Publications and preprints

Asymptotic differential algebra

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Julia's Equation and differential transcendence (with W. Bergweiler), Illinois J. Math., to appear.
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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.)

Model theory and tame geometry

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Whitney's Extension Problem in o-minimal structures (with A. Thamrongthanyalak), submitted.
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Michael's Selection Theorem in a semilinear context (with A. Thamrongthanyalak), Adv. Geom., to appear.
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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., to appear.
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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.

Group theory, 3-manifold groups

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Decision problems for 3-manifolds and their fundamental groups (with S. Friedl and H. Wilton)
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3-manifold groups (with S. Friedl and H. Wilton)
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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.

Bounds and algorithms in algebra

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An effective Weierstrass Division Theorem
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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)
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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.
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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.
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Ideal membership in polynomial rings over the integers
J. Amer. Math. Soc. 17 (2004), 407-441.

Miscellaneous unpublished notes

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An elimination theorem for mixed real-integer systems


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