Lou van den Dries

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Lou van den Dries, Oberwolfach, 1988

Laurentius Petrus Dignus "Lou" van den Dries (born May 26, 1951) is a Dutch mathematician working in model theory. He is a professor of mathematics at the University of Illinois at Urbana–Champaign.

He completed his PhD at Utrecht University in 1978 under the supervision of Dirk van Dalen with a dissertation entitled Model Theory of Fields.[1]

Van den Dries is most known for his seminal work in o-minimality. He has also made contributions to the model theory of p-adic fields, valued fields, and finite fields, and to the study of transseries. With Alex Wilkie, he improved Gromov's theorem on groups of polynomial growth using nonstandard methods.

Van den Dries has been a corresponding member of the Royal Netherlands Academy of Arts and Sciences since 1993.[2] He was an invited speaker at the International Congress of Mathematicians in 1990 and 2018, and delivered the Tarski Lectures at the University of California, Berkeley in 2017.[3][4] He was awarded the Shoenfield Prize from the Association for Symbolic Logic in 2016 for his chapter "Lectures on the Model Theory of Valued Fields" in Model Theory in Algebra, Analysis and Arithmetic, edited by Dugald Macpherson and Carlo Toffalori.[5] Van den Dries was jointly awarded the 2018 Karp Prize with Matthias Aschenbrenner and Joris van der Hoeven "for their work in model theory, especially on asymptotic differential algebra and the model theory of transseries."[6]

His doctoral students include Matthias Aschenbrenner.

Selected publications[edit]

  • M. Aschenbrenner; L. van den Dries; J. van der Hoeven (2017). Asymptotic Differential Algebra and Model Theory of Transseries. Annals of Mathematics Studies. 195. Princeton University Press. arXiv:1509.02588. doi:10.1515/9781400885411. ISBN 9781400885411. MR 3585498. Zbl 06684722.
  • Z. Chatzidakis; L. van den Dries; A. Macintyre (1992). "Definable sets over finite fields". J. Reine Angew. Math. 427 (427): 107–135. doi:10.1515/crll.1992.427.107. MR 1162433. Zbl 0759.11045.
  • J. Denef; L. van den Dries (1988). "p-adic and real subanalytic sets". Ann. of Math. Series 2. 128 (1): 79–138. doi:10.2307/1971463. JSTOR 1971463. MR 0951508. Zbl 0693.14012.
  • L. van den Dries; A. Wilkie (1984). "Gromov's theorem of groups of polynomial growth and elementary logic". J. Algebra. 89 (2): 349–374. doi:10.1016/0021-8693(84)90223-0. MR 0751150. Zbl 0552.20017.
  • L. van den Dries; A. Macintyre; D. Marker (1994). "The elementary theory of restricted analytic fields with exponentiation". Ann. of Math. Series 2. 140 (1): 183–205. doi:10.2307/2118545. JSTOR 2118545. MR 1289495. Zbl 0837.12006.
  • L. van den Dries; C. Miller (1996). "Geometric categories and o-minimal structures". Duke Math. J. 84 (2): 497–540. doi:10.1215/S0012-7094-96-08416-1. MR 1404337. Zbl 0889.03025.
  • L. van den Dries (1998). Tame topology and o-minimal structures. London Mathematical Society Lecture Notes. 248. Cambridge University Press. doi:10.1017/CBO9780511525919. ISBN 9780511525919. MR 1633348. Zbl 0953.03045.
  • L. van den Dries (2014), "Lectures on the Model Theory of Valued Fields", in H. Dugald Macpherson; C. Toffalori (eds.), Model Theory in Algebra, Analysis and Arithmetic, Lecture Notes in Mathematics, 2111, Springer-Verlag, pp. 55–157, doi:10.1007/978-3-642-54936-6_4, ISBN 978-3-642-54935-9, MR 3330198, Zbl 1347.03074