseries (with L. van
den Dries and J. van
der Hoeven)Ann. of Math. Stud., no. 195, Princeton University Press, Princeton, 2017. (For errata to the printed version see here.) |
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Julia's Equation and differential
transcendence (with W.
Bergweiler), Illinois J. Math. 59 (2015), no. 2, 277-294. |
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Transseries and Todorov-Vernaeve's asymptotic
fields (with I. Goldbring) Arch. Math. Logic 53 (2014), 65-87. |
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Toward a model theory for transseries
(with L. van
den Dries and J. van
der Hoeven) Notre Dame J. Form. Log. 54 (2013), no. 3-4,
279-310. |
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Logarithms of iteration matrices, and proof of a
conjecture by Shadrin and Zvonkine J. Combin. Theory Ser. A 119 (2012), 627-654. |
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Differentially algebraic gaps (with L. van
den Dries and J. van
der Hoeven) Selecta Math. 11 (2005), 247-280. |
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Asymptotic differential algebra (with L. van
den Dries) In: O. Costin, M. D. Kruskal, A. Macintyre (eds.), Analyzable Functions and Applications, Contemp. Math. 373, Amer. Math. Soc., Providence, RI (2005), 49-85. |
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Liouville closed H-fields (with L. van
den Dries) J. Pure Appl. Algebra 197 (2005), 83-139. |
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Some remarks about asymptotic couples In: F.-V. Kuhlmann, S. Kuhlmann, M. Marshall (eds.), Valuation Theory and its Applications, II, Fields Institute Publications 33, AMS, Providence, RI (2003), 7-18. |
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H-fields and their Liouville extensions
(with L. van
den Dries) Math. Z. 242 (2002), 543-588. |
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Closed asymptotic couples (with
L. van den Dries) J. Algebra 225, 309-358 (2000). (For an expanded version of this paper click here.) |

The logical complexity of finitely
generated commutative rings (with A.
Khélif, E.
Naziazeno, and T. Scanlon),
submitted. |
||

Whitney's Extension Problem in o-minimal
structures (with A.
Thamrongthanyalak), submitted. |
||

Michael's Selection Theorem in a
semilinear context (with A.
Thamrongthanyalak)Adv. Geom. 15 (2015), no. 3, 293-313. |
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Vapnik-Chervonenkis density in some theories
without the independence property, I (with A. Dolich, D. Haskell,
D.
Macpherson, and S. Starchenko) Trans. Amer. Math. Soc. 368 (2016), 5889-5949. |
||

Vapnik-Chervonenkis density in some theories
without the independence property, II (with A. Dolich, D. Haskell,
D.
Macpherson, and S. Starchenko) Notre Dame J. Form. Log. 54 (2013), no. 3-4,
311-363. |
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Definable
versions
of theorems by Kirszbraun and Helly (with A. Fischer) Proc. London Math. Soc. 102 (2011), 468-502. |
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Strongly minimal groups in the theory of compact
complex spaces (with R. Moosa
and T.
Scanlon) J. Symbolic Logic 71 (2006), 529-552. |

Decision problems for 3-manifolds
and their fundamental groups (with S.
Friedl and H.
Wilton)Geom. Topol. Monogr. 19 (2015), 201-236. |
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3-Manifold Groups (with S.
Friedl and H.
Wilton) EMS Series of Lectures in Mathematics, vol. 20, European Mathematical Society (EMS), Zürich, 2015. |
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3-manifold groups are virtually residually p (with S.
Friedl) Mem. Amer. Math. Soc. 225 (2013), no. 1058. |
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Residual properties of graph manifold groups
(with S.
Friedl) Topology Appl. 158 (2011), 1179-1191. |
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A criterion for HNN extensions of finite p-groups
to be residually p (with S.
Friedl) J. Pure Appl. Algebra 215 (2011), 2280-2289. |

An effective Weierstrass Division Theorem | ||

Algorithms for computing saturations of ideals in
finitely generated commutative rings Appendix to: Automorphisms mapping a point into a subvariety, J. Algebraic Geom. 20 (2011), 785-794. (by B. Poonen) |
||

Degree bounds for Gröbner bases in algebras of
solvable type (with A.
Leykin) J. Pure Appl. Algebra 213 (2009), 1578-1605. |
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Lefschetz extensions, tight closure, and big
Cohen-Macaulay algebras (with H.
Schoutens) Israel J. Math. 161 (2007), 221-310. |
||

Finite generation of symmetric ideals
(with C.
Hillar) Trans. Amer. Math. Soc. 359 (2007), 5171-5192. |
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Finiteness theorems in stochastic integer
programming (with R.
Hemmecke) Found. Comput. Math. 7 (2007), 183-227. |
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Bounds and definability in polynomial rings Quart. J. Math. 56 (2005), 263-300. |
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Reduction mod p of standard bases Comm. Algebra 33 (2005), 1635-1661. |
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Orderings of monomial ideals (with W.-Y. Pong) Fund. Math. 181 (2004), 27-74. |
||

Ideal membership in polynomial rings over the
integers J. Amer. Math. Soc. 17 (2004), 407-441. |

An elimination theorem for mixed real-integer
systems |
||

Differential transcendence of iterative
logarithms |