# Clayton Petsche

Professor

Department of Mathematics

# Clayton Petsche

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

- Chifan Leung (2024)
- Peter Oberly (2023)
- Chatchai Noytaptim (2023)
- Naveen Somasunderam (2019)
- Emerald Stacy (2018)
- Brian Stout (2013)

### M.S. Students

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

## Links

- ‘Entropy Bagels’ and Other Complex Structures Emerge From Simple Rules (Quanta Magazine)
- The Number Theory Group at OSU
- The Number Theory Seminar at OSU
- The Dynamical Systems Group at OSU
- The Dynamical Systems Seminar at OSU
- AIM Workshop on Moduli Spaces for Algebraic Dynamical Systems, September 27- October 1, 2021
- Oregon Number Theory Days
- AMS Special Session on Diophantine Approximation and Analytic Number Theory in honor of Jeffrey Vaaler, January 12-13, 2018
- 2016 Pacific Northwest Number Theory Conference
- The REU Program in Mathematics and Computer Science at OSU

## Education

Ph.D. The University of Texas at Austin

B.S. Virginia Tech

## Publications

**Non-abelian arboreal Galois groups associated to PCF rational maps**

Chifan Leung and Clayton Petsche

Submitted for publication

(arxiv)**Totally real algebraic integers in short intervals, Jacobi polynomials, and unicritical families in arithmetic dynamics**

Chatchai Noytaptim and Clayton Petsche

Bulletin of the London Mathematical Society (2023)

(journal) (arxiv)**Non-Archimedean Koksma inequalities, variation, and Fourier analysis**

Clayton Petsche and Naveen Somasunderam

Uniform Distribution Theory (2022)

(journal) (arxiv)**Totally T-adic functions of small height**

Xander Faber and Clayton Petsche

Rendiconti Lincei Matematica e Applicazioni (2020)

(journal) (arxiv)**Abelian extensions in dynamical Galois theory**

Jesse Andrews and Clayton Petsche

Algebra and Number Theory (2020)

(journal) (arxiv)**Attractors associated to a family of hyperbolic***p*-adic plane automorphisms

Clayton Petsche

Ergodic Theory and Dynamical Systems (2020)

(journal) (arxiv)**A dynamical construction of small totally***p*-adic algebraic numbers

Clayton Petsche and Emerald Stacy

Journal of Number Theory (2019)

(journal) (arxiv)**A Dirichlet approximation theorem for group actions**

Clayton Petsche and Jeffrey D. Vaaler

Functiones et Approximatio Commentarii Mathematici (2019)

(journal) (arxiv)**Non-Archimedean Hénon maps, attractors, and horseshoes**

Kenneth Allen, David DeMark, and Clayton Petsche

Research in Number Theory (2018)

(journal) (arxiv)**Energy integrals and small points for the Arakelov height**

Paul Fili, Clayton Petsche, and Igor Pritsger

Archiv der Mathematik (2017)

(journal) (arxiv)**A p-adic Perron-Frobenius theorem**

Robert Costa, Patrick Dynes, and Clayton Petsche

Acta Arithmetica (2016)

(journal) (arxiv)**On the distribution of orbits in affine varieties**

Clayton Petsche

Ergodic Theory and Dynamical Systems (2015)

(journal) (arxiv)**Energy integrals over local fields and global height bounds**

Paul Fili and Clayton Petsche

International Mathematics Research Notices (2015)

(journal) (arxiv)**On quadratic rational maps with prescribed good reduction**

Clayton Petsche and Brian Stout

Proceedings of the American Mathematical Society (2015)

(journal) (arxiv)**Global minimal models for endomorphisms of projective space**

Clayton Petsche and Brian Stout

Journal de Théorie des Nombres de Bordeaux (2014)

(journal) (arxiv)**Critically separable rational maps in families**

Clayton Petsche

Compositio Mathematica (2012)

(journal) (arxiv)**A dynamical pairing between two rational maps**

Clayton Petsche, Lucien Szpiro, and Thomas J. Tucker

Transactions of the American Mathematical Society (2012)

(journal) (arxiv)**A criterion for weak convergence on Berkovich projective space**

Clayton Petsche

Mathematische Annalen (2010)

(journal) (arxiv)**Isotriviality is equivalent to potential good reduction for endomorphisms of P**^{N}over function fields

Clayton Petsche, Lucien Szpiro and Michael Tepper

Journal of Algebra (2009)

(journal) (arxiv)**Non-archimedean equidistribution on elliptic curves with global applications**

Clayton Petsche

Pacific Journal of Mathematics (2009)

(journal) (arxiv)**S-integral preperiodic points for dynamical systems over number fields**

Clayton Petsche

Bulletin of the London Mathematical Society (2008)

(journal) (arxiv)**Small rational points on elliptic curves over number fields**

Clayton Petsche

New York Journal of Mathematics (2006)

(journal) (arxiv)**Global discrepancy and small points on elliptic curves**

Matthew Baker and Clayton Petsche

International Mathematics Research Notices (2005)

(journal) (arxiv)**A quantitative version of Bilu's equidistribution theorem**

Clayton Petsche

International Journal of Number Theory (2005)

(journal)**The height of algebraic units in local fields**

Clayton Petsche

Unpublished preprint (2003)

(PDF)