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Faculty

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Thomas Tucker

  • Professor of Mathematics
  • Chair for Mathematics

PhD, University of California at Berkeley, 1998

918 Hylan Hall
(585) 275-9421
thomas.tucker@rochester.edu

Office Hours: MW 10:30 – 11:50

Website
Curriculum Vitae


Courses Offered (subject to change)

  • MTH 172  Honors Calculus II

Selected Publications

Papers and preprints

  • J.~P.~Bell, D.~Ghioca, and T.~J. Tucker. ''The Dynamical Mordell-Lang problem for Noetherian spaces." In submisison, 2014. (preprint pdf)
  • H. Krieger, A. Levin, Z. Scherr, T. J. Tucker, Y. Yasufuku, M. Zieve. ''Uniform Boundedness of S-Units in Arithmetic Dynamics.'' To appear in Pacific J. Math. (preprint pdf)
  • T.~J.~ Tucker. ''Integer points in arithmetic sequences.'' To appear in Bull. Inst. Math. Acad. Sin. (N.S.) (preprint pdf)
  • J.~P.~Bell, D.~Ghioca, and T.~J. Tucker. ''Applications of p-Adic Analysis for Bounding Periods of Subvarieties Under Etale Maps.'' Int. Math. Res. Not. Vol. 2014; doi: 10.1093/imrn/rnu046 (paper pdf)
  • D. Ghioca, L.-C. Hsia, and T. J. Tucker. ''Preperiodic points for families of rational maps''. To appear in Proc. London Math. Soc. (preprint pdf)
  • D. Ghioca, L.-C. Hsia, and T. J. Tucker. ''Preperiodic points for families of polynomials''. Algebra Number Theory7 (2013) ( 701--732 (paper pdf)
  • P. Corvaja, V. Sookdeo, T. J. Tucker, and U. Zannier. "Integral points in two-parameter orbits." To appear in Crelle. (preprint pdf)
  • R. Benedetto, D. Ghioca, B. Hutz, P. Kurlberg, T. Scanlon, and T. J. Tucker. ''Periods of rational maps modulo primes''. Math. Ann.355 (2013), 637--660. (paper pdf)
  • C. Gratton, K. Nguyen, and T. J. Tucker. ''ABC implies primitive prime divisors in arithmetic dynamics.'' Bulletin of the LMS (2013); doi: 10.1112/blms/bdt049. (paper pdf)
  • D. Ghioca, T. J. Tucker, and S.-W. Zhang. "Towards a dynamical Manin-Mumford conjecture." Int. Math. Res. Not. Vol. 2011, DOI: 10.1093/imrn/rnq283, 14 pages. (paper pdf)
  • D. Ghioca, T. J. Tucker, and M. E. Zieve. "The Mordell-Lang question for endomorphisms of semiabelian varieties." Journal de Théor. Nombres Bordeaux23 (2011), 645--666. (preprint pdf)
  • C. Petsche, L. Szpiro, and T. J. Tucker. "Dynamical Pairing Between Two Rational Maps." Trans. Amer. Math. Soc.364 (2012), 1687--1710 (paper pdf)
  • R. Benedetto, D. Ghioca, P. Kurlberg, T. J. Tucker. "A gap principle for dynamics." Compositio Math. 146 (2010), 1056--1072 . (paper pdf
  • J. P. Bell, D. Ghioca, and T. J. Tucker. "The dynamical Mordell-Lang problem for etale maps."Amer. J. Math. 132 (2010), 1655--1675 (paper pdf
  • D. Ghioca, T. J. Tucker, and M. E. Zieve. "Linear relations between polynomial orbits." Duke Math. J. 161 (2012), 1379--1410. (paper pdf)
  • D. Ghioca and T. J. Tucker. "Proof of a dynamical Bogomolov conjecture for lines under polynomial actions." Proc. Amer. Math Soc. 138 (2010), 937-942. (paper pdf
  • D. Ghioca and T. J. Tucker. "Periodic points, linearizing maps, and the dynamical Mordell-Lang problem." J. Number Theory 129 (2009), 1392--1403. (paper pdf)
  • X. Faber, B. Hutz, P. Ingram, R. Jones, M. Manes, T. J. Tucker, M. E. Zieve. "Uniform bounds on pre-images under quadratic dynamical systems." Math. Res. Lett. 16 (2009), 87--101. (paper pdf)
