Publications and preprints

Asymptotic differential algebra

		The surreal numbers as a universal H-field (with L. van den Dries and J. van der Hoeven) J. Eur. Math. Soc. (JEMS) 21 (2019), no. 4, 1179–1199.
		Hardy fields, the intermediate value property, and $\omega$-freeness (with L. van den Dries and J. van der Hoeven) Séminaire de structures algébriques ordonnées, prépublications de l'Équipe de Logique Mathématique, vol. 93, Institut de Mathématiques de Jussieu, Paris, 2018.
		On numbers, germs, and transseries (with L. van den Dries and J. van der Hoeven) B. Sirakov et al. (eds.): Proceedings of the International Congress of Mathematicians, Rio de Janeiro 2018, vol. 2, pp. 19–42, World Scientific Publishing Co., Singapore, 2018.
		Maximal immediate extensions of valued differential fields (with L. van den Dries and J. van der Hoeven) Proc. London Math. Soc. 117 (2018), no. 2, 376–406.
		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.
		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.)
		Julia's Equation and differential transcendence (with W. Bergweiler) Illinois J. Math. 59 (2015), no. 2, 277-294.
		Transseries and Todorov-Vernaeve's asymptotic fields (with I. Goldbring) Arch. Math. Logic 53 (2014), 65-87.
		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.
		Logarithms of iteration matrices, and proof of a conjecture by Shadrin and Zvonkine J. Combin. Theory Ser. A 119 (2012), 627-654.
		Differentially algebraic gaps (with L. van den Dries and J. van der Hoeven) Selecta Math. 11 (2005), 247-280.
		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.
		Liouville closed H-fields (with L. van den Dries) J. Pure  Appl. Algebra 197 (2005), 83-139.
		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.
		H-fields and their Liouville extensions (with L. van den Dries) Math. Z. 242 (2002), 543-588.
		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

		Distality in valued fields and related structures (with A. Chernikov, A. Gehret, and M. Ziegler)
		The logical complexity of finitely generated commutative rings (with A. Khélif, E. Naziazeno, and T. Scanlon) Int. Math. Res. Not. IMRN 2020, no. 1, 112–166.
		Whitney's Extension Problem in o-minimal structures (with A. Thamrongthanyalak)  Rev. Mat. Iberoam. 35 (2019), no. 4, 1027–1052.
		Michael's Selection Theorem in a semilinear context (with A. Thamrongthanyalak) Adv. Geom. 15 (2015), no. 3, 293-313.
		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.
		Definable versions of theorems by Kirszbraun and Helly (with A. Fischer) Proc. London Math. Soc. 102 (2011), 468-502.
		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

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

		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.
		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.
		Finiteness theorems in stochastic integer programming (with R. Hemmecke) Found. Comput. Math. 7 (2007), 183-227.
		Bounds and definability in polynomial rings Quart. J. Math. 56 (2005), 263-300.
		Reduction mod p of standard bases Comm. Algebra 33 (2005), 1635-1661.
		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.

Miscellaneous unpublished notes

		An elimination theorem for mixed real-integer systems
		Differential transcendence of iterative logarithms

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