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Clayton Petsche in front of shrubbery

Clayton Petsche

Associate Professor
Department of Mathematics

Clayton Petsche

Associate Professor
Department of Mathematics

Biography

Before joining Oregon State University in 2011, Clayton Petsche held positions at the University of Georgia, the CUNY Graduate Center, and Hunter College.

Research

Clayton Petsche's research includes the study of algebraic and arithmetic dynamical systems on varieties and analytic spaces, as well as the theory of height functions over global fields.

Research Interests

  • Number Theory
  • Dynamical Systems

Students

Ph.D. Students

  • Peter Oberly (current)
  • Chatchai Noytaptim (current)
  • Chifan Leung (current)
  • Naveen Somasunderam (2019)
  • Emerald Stacy (2018)
  • Brian Stout (2013)

M.S. Students

  • Peter Oberly (2022)
  • Naveen Somasunderam (2016)
  • Jesse Andrews (2016)
  • Evan Hedlund (2015)
  • Emerald Stacy (2015)
  • Jeff Monroe (2014)
  • Jason McClelland (2014)

Links

Background

Education

Ph.D. The University of Texas at Austin

B.S. Virginia Tech

Publications

  • Totally real algebraic integers in short intervals, Jacobi polynomials, and unicritical families in arithmetic dynamics
    Chatchai Noytaptim and Clayton Petsche
    Submitted for publication
    (arxiv)
  • Non-Archimedean Koksma inequalities, variation, and Fourier analysis
    Clayton Petsche and Naveen Somasunderam
    Uniform Distribution Theory, to appear
    (arxiv)
  • Totally T-adic functions of small height
    Xander Faber and Clayton Petsche
    Rendiconti Lincei Matematica e Applicazioni, Vol. 31 (4), (2020), 699–732
    (journal) (arxiv)
  • Abelian extensions in dynamical Galois theory
    Jesse Andrews and Clayton Petsche
    Algebra and Number Theory, Vol. 14 (2020), No. 7, 1981–1999
    (journal) (arxiv)
  • Attractors associated to a family of hyperbolic p-adic plane automorphisms
    Clayton Petsche
    Ergodic Theory and Dynamical Systems, Vol. 41 (2020), No. 6
    (journal) (arxiv)
  • A dynamical construction of small totally p-adic algebraic numbers
    Clayton Petsche and Emerald Stacy
    Journal of Number Theory, Vol. 202 (2019) 27-36
    (journal) (arxiv)
  • A Dirichlet approximation theorem for group actions
    Clayton Petsche and Jeffrey D. Vaaler
    Functiones et Approximatio Commentarii Mathematici, Vol. 60, No. 2 (2019) 263-275
    (journal) (arxiv)
  • Non-Archimedean Hénon maps, attractors, and horseshoes
    Kenneth Allen, David DeMark, and Clayton Petsche
    Research in Number Theory, Vol. 4 Issue 1 (2018)
    (journal) (arxiv)
  • Energy integrals and small points for the Arakelov height
    Paul Fili, Clayton Petsche, and Igor Pritsger
    Archiv der Mathematik, Vol. 109 (2017), 441–454
    (journal) (arxiv)
  • A p-adic Perron-Frobenius theorem
    Robert Costa, Patrick Dynes, and Clayton Petsche
    Acta Arithmetica Vol. 174 (2016), 175-188
    (journal) (arxiv)
  • On the distribution of orbits in affine varieties
    Clayton Petsche
    Ergodic Theory and Dynamical Systems, Vol. 35 (2015), 2231-2241 (journal) (arxiv)
  • Energy integrals over local fields and global height bounds
    Paul Fili and Clayton Petsche
    International Mathematics Research Notices, Vol. 2015 (2015) 1278-1294
    (journal) (arxiv)
  • On quadratic rational maps with prescribed good reduction
    Clayton Petsche and Brian Stout
    Proceedings of the American Mathematical Society, Vol. 143 (2015), 1145-1158
    (journal) (arxiv)
  • Global minimal models for endomorphisms of projective space
    Clayton Petsche and Brian Stout
    Journal de Théorie des Nombres de Bordeaux, Vol. 26 no. 3 (2014), p. 813-823
    (journal) (arxiv)
  • Critically separable rational maps in families
    Clayton Petsche
    Compositio Mathematica, Vol. 148, Iss. 06 (2012), 1880-1896
    (journal) (arxiv)
  • A dynamical pairing between two rational maps
    Clayton Petsche, Lucien Szpiro, and Thomas J. Tucker
    Transactions of the American Mathematical Society, Vol. 364 (2012), 1687-1710
    (journal) (arxiv)
  • A criterion for weak convergence on Berkovich projective space
    Clayton Petsche
    Mathematische Annalen, Vol. 348 Iss. 2 (2010) 449-465
    (journal) (arxiv)
  • Isotriviality is equivalent to potential good reduction for endomorphisms of PN over function fields
    Clayton Petsche, Lucien Szpiro and Michael Tepper
    Journal of Algebra, Vol. 322 Iss. 9 (2009) 3345-3365
    (journal) (arxiv)
  • Non-archimedean equidistribution on elliptic curves with global applications
    Clayton Petsche
    Pacific Journal of Mathematics, Vol. 242 No. 2 (2009) 345-375
    (journal) (arxiv)
  • S-integral preperiodic points for dynamical systems over number fields
    Clayton Petsche
    Bulletin of the London Mathematical Society, Vol. 40 No. 5 (2008) 749-758
    (journal) (arxiv)
  • Small rational points on elliptic curves over number fields
    Clayton Petsche
    New York Journal of Mathematics, Vol. 12 (2006) 257-268
    (journal) (arxiv)
  • Global discrepancy and small points on elliptic curves
    Matthew Baker and Clayton Petsche
    International Mathematics Research Notices, Vol. 61 (2005) 3791-3834
    (journal) (arxiv)
  • A quantitative version of Bilu's equidistribution theorem
    Clayton Petsche
    International Journal of Number Theory, 1 (2) 2005, 281-291
    (journal)
  • UnpublishedThe height of algebraic units in local fields
    Clayton Petsche
    Preprint (2003) (PDF)
  • Doctoral DissertationThe distribution of Galois orbits of low height
    Clayton Petsche.
    Advisor: Jeffrey Vaaler
    The University of Texas at Austin (2003)
    (UT Library)