  • S.-I. Ih and T. J. Tucker. "A finiteness property for preperiodic points of Chebyshev polynomials." Int. J. Number Theory 6 (2010), 1011--1025. (preprint pdf)
  • R. Benedetto, D. Ghioca, P. Kurlberg, T. J. Tucker, U. Zannier. "The dynamical Mordell-Lang conjecture." Math Ann. 352 (2012), 1--26 (paper pdf)
  • D. Ghioca, T. J. Tucker, and M. E. Zieve. "Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture." Inventiones Math. 171 (2008), 463--483. (paper pdf)
  • D. Ghioca and T. J. Tucker. "p-adic logarithms for polynomial dynamics." 11 pages, the results of this paper have been subsumed by recent more general results. (preprint pdf)
  • D. Ghioca and T. J. Tucker. "Mordell-Lang and Skolem-Mahler-Lech theorems for endomorphisms of semiabelian varieties." 13 pages, the results of this paper have been subsumed by recent more general results. (preprint pdf)
  • D. Ghioca and T. J. Tucker. "A dynamical version of the Mordell-Lang conjecture for the additive group." Compositio Math.144 (2008), 304--316. (paper pdf)
  • D. Ghioca and T. J. Tucker. "Siegel's theorem for Drinfeld modules." Math. Ann. 339 (2007), 37--60.
  • D. Ghioca and T. J. Tucker. "Equidistribution and integral points for Drinfeld modules." Trans. Amer. Math. Soc. 360 (2008), 4863--4887. (paper pdf)
  • L. Szpiro and T. J. Tucker. "Equidistribution and generalized Mahler measures." In, Goldfeld, D.; Jorgenson, J.; Jones, P.; Ramakrishnan, D.; Ribet, K.A.; Tate, J., editors, Number Theory, Analysis and Geometry: In Memory of Serge Lang, pages 609--638, Springer-Verlag, New York, 2012. (preprint pdf)
  • L. Szpiro and T. J. Tucker. "A Shafarevich-Faltings theorem for rational maps." Pure Appl. Math. Q. 4 (2008), 715--728. (paper pdf)
  • L. Szpiro and T. J. Tucker. "One half log discriminant." Diophantine Geometry Proceedings(Pisa, April-July 2005), Publications of the Scuola Normale Superiore, Pisa, 2007. (preprint pdf)
  • R. M. Guralnick, T. J. Tucker, and M. E. Zieve. "Exceptional covers and bijections on rational points." Int. Math. Res. Not., Vol. 2007, article ID rnm004, 19 pages. (paper pdf)
  • J. Pineiro, L. Szpiro, and T. J. Tucker. "Mahler measure for dynamical systems on P1 and intersection theory on a singular arithmetic surface." In, F. Bogomolov and Y. Tschinkel, editors, Geometric methods in algebra and number theory, Progress in Math 235, pages 219--250, Birkhauuser, 2004. (preprint pdf)
  • P. Cutter, A. Granville, and T. J. Tucker. "The number of fields generated by the square root of a given polynomial." Canad. Math. Bull. 46 (2003), 71--79. (paper pdf)
  • A. Granville and T. J. Tucker. "It's as easy as abc." Notices Amer. Math. Soc. 49 (2002), no. 10, 1224--1231. (paper pdf)
  • D. Lorenzini and T. J. Tucker. "Thue equations and the method of Chabauty-Coleman."Inventiones Math. 148 (2002), 47--77. (paper pdf)
  • T. J. Tucker. "Irreducibility, Brill-Noether loci, and Vojta's inequality." Trans. Amer. Math. Soc.354 (2002), 3011 -- 3029. (paper pdf)
  • X. Song and T. J. Tucker. "Arithmetic discriminants and morphisms of curves." Trans. Amer. Math. Soc. 353 (2001) 1921--1936. (paper pdf)
  • X. Song and T. J. Tucker. "Dirichlet's Theorem, Vojta's inequality, and Vojta's conjecture."Compositio Math. 116 (1999), 219--238. (paper pdf)

Recent Talks