Papers written or cowritten by Thomas Scanlon

Thesis

Model Theory of Valued D-Fields, PhD thesis, Harvard University, May 1997. Postscript or PDF

Published papers

  1. The abc-theorem for commutative algebraic groups in characteristic p, International Mathematics Research Notices 1997, no. 18, 881 -- 898. Postscript or PDF
  2. p-adic distance from torsion points of semi-abelian varieties, J. reine angew. Math. 499 (1998), 225 -- 236. Postscript or PDF
  3. Supersimple fields and division rings, with Anand Pillay and Frank Wagner , Mathematics Research Letters 5 (1998), 473 -- 483. Postscript or PDF
  4. Difference algebraic subgroups of commutative algebraic groups over finite fields, with J. F. Voloch, Manuscripta Math. 99 (1999), no. 3, 329--339. Postscript or PDF
  5. The conjecture of Tate and Voloch on p-adic proximity to torsion, International Mathematics Research Notices 1999 , no. 17, 909 -- 914. Postscript or PDF
  6. Lascar and Morley ranks differ in differentially closed fields, with Ehud Hrushovski, Journal of Symbolic Logic 64 , no. 3, Sept. 1999, 1280 -- 1284. Postscript or PDF
  7. Combinatorics with definable sets: Euler characteristics and Grothendieck rings, with Jan Krajicek, Bulletin of Symbolic Logic 6 , no 3, September 2000, 311 -- 330. Postscript or PDF
  8. A model complete theory of valued D-fields, Journal of Symbolic Logic, 65 , no. 4, December 2000, 1758 - 1784. Postscript or PDF
  9. Diophantine geometry from model theory, Bulletin of Symbolic Logic, 7 , no. 1, March 2001, 37 - 57. Postscript or PDF
  10. Public key cryptosystems based on Drinfeld modules are insecure, Journal of Cryptology, 14, no. 4, 2001, 225--230. Postscript or PDF
  11. Compact complex manifolds with the DOP and other properties, with Anand Pillay, Journal of Symbolic Logic, 67, no. 2, June 2002, 737 - 743. Postscript or PDF
  12. Model theory and differential algebra, in Differential Algebra and Related Topics Proceedings of the International Workshop (Newark, November 2000), eds. L. Guo, P. J. Cassidy, W. F. Keigher & W. Y. Sit, World Scientific 2002, pp. 125 - 150. Postscript or PDF
  13. Stable Groups (a review of the English translation of B. Poizat's Groupes Stables), Bull. AMS 39 no. 4 (2002), 573-579. Postscript or PDF
  14. Diophantine geometry of the torsion of a Drinfeld module, Journal of Number Theory 97 no. 1 (November 2002), 10 - 25. Postscript or PDF
  15. Meromorphic groups, with Anand Pillay, Trans. AMS, 355 (2003), 3843-3859. Postscript or PDF
  16. Quantifier elimination for the relative Frobenius, in Valuation Theory and Its Applications Volume II, conference proceedings of the International Conference on Valuation Theory (Saskatoon, 1999), Franz-Viktor Kuhlmann, Salma Kuhlmann, and Murray Marshall, eds., Fields Institute Communications Series, (AMS, Providence), 2003, 323 - 352. Postscript or PDF
  17. F-structures and integral points on semiabelian varieties over finite fields, with Rahim Moosa, Amer. J. Math. 126 (2004), 473 - 522. Postscript or PDF
  18. Automatic uniformity, International Mathematics Research Notices 2004, no. 62, 3317 - 3326. Postscript or PDF
  19. The Mordell-Lang conjecture in positive characteristic revisited, with Rahim Moosa, in Model Theory and Applications (eds. L. Bélair, P. D'Aquino, D. Marker, M. Otero, F. Point, & A. Wilkie), 2003, 273 - 296. Postscript or PDF
  20. Local André-Oort conjecture for the universal abelian variety, Inventiones mathematicae, (Online first, 19 October 2005), 163, no. 1, January 2006, 191 - 211. Postscript or PDF
  21. Positive characteristic Manin-Mumford theorem, Compositio mathematica 141, no. 6 (November 2005), 1351-1364. Postscript or PDF
  22. Nonstandard meromorphic groups, Electronic Notes in Theoretical Computer Science, Volume 143, (6 January 2006) Proceedings of the 12th Workshop on Logic, Language, Information and Computation (WoLLIC 2005) Florianópolis, Santa Catarina, Brazil 19-22 July 2005, 185 - 196.
  23. Groups in the theory of compact complex analytic spaces, with Matthias Aschenbrenner and Rahim Moosa, J. Symbolic Logic 71 (2006), 529-552.
  24. Analytic difference rings, Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006, Volume II, 71 -- 92.
  25. Model theory of the Frobenius on the Witt vectors, with Luc Bélair and Angus Macintyre, American Journal of Mathematics, Volume 129, Number 3, June 2007, 665 - 721.
  26. Differential arcs and regular types in differential fields, with Rahim Moosa and Anand Pillay, J. Reine Angew. Math. 620 (2008), 35 - 54.
  27. Differentially valued fields are not differentially closed, Model theory with applications to algebra and analysis. Vol. 1, 111--115, London Math. Soc. Lecture Note Ser., 349, Cambridge Univ. Press, Cambridge, 2008.
  28. Infinite finitely generated fields are biinterpretable with N, J. Amer. Math. Soc. 21 (2008) 893 - 908. (Erratum, J. Amer. Math. Soc. 24 (2011), no. 3, 917. There is a serious mistake in the proof of the definability of valuations. As it stands, Pop's Conjecture is still open.)
  29. Jet and prolongation spaces, with Rahim Moosa, Journal of the Institute of Mathematics Jussieu 9 (2010), no. 2, 391 - 430.
  30. Counting special points: Logic, diophantine geometry, and transcendence theory., Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 51 - 71.
  31. A Euclidean Skolem-Mahler-Lech-Chabauty method, Math. Res. Lett. 18 (2011), no. 5, 833 - 842.
  32. Artin-Schreier extensions in nip and simple fields, with Itay Kaplan and Frank Wagner, Israel J. Math. 185 (2011), 141 - 153.
  33. Generalized Hasse-Schmidt varieties and their jet spaces, with Rahim Moosa, Proc. Lond. Math. Soc. (3) 103 (2011), no. 2, 197 - 234.
  34. Algebraic equations on the adèlic closure of a Drinfeld module, with Dragos Ghioca, Israel J. Math., on-line first, 2012.
  35. Periods of rational maps modulo primes, with R. Benedetto, D. Ghioca, B. Hutz, P. Kurlberg, and T. Tucker, Math. Ann., on-line first, 2012.
  36. A proof of the André-Oort conjecture using mathematical logic [after Pila, Wilkie and Zannier], Astérisque, Séminaire Bourbaki, Exposé 1037, 2010 - 2011.
  37. Exponential-polynomial equations and dynamical return sets, with Yu Yasufuku, International Mathematics Research Notices, published on-line April 30, 2013 doi:10.1093/imrn/rnt081
  38. Invariant varieties for polynomial dynamical systems, with Alice Medvedev, Annals of Mathematics, 179 (2014), no. 1, 81 - 177.
  39. Model theory of fields with free operators in characteristic zero, with Rahim Moosa, Journal of Mathematical Logic 14 (2014), no. 2, 1450009, 43 pp.
  40. Density of orbits of endomorphisms of abelian varieties, with Dragos Ghioca, Trans. AMS, 14 April 2016, (to appear).
  41. Strong minimality and the j-function, with James Freitag, Journal of the European Mathematical Society, 2015, (to appear).
  42. Differential Chow varieties exist, with James Freitag and Wei Li (and an appendix by William Johnson), 27 pages with a 4 page appendix, Journal of the London Mathematical Society, 2016, (to appear).

Papers under review

  1. Communication lower bounds and optimal algorithms for programs that references arrays - part I, with F. Micahel Christ, James Demmel, Nicholas Knight, and Katherine Yelick, 2013.
  2. O-minimality as an approach to the André-Oort conjecture, 53 pages, 2016.
  3. Algebraic differential equations from covering maps, 25 pages, 2014.
  4. The logical complexity of finitely generated commutative rings, with Matthias Aschenbrenner, Anatole Khélif, and Eudes Naziazeno, 39 pages, 2016.

Preprints and Notes not intended for formal publication

  1. The absolute Mordell-Lang conjecture in positive characteristic, 1998.
  2. Infinite stable fields are Artin-Schreier closed, 1999.
  3. Fields admitting ordered nontrivial strong Euler characteristics are quasifinite, 2000.
  4. An elementary proof that order one sets living on curves of general type have no structure, 2000.
  5. Uniformity in the Mordell-Lang theorem, 2001.
  6. Superstability for F-structures, with Rahim Moosa, 2003.
  7. Algebraic relations amongst periodic points of a lifting of Frobenius, 2007.
  8. Analytic relations on a dynamical orbit, 2008.

Slides from recent talks

  1. Higher dimensional dynamical Mordell-Lang problems, Conference on Diophantine Problems and Arithmetic Dynamics, Academia Sinica, Taipei, Taiwan, 27 June 2013.
  2. Lectures on Model Theory and Algebraic Dynamics, CUNY 7 - 11 June 2010 Day 1 Day 2 Day 3 Day 4 Day 5
  3. "Dynamical Mordell-Lang problems, Będlewo, Poland, 13 August 2009
  4. "Motivic Integration: An outsider's tutorial, Durham, England, 21 & 22 July 2009
  5. Definability in fields, Computable model theory, University of Florida at Gainesville, 5-6 February 2007. Lecture 1 Lecture 2 Lecture 3
  6. Pop's conjecture on the elementary theory of finitely generated fields, Paris VII, 8 June 2006.
  7. Groups in the theory of compact complex manifolds, III Encuentro de la Teoría de Modelos, (Villa de Leyva, Colombia), 18 August 2005.
  8. Categoricidad relativa para campos finitamente generados, XV Congreso Nacional de Matemáticas, (Bogotá), 12 August 2005.
  9. Additive groups, Model Theory and Its Applications to Algebra and Analysis, Isaac Newton Institute, (Cambridge, UK), 15 July 2005.
  10. A local André-Oort theorem via ACFA, Model Theory and Its Applications to Algebra and Analysis, Isaac Newton Institute, (Cambridge, UK), 31 March 2005.
  11. Geometric stability theory, Logic Colloquium 2004 (Torino), 27, 28 & 30 July 2004.
  12. Model theory of valued difference fields, Maurice Boffa Lecture (Mons, Belgium), 27 May 2004.
  13. Differential arcs, Interactions between model theory and geometry, Banff, 15 March 2004.
  14. Model Theory of Enriched Valued Fields, Logic Colloquium 2002 (Münster), 4 August 2002.
  15. A Drinfeld module version of the Mordell-Lang conjecture, Arizona Winter School 2003, 17 - 19 March 2003.
  16. p-Jets and Uniform Unramified Manin-Mumford, Joint AMS-SMF Meeting, Lyon 19 July 2001. Postscript or PDF
  17. Model Theory and Differential Algebra, Newark meeting on differential algebra and related topics, 3 November 2000. Postscript or PDF
  18. Grothendieck Rings, Euler Characteristics, and Schanuel Dimensions, Berkeley Logic Colloquium, 29 September 2000. Postscript or PDF

Lecture notes

    Math 225a, Autumn 2013
Note that most of the work described on this page has been supported by grants of the National Science Foundation.